vpFREE2 Forums

Using Double Down

#21

Steve Jacobs wrote:
> > Steve Jacobs:
> > > As usual, if the game is negative, then using the double feature
> > > reduces risk. This holds for all size payoffs.
> >
> > I'll venture a question here, Steve.
> >
> > Mind you, I get a little nervous in our discussions these days
> > whenever the word "risk" is floating about. For that matter, I start
> > questioning the agility of my mind once we get going :slight_smile: ...
> >
> >
> > Simply put, is a 9/6 Jacks player who doubles and redoubles on every
> > win, to jackpot or bust, playing a less risky game than the Jacks
> > player who never doubles?
> >
> > I don't think this is what you suggesting, but it wouldn't be at all a
> > kick to the head if you came back and said you were :wink:
>
> The answer might depend on the precise definition of the phrase
> "to jackpot or bust". But, I suspect that is precisely what I'm
> suggesting. Risk works "backwards" in negative games, compared
> to what one would expect from a positive game. The critical question
> is when will you stop doubling in order to cash out and go home.
>
> Suppose you have $1000 in your pocket and you desperately need
> $1100 or else Guido and The Boys will go 9 innings against your
> knees with a baseball bat. The only game is 9/6 JoB with a double
> feature. If you play normal max-EV strategy for 9/6 JoB, and stop
> doubling whenever your total bankroll hits/exceeds the $1100 goal,
> then your knees have a higher probability of going unsmashed if you
> use the double feature. This assumes that the double feature is "fair"
> in that it increases variance while leaving ER unchanged.

Well, not to quibble, but technically I think it would be incorrect to
double if it will cause you to exceed goal, as I explain further,
below.

You're partly right. If doubling can't reach the goal, then doubling
is correct. If doubling exceeds the goal only by a tiny amount, then
doubling can still be the correct thing to do. This holds more for large
payoffs -- if the goal is 9,999 away and you get a 5,000 unit royal,
then doubling gives you a 50/50 shot at reaching the goal right now.

But subject to that -- and to a very small percentage of
exceptions based upon relative stake/goal sizes -- I'm confident that
what you have said is true so long as we have a particular goal.

I'll start with what I think are likely exceptions. I don't know what
the curve of a graph would look like, but at some point with a small
enough stake -- relative to your goal -- you do cross the line (which I
mention only academically for the sake of discussion, because such
extremes have little practical application). For instance, JoB-9/6 has
approximately a 45% winning-game rate. If your session stake is only a
single bet, then out of the mere 45% of the time that a normal player
would survive the first vp bet, a player who then doubles has only half
that chance of surviving to bet again.

The real question is whether doubling improves the overall probability of
reaching the goal. Playing the negative game is mathematically equivalent
to flipping a biased coin. It is the bias that hurts you. Doubling is
exactly like removing the bias from the coin for some of the flips.
For example, doubling a win of 100 units is like committing to flipping
a _fair_ coin repeatedly until you either win 100 additional units or
suffer a net loss of 100 units. If you forego doubling, but you still need
more than 100 units to reach the goal, then you just conciously chose
to flip a coin that is biased against you instead of flipping a fair coin.

Let me make this more concrete. Say you start with a single unit, and
your goal is 200 units. Your very first play results in a win of 100 units.
If you choose to double, you will have a 50/50 chance of reaching
your goal. If you decide not to double, and you are playing 9/6 JoB,
then based on the "equivalent coin" for this game, your probability of
reaching the goal with your (new) bankroll of 100 units is only 48.97%.

I think this can probably be reduced to a reasonably simple formula
that tells us precisely when to double. I'll try to work out the formula
for this.

If a person has only a 2 bet
stake, it would seem to me that a doubler also has a worse chance of
survival; 55% will lose their first bet on vp before ever reaching the
doubling option; of the 45% who win their first bet on vp, only 22.5%
will win the doubling, although some will now have much more than their
original 2 bet stake. But 77.5% are now down to a single bet remaining,
and if we use the same math, 77.5% of them will also lose their second
bet, so after 2 bets, over 60% will be busted without ANY hope of saving
their knees. Now, in comparison to the regular win-loss rates for the
same game, with a 55% chance of losing each vp game, after two bets,
only 30% will be busted without any hope of saving their knees. I used
a VERY small bankroll just to make it easy for folks to see what I
mean. Now, I don't know where the lines cross on a graph, and I'm not
going to go through that much work for this, but at some point, and no
doubt VERY quickly, as soon as your stake is increased to a certain
point, then it would immediately become advantageous to switch to
doubling all winning hands for as long as your stake does not dip below
that level.

The mathematics for risk is complicated for VP, because the equation is
nonlinear. However, I've studied this enough to say that your intuition
is incorrect. The correctness of doubling isn't a matter of how much you
_have_ but rather it is how much you _need_ to reach the goal. In a
sense, you're approaching the problem from the "wrong end." Suffice
to say that if doubling is correct for a large bankroll, it remains correct
for any smaller bankroll size, right down to a single unit.

Now before going on to my other theory that you would never double if it
will put you beyond your goal, lets take another example of a more
realistic figure. Let's say that you owe Guido $1500.00 and you have a
modest but perhaps somewhat realistic $65.00 in your pocket (in other
words, you have a 52 bet stake on a JoB quarter machine, and you need to
build it into a 1200 bet stake). I had arbitrarily started with an even
50-bet stake ($62.50) but discovered that I could not enter a fraction
of a dollar in Jeff Lotspiech's "Gambler Ruin Calculator", so I bumped
it up to an even $65.00 and then also ran it for an even $60.00 (48
bets). So for this discussion I will speak in terms of 'betting units'
rather than dollars or coins, because it's easier, and when I speaking
about 1, 2, 3, etc., "wins", I am still talking about full-coin such
that 1 win really means 5 quarters.

That's fine, working in units is easier.

On each winning-bet you proposed
doubling until you either bust or your stake exceeds 1000, so that's
what we'll do.

No, with a goal of 1200 units, you would definitely double whenever
winning the double will leave you with less than (or exactly) 1200
units. You'd never double a win that causes you to go far beyond
the goal. You'd sometimes double a win that goes slightly beyond
the goal, but only if the "excess" is a small enough fraction of the
final win.

On your first bet, you need to win 1151 to meet you
goal, with the following expected results:
54.543% of the time you lose the VP bet and never get a chance to double
21.459% of the time you win 1 and must then double-down 11 times with
chances of winning = 1/2048 x the 21.459% = 1/2048*.21459=
0.0001047802734375
12.928% -- you win 2 and d-d 10 times = 1/1024*.12928= 0.00012625
7.445% -- you win 3 and d-d 9 times = 1/512*.07445= 0.00014541015625
1.123% -- win 4 d-d 9 times = 1/512*.01123= 0.00002193359375
1.101% -- win 6 d-d 8 times = 1/256*.01101= 0.0000430078125
1.151% -- win 9 d-d 8 times = 1/256*.01151= 0.0000449609375
0.236% -- win 25 d-d 6 times = 1/64*.00236= 0.000036875
0.011% -- win 50 d-d 5 times = 1/32*.00011= 0.0000034375
0.002% -- win 800 d-d 1 time = 1/2*.00002= 0.00001
Your Total odds of meeting your goal on the first bet is 0.0005366552734375
Your odds of failing and having to bet further is 0.9994633447265625

In all of these cases, the final double is incorrect.

Now, your 'stake' at the end of each "try" will NEVER be bigger than it
is when you start, or else you will have already met your goal and
stopped. This means that your stake is constantly diminishing as you
repeat your attempts, and the amount that you need to meet your goal
constantly increases. The result is that for each bet (assuming the
same size gap between stake and goal), your odds are NEVER going to be
better than the above, although for this particular beginning stake and
goal, they won't get any worse, either.

With a stake of 52 bets and odds of failing of 0.9994633447265625 each
time, your chances of ultimately going bust is
0.9724724189488650115689794580225
or a chance of making it of only 0.027527581051134988431020541977496 =
2.75% This compares to a success rate of 3.10% when using what I
presume is max-ER strategy and NEVER doubling. This can be confirmed on
Jeff Lotspiech's Calculator at
http://www.lotspiech.com/GamblersRuin.html -- which I presume is max-ER
-- but you need to be patient since Jeff's calculator needs to run
somewhat over 100K hands to reach at least 3.1% 'retired', and it was
still at that level about 250,000 hands. I would also assume that that
figure could also be improved slightly using your own min-risk strategy,
Steve.

The equivalent coin model says that there is a 3.38% chance of turning
a 52 unit bankroll into 1200 units. The real value is slightly smaller than
this. I have no doubt that correct doubling will improve on the real value.

By the way, the figures when starting with a 48-bet stake ($60.00) are
as follows: using 'doubling', your chances of success drop from 2.75%
to only 2.54%, and with NO doubling, your chances drop from 3.10% to
2.80%, which is still better than the doubling success-rate.

Again, the analysis doesn't match what I'm claiming.

I do agree with a comment that Harry Porter recently made that this
probably doesn't matter as much to folks who are planning to stop
playing when they hit a particular goal;

I think you've got that backwards -- those are exactly the people
who this should matter to.

If they are planning to play a negative game endlessly, then they
are simply planning to lose whatever amount they consider to be
"entertainment value" for the game.

oh, they might stop after a
big win -- for that particular trip -- but if they even return to the
casino again, then in keeping with the concept of just a single session
in life, doubling during parts of their session isn't expected to really
make any difference in the long-run.

Heh. Yes, if you are planning to ensure a long term loss, then slowing
the bleed rate is about all you can hope for. The concept of "risk"
becomes completely meaningless in that scenario, so none of this
discussion applies.

HOWEVER, all of that having been said, your point is well-taken Steve,
and I think you are correct that in the vast marjority of instances
where you have a goal that must be met -- especially with 'Guido and The
Boys' breathing down your back -- it is no doubt best to add doubling.
But I do think that one should use a blend of not-doubling when their
stake is about to bottom-out, but doubling whenever their stake is
'safe' ... but not when doubling will exceed the goal.

You are mistaken in regard to the small stake. That is precisely when
doubling gives the most benefit.

This last point
can be seen quite easily when you are in the situation of hitting a
Royal to bring you within a few dollars of your goal; it would clearly
be insane to double at that point. Instead, you take your winnings and
resuming doubling on the following hands.

Right. But, if doubling a royal will take you to (goal + 1 unit) then it
is clearly correct to double.

···

On Tuesday 17 February 2004 02:13 pm, Bill Velek wrote:

> On Monday 16 February 2004 07:09 pm, Harry Porter wrote:

#22

... snip

It seems to me that you might be thinking about the scenario where
the player always keeps doubling until inevitably losing each wager.
This scenario is equivalent to attempting to extract a long-term
win from a negative game, which is mathematically impossible.

It does raise an interesting question though -- is it more important
to double small payoffs, or large payoffs? I'll have to look into
this some more...

While mathematically interesting I believe all VP machines have a
maximum number of credits where you can no longer double. I'm
guessing around 10-20K credits. Kind of like using Martigale in
blackjack. Might work except for the table maximum (and less than
infinite bankroll). Don't get me wrong, clearly Martigale is
different in the risk sense since you are "doubling" with your own
bankroll.

From the earlier discussion, correct me if I'm wrong, it sounds like
you SHOULD always double up to this maximum to "minimize risk" when
playing a negative EV game (or playing a positive EV game poorly).

Maybe this is why Nevada casinos make it more difficult to double
than the Indian casinos I visit?

Dick

···

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:

#23

Steve Jacobs wrote:

In the context of favorable games, one can always use the present
goal as a "stepping stone" toward higher goals. This amounts to using
pure dollars as the benchmark for progress, without accounting for
(or even worrying about) the number of hands played. In favorable
games, the min-risk strategy can be played endlessly, and will move
from one min-risk stepping stone to the next, in sequence, all the
while minimizing the risk of going broke before reaching the next
stepping stone.

That makes sense. I like that approach.

In contrast, if you employ a max-EV strategy, you will experience
a greater probability of going broke before reaching any chosen
stepping stone. This may be worth thinking about. If you start
with a small bankroll and play to play far into the future, and
you compute your EV for 1 million hands of play, the resulting
EV will be based on a large number of "paths" that would take
the bankroll negative, possibly very negative, before reaching
the 1 million hand mark. Now, unless you allow yourself infinite
credit, those path shouldn't really be counted as part of your
average outcome. Thus, max-EV is perhaps somewhat bogus,
because it assumes unlimited credit.

I think it is one thing to suggest that max-EV strategy might not be appropriate for someone with a smaller bankroll when considering the play that they hope to engage in during their expected lifetime; I'm sure that min-risk strategy is better in many cases. But I think it is another matter altogether to suggest that the max-ER strategy is not accurate for what it intends to do -- maximize profits in a positive game, or minimize losses in a negative game -- or that the ER itself, when using that strategy, should in anyway be adjusted to somehow take into consideration that a number of people will never be able to attain long-term play due to ruin. The long-term ER of a game -- and the max-ER strategy which pursues it -- are mathematically accurate and valid for the purposes for which most of us use them. Perhaps there is an additional 'adjusted' figure which could be derived and have some value, but that doesn't make max-ER in any sense inaccurate, in the least bit. I like to use simple examples which, although extreme and unrealistic, magnify my point; I have therefore entered a paytable in JoB in which only the Royal has a value -- $4,000,000 for full-coin dollars (4,000,000 units for a 5-unit bet) -- but with every other hand having a value of zero. Being a gimmick promotion, no player would be allowed to play more than one hand per day. WinPoker's analysis gives this an ER of 3,466% -- or paying almost 35 to 1. The problem is that you will win only 112.6 times out of every 2,598,960 hands, for a average Royal cycle of about 23,081 hands and an average dip in your stake/bankroll of $115,405.00 before hitting one. Even if you borrowed money to play, a player would average hitting one every 63.24 years if the player went EVERY day. There is no doubt that the overwhelmingly vast majority of players would die of old age without ever winning, if they didn't go bankrupt first. But does that fact alter in any way the ER of the game or anything connected with it? I don't think so. It's ER is what it is; on average, for every 23,081 people who put $5.00 in it on their first try, one of them is expected to win 4-million dollars. I know that I sure would drop $5.00 into it during each one of my trips to the casino; it's one HELL of a lot better than the lottery.

So I think it is more accurate to say that the very precise expected return, when using max-ER strategy, is based on an amount of play that none of us can ever expect to engage in during our lifetimes, but rather that, except for pure luck, such an absolutely precise figure is true only in the abstract world of mathematics or for the _POOL_ of all vp players with all of our play combined, as if we were just one player with one session playing one machine. A few of us, after a very large number of games that we have _personally_ played, might actually happen (by sheer coincidence) to experience a return that has almost exactly the expected frequencies of hands (perhaps even within 10 decimal places of accuracy). But the _vast_ majority of us ... perhaps all but a trillionth of a percent or less ... will experience something somewhat different, probably with about half of us somewhere above and about half somewhere below that ER. But that doesn't change the ER of the game, and the fact that a number of members of the pool might have gone bankrupt in the process and ceased playing doesn't alter the ultimate expectations of the 'pool' either, and certainly doesn't alter the ER of the game. And while the aggregate play of the pool doesn't even begin to approach infinity, but it is certainly large enough for government work :wink: ... and for our purposes here.

Now, given that few of us are ever going to actually experience a very precise ER -- with about half of us below that result for our given amount of play (and that group includes folks who have bankrupted just as it includes those who stop playing for various other reasons, while the other half includes folks who also stopped playing for various reasons, whether they were goal-related or not) -- our eventual outcome, even after using perfect strategy, still depends upon luck. So the person who decides to play just one single hand for their entire session, for whatever reason, still has an ER equal to whatever the math says it is, although in reality, the only possible outcomes are zero or any one of the pay amounts listed on the paytable. But what that ER really is is an expression of value of the hand based upon the probability of ending with those various amounts, whether I do or don't. In other words, with perfect play, I have an ER for a single game of 'x'; I have the same ER if I choose to play 2 games of 'x; ... or 3 games ... or 300,000. My stake or bankroll has nothing to do with the ER, and so the fact that I have a limited bankroll and perhaps have an extremely high risk of ruin has nothing to do with ER.

As for whether I 'plan' (hope?) to play long-term, i.e., maybe a million hands or more, this naturally also depends upon luck, which is part of the game. I will conceded that luck is perhaps a bigger factor when using max-ER strategy versus a minimum-risk or goal-oriented strategy, but if you are suggesting that the ER figure should somehow be reduced slightly to compensate for a percentage of folks who are never able play long-term due to ruin, I think that that is incorrect -- or at least you would need to adopt a separate name to identify your adjusted figure -- which I suppose could augment the ER and be of some value. But one problem in trying to derive any such useful information is that you would end with so many different figures by pairing such a large number of possible initial bankrolls with a wide variety of life-time session-sizes (total number of hands played).

... In contrast, min-risk is
ever mindful of the finite nature of your bankroll, and so risk-
based computations/predictions are in a sense more exact
than the corresponding EV based computations/predictions.
In other words, some of the "value" of EV is inherently
unattainable for a player who starts with a bankroll that is
truly finite.

I think I understand what you are saying, but as I said -- ER, as an expression of 'averages' -- of your overall probabilities, whether you play a single hand or a million hands -- has its usefulness in its simplicity of use for comparisons. Most folks then look at variance to get a rough idea of the volatility of the game, which many of us equate with risk with at least some degree of validity. If we want a more precise picture of the risk we face with our given bankroll, we need to run Jeff's Lotspiech's calculator that is available through vpFREE links along with other bankroll calculators.

> Or perhaps I'm short selling the extent to which "targeted bankroll"
> strategies come into play for the average player.

I don't know. But, I think similar objections can be raised in regard
to _any_ means of measuring "progress". EV measure progress in
terms of dollars per game played, but do you know _anyone_ who
actually keeps track of the exact number of games played in order
to assess how well they are doing? The more I study alternate
strategies, the more I realize that EV just isn't that great of a way
to measure progress. I've always said "EV isn't everything" but
lately I'm leaning more and more toward "EV isn't much of anything".
(Blasphemy!)

REPENT! ... or you will be stoned. :wink: Personally, I don't use EV as a way of measuring progress. I use ER as a way of comparing one idea of 'value' in one game against another, with that value being the aggregate of the probabilities of ending with the various possible hands multiplied times the values of those hands. That's all ER is ... whether you play one hand or a million. Other ideas of 'value' -- or at least factors or considerations that vary from game to game -- are variance (generally associated with volatility and risk), pleasure (whether you find JoB 'boring' or 5-card Jokers to be 'challenging'), and things like comfort and location. If you are a recreational player like me, then you might sometimes put a higher value on playing JoB-8/5 at the bar while a ball game is on the big-screen, than on playing JoB-9/6 at an uncomfortable upright in a bank where there is little elbow room and a slow waitress. People who are trying to earn an hourly income from vp likely have a different set of values.

The nice thing about framing things in terms of a fixed goal is
that it makes clear exactly what the player is trying to accomplish.
The objective then becomes maximization of the expected value
of the player's final bankroll, which is equivalent to maximizing
the probability of reaching the goal, which is equivalent to
minimizing risk. I still find it rather striking that in this scenario,
the way to get the most average dollars overall is _not_ to play
for the most average dollars on each individual wager.

It seems to me that if you were to want to reach an ultimate goal -- let's say turning a thousand dollars into a million dollars -- you would need to pursue quite a number of smaller goals, and the more small-goals you have, probably the less-risk and greater likelihood of reaching each sub-goal and eventually the ultimate goal.. But it also seems to me that, while you perceive fault in max-ER by not including ruined-players who are therefore incapable of completing long-term play, you are overlooking the time factor in min-risk strategy when employed to its greatest degree by presumably setting a vast number of smaller goals, and the much slower rate of growth that is also the result of min-risk. Perhaps it is not really a significant factor at all, and I'm not inclined to check ... especially since I'm not as familiar with the strategy as you obviously are. So my questions are simple: in fully utilizing min-risk strategy, is it possible that the time necessary to reach the goal becomes so long that it begins to eliminate a significant enough number of players due to a finite life-span? And if so, how do you adjust your min-risk ER to compensate for those players who will never complete their play? And wouldn't a failure to do so amount to the same sort of concern that you think makes max-EV "somewhat bogus"?

Thanks for an enjoyable discussion. This has been a very interesting thread. I really need to look more closely at your min-risk strategy and what would probably be great would be to devise a strategy that begins with min-risk when a bankroll is low, but which gradually morphs into max-EV as the bankroll grows into a more secure size.

Bill Velek

#24

Steve Jacobs <jacobs@x> wrote:

There is more value here than excitement. If the player has a fixed
target, reducing risk is the same as increasing the probability of
reaching the target.

I didn't occur to me to think this way, since that's not the mind I
take into a casino. I play for recreation, & also to get (over time)
some extra income to spend a bit frivolously. I intentionally keep my
level of play high enough be interesting, but low enough so that I'll
never need to cut a session or vacation short for financial reasons.

I've never had Guido threatening to take a bat to my kneecaps if I
don't come up with $1199 by sunset, or anything close to that
scenario. My short-term losses are never significant enough to affect
my choices about gambling.

Almost always, my decisions to start or stop playing are governed by
how much I'm enjoying myself. It's different than, say, playing the
stock market, where the money is more significant & the recreation
more secondary. In trading stocks, I'm considering serious impact on
my overall financial situation. In playing VP, I'm not going to deny
myself the fun of the game just because I've won or lost a particular
amount.

(Sometimes I'll take a quick stab at a level that's way above my
bankroll, with a strategy of "I'll keep playing till I either get a
jackpot or lose $x." But those are exceptions. I'm usually playing at
a level where short-term fluctuations won't affect my lifestyle, so
stop-loss & stop-gain strategies don't come into consideration.)

The strategies appropriate for people who need to pay off Guido, or
who are risking their retirement funds, don't come into play for me
(though I do appreciate the discussion in the theoretical
mathematical sense).

I've in fact often wondered how many players are like me (playing
with "fun money"), & how many are risking the rent. I watch the folks
at Ceasars playing blackjack with stacks of $1000 chips, & I truly
don't know whether they've got assets such that their bets are
equivalent to my quarter VP... or whether they're into a realm of
life-risk that's unknown to me.

Stuart (RandomStu)
sresnick2@comcast.net
http://home.comcast.net/~sresnick2/mypage.htm

#25

Bill Velek wrote:

But I think it is another matter altogether to suggest that the
max-ER strategy is not accurate for what it intends to do --
maximize profits in a positive game, or minimize losses in a
negative game

I'm side-stepping the broader "Double Down" discussion. From my
perspective, it runs far afield of what is a practical consideration
for most players.

But I wanted to touch on your comment above, Bill. Max-ER strategy
doesn't translate to maximizing expected profits (other than for a
single played hand).

Given a fixed bankroll (mind you, one that is considered ample, not
"limited") which when exausted will translate to the end of play, then
clearly ROR and ER both (not ER alone) must be considered in
determining what would maximize expected profit.

Expected profit = Expected win per play x Expected number of plays.

If, for a given strategy the ROR is lower than the max-ER stratgy, the
"Exp no. of plays" will be larger. Thus the lower ROR strategy, with
a smaller "Exp win per play" but higher "Exp no. of plays", can
potentially produce a higher Expected profit than a max-ER strat.

This may well be the case when you're playing on a 5% or 10%+ ROR
bankroll, as I suspect a large number of players do.

- Harry

#26

Steve Jacobs wrote:

> In the context of favorable games, one can always use the present
> goal as a "stepping stone" toward higher goals. This amounts to

using

> pure dollars as the benchmark for progress, without accounting

for

> (or even worrying about) the number of hands played. In

favorable

> games, the min-risk strategy can be played endlessly, and will

move

> from one min-risk stepping stone to the next, in sequence, all

the

> while minimizing the risk of going broke before reaching the next
> stepping stone.

That makes sense. I like that approach.

skip....

Thanks for an enjoyable discussion. This has been a very

interesting

thread. I really need to look more closely at your min-risk

strategy

and what would probably be great would be to devise a strategy

that

begins with min-risk when a bankroll is low, but which gradually

morphs

into max-EV as the bankroll grows into a more secure size.

Bill Velek

This has been quite interesting...

My thoughts are:
there is lots of talk about ROR and limited bankrolls....
maybe because I am not from Vegas, but I only know of 1 person who
plays VP on a properly funded bankroll, and it isnt me.
I am what I consider "in the middle" in that I do have a bankroll
set aside for VP and it could very well be bankrupted, but if that
did happen, I would just create another bankroll and keep on going.
So ROR isnt the greatest factor. I also dont have any specific win
goal, I have had sessions that were constrained by time, or went
poorly and were constrained by $, and others that I just ended up
even, or was ahead anywhere from $100 to thousands of $.

If I dont play max ER stratagy, dont I comprimise my return??
As has been pointed out, LUCK has sooo much to do with any given
session or even month or year of play. I dont really understand
why I would want to lower my return by playing a stratagy that
MIGHT extend my playing time (what about luck)?

I enjoy the whole casino environment, and I dont play with the food
or rent money, so even if I go broke (with my current bankroll)
several times, I will most likely just build another one and keep on
playing with the expectation that if I am playing games that are
positive, at least with the associated cash and comps, then things
will likely improve.

My wife and I have been very lucky this year and after about 2 weeks
into the year we were ahead a good amount, and I worried (a little)
that things would soon turn around (thinking about the math), but we
won more, and more and more.... we are ahead more this year then
some people make in a year, so we locked away a good part of it and
we will keep playing on the rest, who knows we may keep winning...

I would like to know how many players really have a proper bankroll?

Jim

···

--- In vpFREE@yahoogroups.com, Bill Velek <billvelek@a...> wrote:

#27

Some would reply "yes, you do" in response to your question, but
the answer isn't that simple.

The strategy that gives the best return depends on how you _measure_
"return". Some examples:

1) Break up your play into sessions of exactly 100 hands each, starting
each session with a bankroll equal to 100 units so that you are guaranteed
to never runs out of money before the session is over. Measure return by
averaging the final bankrolls of all sessions. This measures in terms of
dollars per game played. When measuring return this way, the max-EV
strategy will appear to give the best results.

2) Start with 100 unit sessions as in case 1), but now continue play until
you have 200 units or go broke trying. Average the final bankrolls of
all sessions. This measures in terms of probability of having a winning
session. In this case, the min-risk strategy will appear to give the best
results.

3) Start with 100 units, and keep playing until you have experienced
100 lost hands. In other words, each time you win (or push) play the
"original" unit over again, and keep doing so until you lose a hand, then
move to the next "original" unit from your stack. Don't play any winnings.
Average the final bankrolls of all sessions. This measures in terms of
dollars lost that are "exchanged" for winnings, or dollars won per lost
game. In this case, using a min-cost strategy will appear to give the
best results.

Three different strategies for three different ways of measuring performance.
Each strategy is best in its own way, in terms of "dollars per something".
There is no absolute meaure of what is "best," and the most effective
strategy is relative to your perspective on how performance "should" be
measured. The only real difference is how you decide when to end one
measurement and start another measurement, or how you choose to break
up an endless stream of play into measurable chunks.

···

On Wednesday 18 February 2004 04:48 pm, jimnkelli wrote:

If I dont play max ER stratagy, dont I comprimise my return??

#28

Dear friends,

Don't most of us look at our VP play as a single continuous session,
throughout our lifetime? If this assumption is wrong, then I
apologize for even saying anything.

But, if it is true, how can anything but a max ER strategy be
correct?

.....bl

> If I dont play max ER stratagy, dont I comprimise my return??

Some would reply "yes, you do" in response to your question, but
the answer isn't that simple.

The strategy that gives the best return depends on how you

_measure_

"return".

Three different strategies for three different ways of measuring

performance.

Each strategy is best in its own way, in terms of "dollars per

something".

There is no absolute meaure of what is "best," and the most

effective

strategy is relative to your perspective on how

performance "should" be

measured. The only real difference is how you decide when to end

one

measurement and start another measurement, or how you choose to

break

···

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:

On Wednesday 18 February 2004 04:48 pm, jimnkelli wrote:
up an endless stream of play into measurable chunks.

#29

bornloser1537 wrote:

Don't most of us look at our VP play as a single continuous session,
throughout our lifetime? If this assumption is wrong, then I
apologize for even saying anything.

But, if it is true, how can anything but a max ER strategy be
correct?

Here's my take on this:

If you're playing on a near-infinite bankroll so that ROR = ~0% and
you have near absolute confidence that you indeed will play
"throughout" your lifetime, then you're absolutely correct.

However, with a more limited bankroll and a risk that you'll bust and
end your play prematurely, there are other factors that enter the
picture in maximizing your expected play profit. Max ER may not be
the way to go.

Further, as Steve notes, there are other circumstances and goals under
which max ER isn't the preferred strategy.

That said, for the large bulk of players such considerations are
necessarily academic. There are far more critical aspects of play
that are sufficiently challenging.

From a practical standpoint, max ER is the appropriate strategy. Most
alternate discussion is esoteric.

- Harry

#30

Dear friends,

Don't most of us look at our VP play as a single continuous session,
throughout our lifetime?

That is a popular view. However, there are many times when it
just doesn't apply. Special promotions such as free play only
last as long as the free credits "survive", and as such they are
a limited resource. The min-cost viewpoint is a good way of
extracting the most dollars from a limited resource. Tournaments
provide special opportunities to outplay human opponents
as opposed to simply grinding out EV/ER.

If this assumption is wrong, then I
apologize for even saying anything.

There is nothing wrong with the assumption (or your question),
and viewing VP play as an endless stream of games is a
useful mental tool for thinking about many situations. However,
it is just a tool and shouldn't be thought of as an edict passed
down from heaven.

But, if it is true, how can anything but a max ER strategy be
correct?

That is an excellent question, and the answer is profound.
Some math problems permit more than one solution. Problems
involving probability permit a virtually unlimited number of
solutions, all of which are correct. Maximizing ER is only
one of the possibilities, and my personal view is that there
is no particular reason to believe that it is superior to other
solutions. Each solution is "best" in its own way. The best
solution for _you_ is a matter of personal preference. Most
people focus on ER because they have been taught that it is
the only correct thing to do, but that belief is unfounded.

Let me make an analogy here. Who is the best singer?
If you ask different people, you'll get different answers.
Some like Celine Dione, others Barbra Streisand, others
Reba McIntyre or whoever. Who is right? It isn't a
meaningful question, because there isn't any right/wrong
about it, it is a matter of taste. Similarly, when choosing
a VP strategy, the best strategy depends on what you
are trying to achieve.

If some machine has a hugenroyal jackpot, you can play
max-ER based on that jackpot or you might play min_cost_royal
strategy to maximize the average number of dollars in your pocket
after hitting the royal. These are two very different objectives
that require different strategies. The max-ER strategy is like
playing for the most dollars per hour. The min_cost_royal
strategy is like playing for the most _overall_ dollars without
regard to how long it takes. Some people can't stand the
thought of being paid an hourly "wage" that is anything less
than the highest possible, and thus prefer max-ER. Others
care more about the total number of dollars extracted rather
than the _rate_ of extraction, and thus prefer min_cost_royal.
Either way, it is a matter of personal taste, and one choice
is not inherently superior than another.

One can also change strategies depending on the situation.

···

On Thursday 19 February 2004 04:41 am, bornloser1537 wrote:

#31

Harry Porter wrote:

Further, as Steve notes, there are other circumstances and goals under
which max ER isn't the preferred strategy.

Preferred by who? Goal is usually a matter of personal choice. People
maximize ER, or minimize risk, or minimize cost, as a matter of choice.
It is their own preferred way to play.

That said, for the large bulk of players such considerations are
necessarily academic. There are far more critical aspects of play
that are sufficiently challenging.

From a practical standpoint, max ER is the appropriate strategy. Most
alternate discussion is esoteric.

I disagree quite strongly. I believe this view that max-ER is somehow
inherently better is a reflection of human bias. Max-ER is what people
are most comfortable with, and most used to thinking about. The
"appropriate" strategy depends on what problem you are trying to
solve. But, if the max-ER hammer is the only tool in your toolbox,
every problem tends to look like a nail :wink:

A player with no pre-disposition to favor one strategy over another
will likely be just as happy using min-risk or min-cost rather than
max-ER, and for most games these strategies have only a small
number of differences. If probability theory had evolved along an
alternate path, the prevailing bias might have been towards cost or
risk (or something else) rather than ER.

#32

> If I dont play max ER stratagy, dont I comprimise my return??

Some would reply "yes, you do" in response to your question, but
the answer isn't that simple.

The strategy that gives the best return depends on how you _measure_
"return". Some examples:

1) Break up your play into sessions of exactly 100 hands each,

starting

each session with a bankroll equal to 100 units so that you are

guaranteed

to never runs out of money before the session is over. Measure

return by

averaging the final bankrolls of all sessions. This measures in

terms of

dollars per game played. When measuring return this way, the max-EV
strategy will appear to give the best results.

2) Start with 100 unit sessions as in case 1), but now continue

play until

you have 200 units or go broke trying. Average the final bankrolls

of

all sessions. This measures in terms of probability of having a

winning

session. In this case, the min-risk strategy will appear to give

the best

results.

3) Start with 100 units, and keep playing until you have

experienced

100 lost hands. In other words, each time you win (or push) play

the

"original" unit over again, and keep doing so until you lose a

hand, then

move to the next "original" unit from your stack. Don't play any

winnings.

Average the final bankrolls of all sessions. This measures in

terms of

dollars lost that are "exchanged" for winnings, or dollars won per

lost

game. In this case, using a min-cost strategy will appear to give

the

best results.

Three different strategies for three different ways of measuring

performance.

Each strategy is best in its own way, in terms of "dollars per

something".

There is no absolute meaure of what is "best," and the most

effective

strategy is relative to your perspective on how

performance "should" be

measured. The only real difference is how you decide when to end

one

measurement and start another measurement, or how you choose to

break

up an endless stream of play into measurable chunks.

Steve, I think your 3 examples sum up the different approaches (max-
EV, min-risk, min-cost) quite well. I, for one, would never have any
interest in 2 and 3. So, I think you're saying a max-EV strategy
would be best for me?

Dick

···

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:

On Wednesday 18 February 2004 04:48 pm, jimnkelli wrote:

#33

Steve Jacobs wrote:

> Dear friends,
>
> Don't most of us look at our VP play as a single continuous session,
> throughout our lifetime?

That is a popular view. However, there are many times when it
just doesn't apply. Special promotions such as free play only
last as long as the free credits "survive", and as such they are
a limited resource. The min-cost viewpoint is a good way of
extracting the most dollars from a limited resource. ...

But don't most casinos that give free play require you to play it through just once? If so, then as soon as you've gone through the 'free play' the first time, and are then capable of withdrawing your credits as real money, then it becomes exactly that, and I would think that it would be inappropriate to continue using the min-cost strategy thereafter. A max-ER or min-RoR, depending upon your priorities, would then be the more appropriate choice, wouldn't it?

... Tournaments
provide special opportunities to outplay human opponents
as opposed to simply grinding out EV/ER.

Yes, I can see that.

> If this assumption is wrong, then I
> apologize for even saying anything.

There is nothing wrong with the assumption (or your question),
and viewing VP play as an endless stream of games is a
useful mental tool for thinking about many situations. However,
it is just a tool and shouldn't be thought of as an edict passed
down from heaven.

> But, if it is true, how can anything but a max ER strategy be
> correct?

That is an excellent question, and the answer is profound.
Some math problems permit more than one solution. Problems
involving probability permit a virtually unlimited number of
solutions, all of which are correct.

snip

This seems technically true when we consider, for example, that we can have unlimited combinations of bankrolls and ending goals, although obviously both of those factors are finite as a practical matter. But to get an idea of how many reasonably valid solutions there are, let's review what would probably be universally considered as _reasonably_legitimate_ alternative goals, and when we do that I have a hard time conceptualizing even a great number of solutions, if by "solution" we mean the best answer for a specific criteria or goal. We have recently discussed three alternative goals: max-ER, min-RoR, and min-Cost. You mention, below, some alternative approaches when 'chasing-the-Royal' (which means "JackPot", whether referring to a Royal or 5-Jokers). I'm sure there are a few others. Maybe there is a good strategy that takes into consideration the average value of quads for a particular gambler who plays 90% of their games on Tuesdays and Wednesdays when the 'card of the day' is different for each day (and pays an extra bonus amount); that really might not be a bad idea, as opposed to learning a different strategy for each of the different cards that one might encounter as 'card of the day'.

I can imagine that there might easily be one or two more, depending upon an individual's concerns and priorities, but I still find it hard to believe that there are more than, let's say, an absolute maximum of a dozen different 'variables' (for lack of a better word) that would not adequately cover every possible scenario. I guess we could find one that has the greatest efficiency of return versus the number of buttons that are pushed :wink: ... which would actually probably be possible to do, for a computer to play. Anyway, for each of those alternative goals, we can have a mathematically perfect strategy, and an "optimum" strategy that comes real close to perfection except that it ignores penalty card situations, and a very "basic" strategy that is the most mathematically flawed but yet the easiest to learn. Maybe we could find some reason for tossing in a couple of others between those varieties for a more gradual progression through the spectrum of difficulty of strategy for each reasonable goal.

But whether we arguably end up with one dozen, or three dozen, or whatever number of approaches/solutions, I think the important point is to be able to able to play your chosen strategy accurately. If you have the ability to _skillfully_ playing min-Cost one day, and then 'chase-the-Royal' another day, and then max-ER a third day, I tip my hat to you. I think I would find it utterly confusing and it would probably cause me to make errors in all three. So my suggestion is that a person ought to determine what their _principle_ priority is, and to learn a _single_ strategy along that line for each of the games that interests them. I think that most of the time most people have been interested in max-ER, but I can see how min-RoR -- which is apparently still profitable for advantage games -- could become the more popular choice. But a big problem is that both WinPoker and FrugalVP are set up on a max-ER basis, so accurate practice will be difficult. Perhaps upgrades will allow at least a little bit of choice along those lines, although I could see how it could be very difficult to write that feature into a program.

Cheers.

Bill Velek

···

On Thursday 19 February 2004 04:41 am, bornloser1537 wrote:

#34

Steve Jacobs wrote:

Harry Porter wrote:

> Further, as Steve notes, there are other circumstances and goals under
> which max ER isn't the preferred strategy.

Preferred by who? Goal is usually a matter of personal choice.

I think Harry was agreeing with you, and was merely saying that if an individual's personal goals and circumstances dictate otherwise, then max-ER is not the _correct_ strategy to best achieve those preferences.

snip

> From a practical standpoint, max ER is the appropriate strategy. Most
> alternate discussion is esoteric.

I disagree quite strongly. I believe this view that max-ER is somehow
inherently better is a reflection of human bias. Max-ER is what people
are most comfortable with, and most used to thinking about. The
"appropriate" strategy depends on what problem you are trying to
solve. But, if the max-ER hammer is the only tool in your toolbox,
every problem tends to look like a nail :wink:

I understand your point, Steve, but I'm inclined to agree with Harry that from a _PRACTICAL_ standpoint -- considering that max-ER is the only strategy that you can practice and easily check with either WinPoker or FrugalVP, and that most articles and discussion seems to make the assumption of a max-ER strategy -- it is the most appropriate _practical_ choice. Sort of like choosing Mac vs. IBM, ... Windows vs. Linux, ... or Netscape vs. MSIE. Beauty is in the eye of the beholder, and arguments can be made as to why one choice is better than the other, but sometimes common practical considerations have a greater influence.

By the way, Steve, if doesn't happen to be that the min-Cost solution is normally short-coin instead of full-coin, is it? My previous arguments in defense of short-coin were not very popular either.

Cheers.

Bill Velek

#35

Who can provide an example, using a dealt vp hand, demonstrating
a "min-RofR(vs)min-cost(vs)max-er(vs)RF chasing strategy decision?
Thank you
Steve
If you have

the ability to _skillfully_ playing min-Cost one day, and then
'chase-the-Royal' another day, and then max-ER a third day, I tip

my hat

···

to you. >
Cheers.

Bill Velek

#36

Your question perfectly illustrates one of the practical difficulties we
immediately encounter with the inability of WinPoker and FrugalVP to use
alternative strategies. It would no doubt be considerably difficult to
give you a precise example without strategy charts to compare, etc. It
is also unlikely that you will have a single hand that would have 4
different holds, depending upon your chosen strategy. Rather, I would
expect for a number of hands, one of the 4 strategies would indicate one
hold, while the other three would agree on a second hold ... but with a
different hand, then another strategy would differ from the hold
indicated by the consensus. With a variety of hands, you would find a
variety of differences, although you would have frequent overlaps
between strategies. In the end, all four would necessarily be quite
distinct, otherwise you would end up with the same frequency of hands.
If it were not true that the differences in holds were large enough or
frequent enough, then there would only be very slight differences in the
expected outcome -- in the ER (whether looking long-term or for just a
stated-term such as with a specific limited goal) and in the
probabilities of survival versus ruin, etc. The fact that these
differing results can be demonstrated proves that there are differences
in strategy; but whether those differences are important to a player or
not is another question. For example, I would think that if the
difference in Risk of Ruin for my particular stake is sufficient in my
mind to justify my sacrificing .4% ER in a game that normally has a
max-ER of 100.7221%, like full-pay All American, then that is a personal
decision of what is more important to me; once I make that decision, any
deviation from whatever is then the proper hold for that strategy is an
error. Of course, there might also be very many borderline calls, so
perhaps many of the strategy differences can be ignored, but the only
way for there to be that much of a difference in expected results is if
there are some major differences in strategy that simply could not be
ignored -- not it you really want to use that min-RoR strategy.

Cheers.

Bill Velek

ddjpus wrote:

Who can provide an example, using a dealt vp hand, demonstrating
a "min-RofR(vs)min-cost(vs)max-er(vs)RF chasing strategy decision?
Thank you
Steve
If you have
> the ability to _skillfully_ playing min-Cost one day, and then
> 'chase-the-Royal' another day, and then max-ER a third day, I tip
my hat
> to you. >
> Cheers.
>
> Bill Velek

[Non-text portions of this message have been removed]

#37

"jimnkelli" <jbecker11@c...> wrote:

there is lots of talk about ROR and limited bankrolls....
maybe because I am not from Vegas, but I only know of 1 person who
plays VP on a properly funded bankroll, and it isnt me.
I am what I consider "in the middle" in that I do have a bankroll
set aside for VP and it could very well be bankrupted, but if that
did happen, I would just create another bankroll and keep on going.
So ROR isnt the greatest factor.

But doesn't this mean that you *do* have a properly funded bankroll?
If you can just create another bankroll when your initial bankroll
disappears, then you haven't gone bankrupt.

It's that way for me, so although ROR discussions are theoretically
interesting, they have little to do with how I actually play. I may
go to Vegas with $1000 cash & play quarter single-line FPDW or triple-
line JOB or NSUD with cashback, or similar, & maybe sometimes the
cash will disappear, & I have to go to the ATM to reload.

I'm playing at a level where I have extremely high confidence that a
losing streak will never wipe out my checking account, & that my
results over time will have minimal effect on my life bankroll. I
make efforts to maximize my EV because it's fun for me in a math geek
way, & because as I make some small profits over time, I feel
psychologically more comfortable spending them on frivolous things
than I would money I'd "earned," so that's fun. But Risk Of Ruin
hardly enters into it.

All the above applies to my bread-and-butter playing, where the
fluctuations never threaten my checking account. It's different if I
dip my toe into over-my-head stakes, & in such cases, I allot a fixed
bankroll & quit if it disappears. But that's the exception, something
I do on occasion for a kick. The great majority of the time I'm
playing VP it isn't like that.

Stuart (RandomStu)
sresnick2@comcast.net
http://home.comcast.net/~sresnick2/mypage.htm

#38

double bonus: AAA33
Max ER: hold trip Aces (ER=10.11,Variance=1001)
Max Bankroll Growth: hold full house (ER=10,Variance=0)
reason: bankroll growth is directly proportional to advantage (ER-1)
AND variance, so a reduction in advantage is a win if it produces a
greater reduction in variance, conversely an increase in advantage is
a loser if it produces a greater increase in variance ...

···

--- In vpFREE@yahoogroups.com, "ddjpus" <doubleb107@a...> wrote:

Who can provide an example, using a dealt vp hand, demonstrating
a "min-RofR(vs)min-cost(vs)max-er(vs)RF chasing strategy decision?
Thank you
Steve
If you have
> the ability to _skillfully_ playing min-Cost one day, and then
> 'chase-the-Royal' another day, and then max-ER a third day, I tip
my hat
> to you. >
> Cheers.
>
> Bill Velek

#39

stanfordwang wrote ...

Now that's an interesting "handle". I take it someone had already
registered bobcancer.

- H.

#40

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@v...>
wrote:

Here's my take on this:

If you're playing on a near-infinite bankroll so that ROR = ~0% and
you have near absolute confidence that you indeed will play
"throughout" your lifetime, then you're absolutely correct.

However, with a more limited bankroll and a risk that you'll bust

and

end your play prematurely, there are other factors that enter the
picture in maximizing your expected play profit. Max ER may not be
the way to go.

Further, as Steve notes, there are other circumstances and goals

under

which max ER isn't the preferred strategy.

That said, for the large bulk of players such considerations are
necessarily academic. There are far more critical aspects of play
that are sufficiently challenging.

From a practical standpoint, max ER is the appropriate strategy.

Most

alternate discussion is esoteric.

- Harry

Has anyone ever published a min risk, or a min hands between royal
strategy or anyothers besides max ER?

DWK