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vp Double Dependency & ER

#1

But determination if it's truly beneficial needs to take into account
whether it exposes the player to a greater potential loss. I belive
it does (as, I sense, D. Paymar does).

I'm inclined to agree, and so I ran the gist of this thread by my
math-wiz-prof friend, who's reaction was, "Who cares? If they want to
double-up, let them. In the end, it's a wash."

I was somewhat disappointed.

I said, "Isn't it contrary to the whole idea of grinding out a win?"

He said, "No."

Disappointment heightens.

I said, "Doesn't a player have to be consistent on which 'wins' he decides
to double-up?"

He said, "It might help."

Feeling of being lost.

I said, "Isn't there a strong argument SOMEWHERE against the double-up
option?

He said, "Nope."

Utter despair.

Which is why I continue to argue against it.

lb
"variance giveth, variance taketh away"

#2

[actually, Harry wrote this part]

But determination if it's truly beneficial needs to take into account
whether it exposes the player to a greater potential loss. I belive
it does (as, I sense, D. Paymar does).

Truly beneficial _in_what_way_? The concept of "beneficial" is
just like the concept of optimal. It doesn't exists in a vacuum, it
is relative to the players goals/objectives.

In negative games, the double up is truly beneficial to a player
to wishes to maximimize the probability of reaching _any_ fixed
target before going broke. But in a positive game, the double
up harms the player who has this very same objective.

Similarly, in a negative game, the double up is beneficial to
a player to wishes to maximize the geometric mean of bankroll
after the bet is resolved. This applies to each an every wager
whether in isolation or as a series of wagers, and is equivalent
to log optimal play.

I believe (but cannot currently prove) that a player whose
objective is virtually anything _other_ than "maximize EV"
will benefit from the double up in negative games. However,
before running out and doubling up like crazy, keep in mind
that "maximize EV" is consistent with "make your bankroll
last the largest number of wagers, on average". One cannot
have that objective in mind and also try to maximize other
objectives at the same time. That is how optimization works
in general -- to get the best performance from one particular
perspective, you must sacrifice performance relative to most
other objectives.

I'm inclined to agree, and so I ran the gist of this thread by my
math-wiz-prof friend, who's reaction was, "Who cares? If they want to
double-up, let them. In the end, it's a wash."

I was somewhat disappointed.

It is a wash in terms of EV, but it is incorrect to say that this implies
that it is a wash in all regards. The double up reduces "Sorokin"
risk (I hate that terminology) in negative games, but increases RoR
in positive games.

I said, "Isn't it contrary to the whole idea of grinding out a win?"

He said, "No."

Disappointment heightens.

I share your disappointment, but don't find this response surprising.
EV isn't the only thing that matters, so the fact that double up is
EV neutral doesn't mean that it makes no difference at all, as your
math-wiz-prof friend claims.

I said, "Doesn't a player have to be consistent on which 'wins' he decides
to double-up?"

He said, "It might help."

Feeling of being lost.

I said, "Isn't there a strong argument SOMEWHERE against the double-up
option?

He said, "Nope."

In positive games, double up increases RoR and decreases geometric
growth rate (assuming the same bet size). This is easily provable.
There are some (many) players who would view these as negatives.
In negative games, the opposite effects occur (after transposing RoR
to risk of going bust before reaching a finite fixed goal).

Utter despair.

Which is why I continue to argue against it.

Then what you are saying is that you argue against it simply because
it doesn't fit your perception of the how the game works?

Don't get me wrong, I'm not suggesting that everyone should go out
and start doubling up. I'm only pointing out that the old school
thinking that "double up is always bad" is mistaken and mythical.

It is beginning to appear that "X is always good/bad/[in]correct" is
likely to be false whether X is "double up" or a wide variety of
other entities. What is best/beneficial _always_ depends on what
the player is trying to accomplish and what constraints the player
is working under.

This is counter to how people are used to thinking about gambling
questions, but it is what math says to be true.

···

On Sunday 04 April 2004 01:30 pm, Lawrence Boxer wrote:

#3

Lawrence Boxer replied to:

> "But determination if it's truly beneficial needs to take into
> account whether it exposes the player to a greater potential
> loss."

with:

I'm inclined to agree, and so I ran the gist of this thread by my
math-wiz-prof friend, who's reaction was, "Who cares? If they want
to double-up, let them. In the end, it's a wash."

I was somewhat disappointed.

I'd be too. Seems like he's speaking solely to ER, not to the
potential of a loss. Ask him if the only considered wager was a lone
50-50 prospect wouldn't the better face a loss risk that's absent with
no wager ... if so, what's the difference in this case.

Utter despair.

Which is why I continue to argue against it.

:wink:
btw, this discussion didn't happen to take place on Thursday, did it?

#4

Lawrence Boxer wrote:

snip

... I ran the gist of this thread by my
math-wiz-prof friend, ...

snip

I said, "Doesn't a player have to be consistent on which 'wins' he decides
to double-up?"

He said, "It might help."

Stating that "it might help" clearly implies that there is at least _some_ particular way of playing a double-up option that would likely lead to an eventual difference from an even-chance outcome, and that is simply _not_ the case at all. We can affect the volatility of the same by decisions such as only playing a double-up on the smaller wins, but there is no right or wrong way to play that game, and no decision we ever make is going to make a difference in the outcome regarding ER. Any difference from a complete wash, after any number of games, is just by sheer chance, and sheer chance along. It surprises me that any "math-wiz-prof" wouldn't recognize that immediately. Perhaps he didn't understand the question. I reiterate -- consistency, or a complete lack thereof -- makes absolutely NO difference in long term ER; it is a complete wash one way or the other ... except for its advantage or disadvantage in comparison with the ER of the game that you are playing, and except that you are not earning cash back, and probably are not earning comps except to the extent that you might accumulate enough "time" on a machine to earn a buffet in some casinos.

Bill Velek

#5

Lawrence Boxer wrote:

snip

> ... I ran the gist of this thread by my
> math-wiz-prof friend, ...

snip

> I said, "Doesn't a player have to be consistent on which 'wins' he
> decides to double-up?"
>
> He said, "It might help."

Stating that "it might help" clearly implies that there is at least
_some_ particular way of playing a double-up option that would likely
lead to an eventual difference from an even-chance outcome, and that is
simply _not_ the case at all.

Care to wager on that?

We can affect the volatility of the same
by decisions such as only playing a double-up on the smaller wins, but
there is no right or wrong way to play that game, and no decision we
ever make is going to make a difference in the outcome regarding ER.

ER is *not* the only thing that can "make a difference" in the player's
outcome. It is just _one_ metric. The variance is different, the risk
of ruin is different, the geometric growth rate is different, etc. The
limited measurement we call "ER" is unable to "see" these differences
in the two strategies.

Any difference from a complete wash, after any number of games, is just
by sheer chance, and sheer chance along. It surprises me that any
"math-wiz-prof" wouldn't recognize that immediately. Perhaps he didn't
understand the question. I reiterate -- consistency, or a complete lack
thereof -- makes absolutely NO difference in long term ER; it is a
complete wash one way or the other ... except for its advantage or
disadvantage in comparison with the ER of the game that you are playing,
and except that you are not earning cash back, and probably are not
earning comps except to the extent that you might accumulate enough
"time" on a machine to earn a buffet in some casinos.

There is a vast difference between "same ER" and "completely
mathematically equivalent". The fact that two games have the same
ER doesn't imply that there is no way to take advantage of the
differences in _other_ parameters of the games. That is what
alternate strategies are all about -- caring about things other
than (or in addition to) ER.

Most bets at roulette have the same ER, but if you want to double
a bankroll of 1000 units to 2000 units, the best play is to bet on
a single number at a time. In addition, using progressions can
help the player to improve the probability of doubling the bankroll
before going broke. This is blasphemy in the blackjack community,
where any talk of progressions is taken as evidence that the author
is incompetent.

But, in order to "see" these differences in the game, you have to
look in a way that is different than what we do to measure ER. ER
is a measurement of average return _per_game_played. So if you
play the same number of rounds for each game, and then compare
results and average over all possibilities, then you will find that the
outcomes look the same.

Changing the "perspective" can be a tricky thing. Measuring ER
is mathematically equivalent to dividing up the ongoing stream of
games into equal sized segments. You can use segments of one
game, or 10 games, or 352 games each, and if you always divide
the playing stream consistently then you are still measuring ER.
In order to measure something other than ER, you need to divide
up the stream of games on a basis other than "number of games
in a segment". Examples:

1) Divide the stream at points where the bankroll has either grown
by 10% or shrunk by 10% compared to the last "measurement".
The grow/shrink percentages don't have to be the same, but you
need to be consistent. You can use 25% for all "grow" and 5% for
all "shrink" if you want to. If you do this using fixed bet sizes, you
are comparing the parameter that I call "risk". For favorable games,
it is equivalent to Risk of Ruin.

2) Divide the stream by ending each segment with a specific payoff,
such as a flush. This measures average gain (or loss) between
flushes. If you do this using the royal flush payoff, and find the
strategy which gives the best performance, you will minimize the
average loss between royals (the strategy I've called min-cost-royal).
You can twist this around by defining arbitrary "families" of hands
that mark the end of a segment. You could use suited hands, or
a family that consists of flushes, straights and 3-of-a-kind.

3) Divide the stream by ending each segment with a loss. Any
string of successive wins is kept in the same segment. Average
dollars won or lost per segment represents the "exchange rate"
you get by feeding dollars in and "recycling" a dollar from each
win in order to keep the string of wins going.

4) Divide the stream by ending each segment with a win. Any
string of successive losses is kept in the same segment. This is
actually an alternate way of measuring the "exchange rate" as
defined in case 3).

How one chooses to divide up the ongoing stream of games
determines what you "measure" when you compare results.
You can measure one parameter while playing to maximize
another parameter. The playing strategy determines which
parameter is maximized, but the way you chop up the stream
of games determines what you are measuring.

···

On Sunday 04 April 2004 05:42 pm, Bill Velek wrote:

#6

Stating that "it might help" clearly implies that there is at

least _some_ particular way of playing a double-up option that would
likely ...<<

I didn't catch that implication at all. I took it to mean that
any "system" of betting won't overide the random aspect of it. Guess
you had to be there.

lb
"variance giveth, variance taketh away"

#7

I'd be too. Seems like he's speaking solely to ER, not to the
potential of a loss. Ask him if the only considered wager was a

lone

50-50 prospect wouldn't the better face a loss risk that's absent

with

no wager ... if so, what's the difference in this case.

But if not for the win, the 50-50 opportunity wouldn't present itself
in the first place. I can't see that taking the initial win out of
the decision to double is helpful. I agree with you that it's not
_preferable_ to go for the double -up, for the same reason that you
say--the potential loss. But I can't say that it's wrong, as much as
I'd like to.

My main concern originally was that by thinking of double-up as the
extension of a single bet, the inference (to some)is that the only
risk is the decision to double. Why jump through all the hoops and
then turn the result into a toss-up? You work hard to get a slight
edge, then throw the results completely to chance? So you're likely
to win as many decisions as you lose...so what?

lb

#8

My main concern originally was that by thinking of double-up as

the

extension of a single bet, the inference (to some)is that the only
risk is the decision to double. Why jump through all the hoops and
then turn the result into a toss-up? You work hard to get a slight
edge, then throw the results completely to chance? So you're

likely

to win as many decisions as you lose...so what?

I find this last part of the statement to be a bit curious.
Assuming you're playing 9/6 JOB. You get a High pair and your 5
coins are returned. You now have 2 choices (not including walking
away entirely).

1) You can double up. As you so elegantly put it, you can turn the
result to a 'toss-up' 50-50 shot, double or nothing.

2) You can bypass double-up and play another hand of JOB. As you
put it, 'you work hard to get a slight edge'. But, quite frankly,
what edge (assuming cash back doesn't put you over 100%)?

You are really picking between 2 choices (boy I wish I could be a
table in the reponse!).

Game 1 (double up) - NET EV - 100%

Hand - prob - EV
Lose - 50% - 0
Win - 50% - 200%

Game 2 (JOB) - NET EV - 99.6%
(*using approximate probabilities for ease)
Hand - prob - EV

Lose - 55% - 0
High Pair - 21.5% - 100%
Two Pair - 13% - 200%
Trips - 7.5% - 300%
STR - 1.1% - 400%
FLU - 1.1% - 600%
FHS - 1.1% - 900%
Quads - .23% - 2500%
SFL - .01% - 5000%
ROY - .0025% - 80000%

Which one do you pick?

From a long term EV perspective, double-up doesn't look that bad.
You have your choice a 100% game or a 99.6% game.

If you have 30 seconds to catch your flight and you desperately want
to double your 5 coins in, Double Up is the way to go. 50/50 shot
of doing it, whereas you have only a 23% (approx) chance of doubling
(or better) your money with one hand.

If on the other hand, doubling your money (5 coins) means little to
you and you really want to go home talking about your big win, you
give your best shot to VP which has the only chance of the two at a
big win.

The bottom line is if Double-Up was a stand alone game, it would
probably get a fair amount of play. AT 100% EV, it would beat most
games in a casino.

The problem with the current configuration for most players
is 'control'. if you double-up after a High Pair and win, and you
keep doubling, you have to remember those are real coins and in
essence you are increasing the amount you are wagering. You only
have two choices. Take it all down or wager it all.

To see some of the positive aspects of playing Double-Up with proper
self control, just (as someone else suggested) simulate it.

Simulate player 1, playing 600/hour of JOB 9/6 VP.

Simulate player 2, playing 600/hour of JOB 9/6VP but who plays
double up ONLY when hitting a High Pair. This player doubles up
once and only once when this happens (win or lose). He plays double-
up at a rate of 600/hour.

Now....have both players play the same amount of TIME (I don't care
how many hours you pick). Let me know which player will have more
money in his pocket at the end of the time, assuming both games play
according to their expected EV's (JOB - 99.6% and Double up - 100%).

This is, of course, NOT the only way to view the world, but it is
the basis for my dad's article that pretty much started this
complete thread, and I again submit it is ONE VALID way of viewing
things.

Elliot

#9

I promised myself that I'd hold back on extensively challenging any
further statements in this thread. But I'm not going to hesitate to
ask questions simply as a means of clarifying a statement, accepting
the reply at face value.

Elliot Frome wrote:

From a long term EV perspective, double-up doesn't look that bad.
You have your choice a 100% game or a 99.6% game.

The bottom line is if Double-Up was a stand alone game, it would
probably get a fair amount of play. AT 100% EV, it would beat most
games in a casino.

You think so? Simply placing a bet on the turn of two cards
(basically war, without the extended play in the event of a tie) seems
pretty dull to me.

The problem with the current configuration for most players
is 'control'. if you double-up after a High Pair and win, and you
keep doubling, you have to remember those are real coins and in
essence you are increasing the amount you are wagering. You only
have two choices. Take it all down or wager it all.

Is this a problem? Seems to me that under the logic you outline if a
double on a 5 cr. win is warranted, the same argument holds and a 100
cr. double is a reasonable wager.

Now....have both players play the same amount of TIME (I don't care
how many hours you pick). Let me know which player will have more
money in his pocket at the end of the time, assuming both games play
according to their expected EV's (JOB - 99.6% and Double up - 100%).

This is, of course, NOT the only way to view the world, but it is
the basis for my dad's article that pretty much started this
complete thread, and I again submit it is ONE VALID way of viewing
things.

It's a rational argument. But a key point that I feel is missing here
is that the player who doubles has greater downside risk (expressed by
Paymar in terms of greater variance). In the case of a 99%+ game with
at least nominal cashback (but still negative ER), I question if the
margin ER advantage of the double warrants the greater downside risk.

But I'll take it that you feel it does and I'll gladly agree to simply
differ :wink:

- Harry

#10

In a positive game, variance is to be avoided because it represents
the risk that you will lose.

In a negative game, avoiding all variance will _guarantee_ that you
lose. In negative games, variance is your friend because it is what
gives you some chance of coming out ahead.

If the game consists of two players with equal bankrolls pitted against
each other, and one has an advantage, then variance can't be bad
for _both_ players. This whole idea that "variance is always bad"
is simply misguided and illogical. If some aspect of the game helps
one side, it must hurt the other side by a corresponding amount.

For every gambling action, there is an equal and opposite
reaction on the "other side" of the wager.

···

On Sunday 04 April 2004 09:09 pm, Harry Porter wrote:

It's a rational argument. But a key point that I feel is missing here
is that the player who doubles has greater downside risk (expressed by
Paymar in terms of greater variance). In the case of a 99%+ game with
at least nominal cashback (but still negative ER), I question if the
margin ER advantage of the double warrants the greater downside risk.

#11

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

> The bottom line is if Double-Up was a stand alone game, it would
> probably get a fair amount of play. AT 100% EV, it would beat

most

> games in a casino.

You think so? Simply placing a bet on the turn of two cards
(basically war, without the extended play in the event of a tie)

seems

pretty dull to me.

I was leaving the concept of 'excitement' out of the picture and was
talking about from a mathematical perspective. I laughed pretty
loud the first time I saw 'War' in a casino. My first thought
was 'what's next?' Go Fish or Old Maid?! Yet, War is still out
there playing!

> The problem with the current configuration for most players
> is 'control'. if you double-up after a High Pair and win, and

you

> keep doubling, you have to remember those are real coins and in
> essence you are increasing the amount you are wagering. You

only

> have two choices. Take it all down or wager it all.

Is this a problem? Seems to me that under the logic you outline

if a

double on a 5 cr. win is warranted, the same argument holds and a

100

cr. double is a reasonable wager.

Using YOUR logic anyone willing to play nickel VP should be willing
to play quarter or dollar or five dollar or more. There is still
significant short and long term risk with ANY form of gambling.
Don't wager more than you're willing to lose at any one time (and
even longer term). Why are you so willing to wager 5 credits on a
99.6% game where there's a 55% chance you'll lose it all and a 22%
chance you'll break even, but so readily dismiss the opportunity to
lose it all 50% of the time and double you're money 50% of the
time. If I were willing to wager 100 quarters on a 50/50, I'd be
ready to play $5 VP ($25 in for max coin). In reverse, if I'm not
willing to play $5 VP at 99.6%, I'm not likely to be willing to play
$25 Double-Up just because it offers long term an additional .4%.

It's a rational argument. But a key point that I feel is missing

here

is that the player who doubles has greater downside risk

(expressed by

Paymar in terms of greater variance). In the case of a 99%+ game

with

at least nominal cashback (but still negative ER), I question if

the

margin ER advantage of the double warrants the greater downside

risk.

But I'll take it that you feel it does and I'll gladly agree to

simply

differ :wink:

At the moment, I'm having a tough time seeing where there is so much
more downside risk in the example I have outlined. If you walk in
with no plan on when to stop doubling and continue to in essence
increase your wager, then I believe your risk of significant loss
will increase.

If you simply choose to substitute ONE game of Double-Up for an
EQUAL game of VP (i.e ONLY when 5 coins are at risk), then the
results may surprise you.

Elliot

#12

lawrenceboxer wrote:

>>Stating that "it might help" clearly implies that there is at
least _some_ particular way of playing a double-up option that would
likely ...<<

I didn't catch that implication at all. I took it to mean that
any "system" of betting won't overide the random aspect of it.

Then he should have said "it can't hurt" instead of "it might help".

Bill Velek

#13

[snip]

Using YOUR logic anyone willing to play nickel VP should be willing
to play quarter or dollar or five dollar or more. There is still
significant short and long term risk with ANY form of gambling.
Don't wager more than you're willing to lose at any one time (and
even longer term). Why are you so willing to wager 5 credits on a
99.6% game where there's a 55% chance you'll lose it all and a 22%
chance you'll break even, but so readily dismiss the opportunity to
lose it all 50% of the time and double you're money 50% of the
time. If I were willing to wager 100 quarters on a 50/50, I'd be
ready to play $5 VP ($25 in for max coin). In reverse, if I'm not
willing to play $5 VP at 99.6%, I'm not likely to be willing to play
$25 Double-Up just because it offers long term an additional .4%.

Time out. Although I've defended your alternate way of computing
"EV" it is important to understand that you are computing "orange"
EV while the method Dan uses computes "apple" EV. They can't
be compared directly. The apple-EV has units of dollars returned
(or gained) per _initial_ wager, while orange-EV has units of dollars
returned (or gained) per _average_ wager, where the big wagers
from double-ups get mixed into the average.

There is an additional factor which makes orange-EV difficult
(if not impossible) to compare to apple-EV. The traditional
computation of EV requires each outcome to be statistically
independent so that groups "chunks" of outcomes together
will not alter EV on a percentage basis. When outcomes
are all statistcally independent, it is impossible to predict
the next outcome except to say that the probabilities are
given by the overall probability distribution for the game.
In contrast, the way you are computing EV (which BJ
players might call "advantage" rather than EV), the outcomes
from double up are not statistically independent from other
outcomes. An intelligent observer who watches only a
continuous stream of outcomes from your game will notice
a pattern that gives additional information that isn't given
by the probability distribution that you used to compute
orange-EV. For example, if the machine in 9/6 JoB and
the player only doubles flushes, then the stream of
outcomes will include "+6 -6" when the player loses
a double and "+6 +6" when a player wins a double.
From this we can predict that whenever we see +6
in the outcome stream, the next value will always be
either +6 or -6 and never any of the other payoffs.

Bottom line: your way of computing EV doesn't correspond
to a "legitimate" random variable, so the formulation isn't
correct from the perspective of "traditional" statistics. So,
although Dan is wrong when he says there is only one
way to view the game, he is correct when he says that
your way of computing EV doesn't work. The expected
value of a random variable can only be computed from
weighting the outcomes by the respective probabilities,
as represented by a probability distribution which describes
independent events. Your "distribution" isn't made up of
independent events, so it doesn't really represent a
probability distribution.

There may be a way to "legitimize" your approach, but
as it stands the entity that you are calling EV is not the
same kind of beast that statisticians describe as an
"expected value."

···

On Sunday 04 April 2004 10:23 pm, Elliot Frome wrote:

#14

To be honest, I believe you are simply reinforcing what I was trying
to say (perhaps I said it poorly).

While my Dad (Lenny Frome) did not invent the term 'Expected Value',
I believe he for the most part brought it to the masses. In doing
so, he didn't use the textbook definition out of the Gaming Theory
books or out of a Math book. He gave it a definition that he felt
the lay person could understand, relate to and use.

Most of the time, the defintions are essentially identical.
Obviously, where Double-Up is concerned, there is some divergence.

When you are starting with a sub 100% game, what true disadvantage
is a player at (if any) IF he doubles only after a High Pair and
only once when this occurs?

I've got a few things on my plate the next few days, but I'd like to
propose the following and see where it goes.

for a simulation of all this, rather than playing VP hands, I'd like
to use the following shortcut which approximates the end result of a
VP JOB game. (If someone wants to use more accurate numbers, pass
em on thru).

Using the following probabilities and paybacks:

0.215 1
0.13 2
0.077 3
0.011 4
0.011 6
0.011 8
0.0025 25
0.0001 50
0.000025 800
0.542375 Lose

draw a random number between 0 and 999999 to decide the outcome of
VP hand.

Assume 2 players playing side by side getting the same hands. If
the Hand winds up as a High Pair, Player A keeps playing VP. Player
B skips this 'next hand' of VP and instead plays Double-Up ONCE.
I'll draw a random number. If 0 he loses, If 1 he wins.

At the end of a 10 hour session (6000 total hands - for Player B
this will be 6000 TOTAL hands VP and DU), we'll compare how they've
each done.

We can look at the results of 1,000,000 or so sessions.

Never Mind EV, ER, Variance, etc...

If the player playing Double-UP consistently winds up with more
money in his pocket than the guy NOT playing, then Double-Up in this
case can't be all bad.

if the player playing VP only consistently winds up with more money
in his pocket than Double-Up guy, then Double-Up is detrimental to
the player.

If there is a split, then I guess Double Up would be neutral.

This is an attempt to show real world implications of Double Up, not
what happens in the textbook.

I'll probably regret this. Before I start writing the code, let the
major 'arguers' agree on the terms.....

Elliot

[snip]

> Using YOUR logic anyone willing to play nickel VP should be

willing

> to play quarter or dollar or five dollar or more. There is still
> significant short and long term risk with ANY form of gambling.
> Don't wager more than you're willing to lose at any one time (and
> even longer term). Why are you so willing to wager 5 credits on

a

> 99.6% game where there's a 55% chance you'll lose it all and a

22%

> chance you'll break even, but so readily dismiss the opportunity

to

> lose it all 50% of the time and double you're money 50% of the
> time. If I were willing to wager 100 quarters on a 50/50, I'd be
> ready to play $5 VP ($25 in for max coin). In reverse, if I'm

not

> willing to play $5 VP at 99.6%, I'm not likely to be willing to

play

> $25 Double-Up just because it offers long term an additional .4%.

Time out. Although I've defended your alternate way of computing
"EV" it is important to understand that you are computing "orange"
EV while the method Dan uses computes "apple" EV. They can't
be compared directly. The apple-EV has units of dollars returned
(or gained) per _initial_ wager, while orange-EV has units of

dollars

···

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

On Sunday 04 April 2004 10:23 pm, Elliot Frome wrote:
returned (or gained) per _average_ wager, where the big wagers
from double-ups get mixed into the average.

There is an additional factor which makes orange-EV difficult
(if not impossible) to compare to apple-EV. The traditional
computation of EV requires each outcome to be statistically
independent so that groups "chunks" of outcomes together
will not alter EV on a percentage basis. When outcomes
are all statistcally independent, it is impossible to predict
the next outcome except to say that the probabilities are
given by the overall probability distribution for the game.
In contrast, the way you are computing EV (which BJ
players might call "advantage" rather than EV), the outcomes
from double up are not statistically independent from other
outcomes. An intelligent observer who watches only a
continuous stream of outcomes from your game will notice
a pattern that gives additional information that isn't given
by the probability distribution that you used to compute
orange-EV. For example, if the machine in 9/6 JoB and
the player only doubles flushes, then the stream of
outcomes will include "+6 -6" when the player loses
a double and "+6 +6" when a player wins a double.
From this we can predict that whenever we see +6
in the outcome stream, the next value will always be
either +6 or -6 and never any of the other payoffs.

Bottom line: your way of computing EV doesn't correspond
to a "legitimate" random variable, so the formulation isn't
correct from the perspective of "traditional" statistics. So,
although Dan is wrong when he says there is only one
way to view the game, he is correct when he says that
your way of computing EV doesn't work. The expected
value of a random variable can only be computed from
weighting the outcomes by the respective probabilities,
as represented by a probability distribution which describes
independent events. Your "distribution" isn't made up of
independent events, so it doesn't really represent a
probability distribution.

There may be a way to "legitimize" your approach, but
as it stands the entity that you are calling EV is not the
same kind of beast that statisticians describe as an
"expected value."

#15

Steve Jacobs wrote:

> Lawrence Boxer wrote:
>
> snip
>
> > ... I ran the gist of this thread by my
> > math-wiz-prof friend, ...
>
> snip
>
> > I said, "Doesn't a player have to be consistent on which 'wins' he
> > decides to double-up?"
> >
> > He said, "It might help."
>
> Stating that "it might help" clearly implies that there is at least
> _some_ particular way of playing a double-up option that would likely
> lead to an eventual difference from an even-chance outcome, and that is
> simply _not_ the case at all.

Care to wager on that?

No, Steve, because we are saying the same thing. See my very next sentence after that, which said: "We can affect the volatility of the same by decisions such as only playing a double-up on the smaller wins, but there is no right or wrong way to play that game, and no decision we ever make is going to make a difference in the outcome regarding ER." What I meant by "we can affect the volatility" was simply an acknowledgment of what you have now taken the time to expand upon, because "volatility" to me is a broad term which includes the terms that you chose to specify, such as "variance", "risk of ruin", "geometric growth rate", and their effects upon alternate strategies on which you have once again spent a lot of time. So what I was saying is that while volatility can certainly be affected by a player's methods, _ER_ can NOT be; that's what I meant when I clearly stated: "... no decision we ever make is going to make a difference in the outcome regarding ER." My point is that if I arbitrarily say that I'll double every tenth win or every 99th win, or am even more arbitrary, no matter whether those resulting double-ups happen to be on large wins or small wins, I will still, on average and in the long term, receive a 100% return on those bets. If you can show me mathematically where such randomness in a 50/50 proposition will produce less than a 100% return long term, then you'd win. Alternatively, if you can show me mathematically where you can make any choices at all that will result in anything different from a 100% return on a 50/50 proposition long term, then you'd also win. But you are speaking about short-term issues, such as "Risk of Ruin" and "growth rate" while I specifically made my statements in regard to long-term play. Why was I addressing long-term ER without focusing on 'volatility' issues? Because the post to which I was responding did too, at least by inference, ... or at least that's how I took it, as follows:

Lawrence Boxer (henceforth LB) said: "But determination if it's truly beneficial needs to take into account whether it exposes the player to a greater potential loss. I believe it does (as, I sense, D. Paymar does)."

[Call me silly, but discussion of "greater potential loss" gives me the impression that we're speaking about ER more so than RoR, growth rate, or anything else that would fall under the penumbra of "volatility".]

LB continued: "I'm inclined to agree, and so I ran the gist of this thread by my
math-wiz-prof friend, who's reaction was, "Who cares? If they want to
double-up, let them. In the end, it's a wash."

[I couldn't agree more.]

LB: "I was somewhat disappointed. I said, "Isn't it contrary to the whole idea of grinding out a win?"

[The idea of _grinding_out_ a win connotes, at least to me, long-term play.]

LB: He said, "No." Disappointment heightens. I said, "Doesn't a player have to be consistent on which 'wins' he decides to double-up?"

[My impression was that his question is directly in regard to what was just immediately discussed -- greater potential _losses_ (i.e., ER) and _grinding_out_ a win (i.e., long-term).]

LB: "He <the expert> said, "It might help."

Now, I stand by my answer, which I thought was clear, that long-term ER is not going to be affected one way or the other by any amount of consistency or inconsistency in using the double-up feature in any particular pattern, based upon size of wins, or any other scheme. And to make it perfectly clear, I _do_agree_ that the manner of using double-up _CAN_ affect other aspects of the game which I lump under the broad category of volatility, including RoR, bankroll requirements, etc.

Frankly, while my original post probably wasn't as _crystal_ clear as this reply, I find it tedious to have to be so very specific at all times when I'm sure that 95% of the members of this group probably assume two things unless stated otherwise: the use of max-ER strategy, and long-term play. I therefore think that it is unnecessary to state those conditions unless the contrary is intended. At least that had been my general practice until, for awhile at least, I began the strained effort of constantly stating "max-ER strategy", etc., which I do not intend to continue. No offense, Steve, but I already conceded to you a long time ago that there are other legitimate strategies besides max-ER; however, it has become equally clear to me that the vast majority of folks on this group are not particularly interested in what most of them view as insignificant differences that your alternatives actually make. Your alternate strategies are interesting to me from a math viewpoint, but I wouldn't spend time trying to develop a strategy around them. No offense meant, and I thank you again for spending as much time as you do so that folks like me can learn and understand.

Cheers.

Bill Velek

···

On Sunday 04 April 2004 05:42 pm, Bill Velek wrote:

#16

Never Mind EV, ER, Variance, etc...

This is like saying "forget math, we'll just assign numbers and
combine them in any way we like." You can do that, but don't
expect the number you get to really be meaningful.

If the player playing Double-UP consistently winds up with more
money in his pocket than the guy NOT playing, then Double-Up in this
case can't be all bad.

This may seem like it should be OK, but it is a deception. That
isn't an accusation, I'm merely saying that I think you're tricking
yourself into seeing something that isn't real.

Instead of doubling up, how about if we simply _pretend_ that we
doubled up, and transfer some coins from our pockets to the coin
tray, and pause briefly while we count that as a "play". Then, if
the normal VP game is negative, we will not only come out with
more money on average, we will have lower variance as well. In
fact, on average this will give us the same amount of money as
actually playing double-up, without any of the potential downside
from the fluctuations that go along with actual wins and losses.

Clearly better than the double-up, but this is obviously bogus.
Should we also forget about EV/ER/Variance here and think this
is really of value? I don't think so, and if we aren't dotting our i's
and crossing our t's with the real double up then we can't be sure
that the "effect" that is making it look better isn't just an illusion that
has no more real value than pretending we played games that we
actually skipped.

if the player playing VP only consistently winds up with more money
in his pocket than Double-Up guy, then Double-Up is detrimental to
the player.

Illusion. Moving coins from pocket to coin tray has equal impact,
and until proven otherwise with actual math, there is no compelling
reason to believe that double-up isn't mathematically equivalent
to just shifting coins around.

That doesn't mean there can be no value in double up, it merely
means that this pseudo-mathematical approach can't carry the kind
of weight that a mathematically correct approach provides. Real
math shows that in negative games, double-up can improve the
player's probability of reaching a target bankroll before going
broke. This is qualitatively different than EV, but it is a real effect
that a simple coin transfer cannot duplicate. The impact on EV is
still zero.

This is an attempt to show real world implications of Double Up, not
what happens in the textbook.

I'll grant you that it is "real world" in the sense that those in the
real world without a strong math background might not see that
there is a problem with this approach. Playing the "real world
vs. textbook" card is a ploy that is also logically invalid. There
are many others, such as appeals to authority, ad hominem
attacks, appeals to emotion, and other "debate tools" that
are used by politicians but avoided by mathematicians and
scientists.

I'll probably regret this. Before I start writing the code, let the
major 'arguers' agree on the terms.....

The whole point of mathematics is to provide the very foundation
which makes it possible to "agree on the terms" in such a way
that logically valid conclusions can be reached. The other
advantage of using a strict mathematical/scientific approach
is that it encourages independent verification by others to
increase our confidence that no mistakes were made along
the way.

Math is a powerful tool, but only if used precisely and without
taking shortcuts. Those who are willing to accept shortcuts
can never be confident that the conclusions they reach are
correct.

···

On Monday 05 April 2004 09:23 am, Elliot Frome wrote:

#17

If it's not EV, don't call it EV!
Call it a Frome or Singer or Pseudo-Science Value!
These terms have mathematical definitions:
EV, ER, Variance, Standard Deviation, Risk of Ruin
If you're going to invent your own terms, give them your own names.
If you're going to use mathematically defined terms, expect to get
called on them if you use them incorrectly.

"Elliot Frome" <compuflyers@p...> wrote:

While my Dad (Lenny Frome) did not invent the term 'Expected

Value',

···

I believe he for the most part brought it to the masses. In doing
so, he didn't use the textbook definition out of the Gaming Theory
books or out of a Math book. He gave it a definition that he felt
the lay person could understand, relate to and use.
Most of the time, the defintions are essentially identical.
Obviously, where Double-Up is concerned, there is some divergence.

#18

Just for the heck of it, I went back and checked the specific text
of my dad's article that started this whole thread.

The specific term my Dad used was:

'The average overall Video Poker/card-match combination payback will
usually exceed that of the Video Poker alone, as we show below

The 'show below' would appear to be this part:

'(b) The players will also sense that they are playing longer for
the same bankrolls, on average. That 1,000 game session will stretch
into a 1,900 game session. Since the house edge for casino games is
based on the number of games played, the edge is reduced
appreciably. To illustrate, in a 98.5 percent payback Joker Wild
session, the players would average 15 bets lost in 1,000 games.
These same 15 bets will now be lost 1n 1,900 games. This, in effect
raises the payback to 99.2 percent. But, for a 97 percent Video
Poker machine, the double-up feature increases the payback to 98.4
percent which suggests we can do much better on other types of
machines.'

I think over the past 10 days (or so), we have distorted the message
that was trying to be conveyed. (*I include myself in this*)

The discussions have been fun nonetheless!

Sad to say, the latest article I submitted from my Dad's archives
probably won't generate as much discussion. Maybe I can dig up the
old one about Keno that he wrote......

As for myself....I wish I could pull as many Deuces play Deuces Wild
as I do when playing Double-Up......

Have a great week!

Elliot

#19

Just for the heck of it, I went back and checked the specific text
of my dad's article that started this whole thread.

The specific term my Dad used was:

'The average overall Video Poker/card-match combination payback will
usually exceed that of the Video Poker alone, as we show below

The 'show below' would appear to be this part:

'(b) The players will also sense that they are playing longer for
the same bankrolls, on average. That 1,000 game session will stretch
into a 1,900 game session. Since the house edge for casino games is
based on the number of games played, the edge is reduced
appreciably. To illustrate, in a 98.5 percent payback Joker Wild
session, the players would average 15 bets lost in 1,000 games.
These same 15 bets will now be lost 1n 1,900 games. This, in effect
raises the payback to 99.2 percent. But, for a 97 percent Video
Poker machine, the double-up feature increases the payback to 98.4
percent which suggests we can do much better on other types of
machines.'

I'm sorry, but this is smoke and mirrors. These effects are an illusion
that is no more significant than transfering coins from pocket to coin
tray and viewing it as losing less during those "plays".

I think over the past 10 days (or so), we have distorted the message
that was trying to be conveyed. (*I include myself in this*)

I realize your father isn't here to defend his position on this, but I
have to say that he fooled himself into thinking this was real when
it was not. I'm sure it wasn't his intent to deceive himself or his
readers, but the conclusions he reached were not mathematically
correct in this particular case.

···

On Monday 05 April 2004 10:41 pm, Elliot Frome wrote:

#20

No, Steve, because we are saying the same thing.

We are saying things that are quite different.

No offense, Steve, but I already conceded to
you a long time ago that there are other legitimate strategies besides
max-ER; however, it has become equally clear to me that the vast
majority of folks on this group are not particularly interested in what
most of them view as insignificant differences that your alternatives
actually make.

Here is the real crux of the difference in what I'm saying and what
you are saying. Your position amounts to "ER is all that really
matters, because the alternate strategies don't make a significant
difference".

But is that really true? Let's take a look. The numbers below are
based on 9/6 JoB with a 1300 unit payoff for royals, but similar
effects occur under a wide variety of playing conditions.

1) A player who prefers an RoR based perspective might choose
to play $100 a day until it is either doubled to $200 or lost. On
average, they will come home a winner 2.34% more often by
using min-risk strategy instead of max-EV strategy. The endpoints
of $100/$200 are arbitrary, any other endpoints still give 2.34%
better performance by this standard of measurement. Is that
really "insignificant"? I don't think so.

2) A player who prefers to minimize losses between royals will
have an average profit of $315.70 by using max-ER strategy,
but this increases to $324.01 by using a strategy that is optimal
for minimizing cost of a royal. This is a 2.63% difference in
performance. Insignificant? I don't think so.

These performance tradeoffs aren't what I would call "massive"
but I don't think it is reasonable to describe them as "insignificant".
By way of comparison, playing this game on a dollar machine
at 600 hand/hr would yield an average profit of $35.73/hr. If
strategy errors were reducing this to $34.84/hr would you feel
that the errors were insignificant?

If your employer were to cut your salary by 2.5% would you
shrug it off as insignificant? Be honest.

···

On Monday 05 April 2004 02:12 pm, Bill Velek wrote: