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"progressive newbies question"

#21

Steve,
   
  Thanks for the explanation. It definitely helps me understand it all a little bit more.
    In other words, when the game is viewed from the perspective of these
virtual payoffs, it appears that we are playing a breakeven game.
  Hmmmm....(light going on)....the max-royal strategy also was based on a break-even paytable.....Does this mean that all of the alternate strategies you've outlined are based on paytables that treat the game *AS IF* it were break-even? I.E. the sum of the probabilities of all of the paytable entries equals 1.
   
  I've often wondered what the 9/6 JoB paytable would look like if the paytable was adjusted to reflect actual probability of hitting each entry, and such that the game would be break-even. For example, it seems that straight flushes should pay much more than 250 for how rare they are. In fact, I'm guessing that a royal should pay exactly 9 times more than a straight flush, since there are 9 straight flushes (Ace-low through 9-low) per suit for every royal (only one per suit).
   
  John

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#22

John Douglass wrote:

I've often wondered what the 9/6 JoB paytable would look like if the
paytable was adjusted to reflect actual probability of hitting each
entry, and such that the game would be break-even. For example, it
seems that straight flushes should pay much more than 250 for how
rare they are. In fact, I'm guessing that a royal should pay exactly
9 times more than a straight flush, since there are 9 straight
flushes (Ace-low through 9-low) per suit for every royal (only one
per suit).

The RF:SF pay ratio would be smaller than that, assuming the strategy
used isn't "monkey at the keyboard" but instead, among other things,
favors high cards.

If you stay within the constraints of multiple bet returns for winning
hands (e.g. high pair returns 1 bet and other hands return multiples
of that), then it's difficult to construct a practical paychart that
achieves this.

However, I expect the game "All American" was named for a paytable
that does a decent job of reflecting the egalitarian principal of
"relative pay for relative difficulty".

-- The SF pay is boosted to 1000, bring the payout ratio relative to
the RF much more closely in line.

-- S/F/FH all pay 40, which more strongly reflects the relative
frequencies than in a game where the FH pays twice the S payout.

-- The quad 200 and trip 15 bookend the S/F/FH with pays that also
decently mirror relative hand frequencies.

-- The 2 pair 5 cr payout reasonably reflects it's probability vs. a
high pair: less frequent, but not half as much.

The SF pay surprisingly overcompensates for the SF probability in AA.
A payout of 750 would more closely reflect the more frequent
occurance under adjusted strategy and also push the ER quite close to
100.0%. It's as if the designer sought a non-wild equivalent to FPDW.

- Harry

#23

Harry, you're right about straight/flush/FH being both underpaid (usually) and being fairly close together in terms of frequency. For JoB, this is as close as I could get the paytable to the actual frequency of occurence of each paytable entry, for 5 coins bet:
   
  6-9-15-58-67-93-458-4889-32081
   
  The actual occurences of each hand in perfect play using the above paytable are:
   
  5.7-8.5-15-58.5-66.3-93.2-458-4895-32109
   
  but I am unable to do fractional values in WinPoker, so I rounded to the closest integer. The exceptions are the SF/RF values, which if even a single coin is added to either one, in turn greatly changes the occurence values. So that's as close as I could get.
   
  The preceding paytable is (close to) correct as far as the occurence of each item, but it returns 182%. To get close to 100% return I cut each item about by about 90%, which results in the following paytable returning 101.65%:
   
  3-5-8-32-37-52-308-2689-17644 [still based on 5 coins bet]
   
  Look for this paytable soon at a casino near you! (j/k, of course...lol) A couple of tweaks here and there could make it 100% or 99%. But a paytable closely weighted to the relative probabilities of occurence has a terrible variance -- almost 450! The standard 9/6 JoB paytable pays more for the 3 most commonly occurring hands and much less for the rest of the more rare ones. This makes the game much more bearable for the average player.
   
  John

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Harry Porter <harry.porter@verizon.net> wrote:
  The RF:SF pay ratio would be smaller than that, assuming the strategy
used isn't "monkey at the keyboard" but instead, among other things,
favors high cards.

-- S/F/FH all pay 40, which more strongly reflects the relative
frequencies than in a game where the FH pays twice the S payout.

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#24

John Douglass wrote:

  The preceding paytable is (close to) correct as far as the
occurence of each item, but it returns 182%. To get close to 100%
return I cut each item about by about 90%, which results in the
following paytable returning 101.65%:
   
  3-5-8-32-37-52-308-2689-17644 [still based on 5 coins bet]

That's a reasonable start. Now complete the exercise to comply with
the practicalities of vp machine conventions.

Notably, each pay should be an even multiple of the number of coins
wagered (i.e. each 5 coin pay should be divisible by 5). This is
necessary to provide an expedient paytable for 1-5 coins wagered.

You necessarily need to set the high pair to a payout of 5. Further,
you want to maintain the other occurance/payout ratios relative to the
high pair hand. Ideally, the 3-kind will go to 15. The 2-pair could
potentially stay at 5 or go to 10.

Once you make these basic changes and recalculate a hand distribution
for optimal strategy, the shift in return to the lower hands will
necessitate that you fine tune higher hands to maintain a roughly 100%
ER game.

Convention again would suggest keeping the RF at 4000. Though there's
no "hard and fast" rule that would mandate this, it serves a second
desirable goal of keeping variance far more moderate than in your
initial paytable workup.

Work this around a bit and I expect that you'll arrive at something
that begins to approximate the standard All American paytable. Maybe
in the spirit of American ingenuity, you'll come up with a better
version :wink:

- Harry

#25

My goal was to come up with a paytable that a) paid 100% (or close to it), and b) closely represented the relative probabilities of each item. I accomplished that. If you have other goals in mind, feel free to explore them :slight_smile:
   
  Thanks for the feedback,
   
  John

···

Harry Porter <harry.porter@verizon.net> wrote:
  That's a reasonable start. Now complete the exercise to comply with
the practicalities of vp machine conventions.

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#26

John Douglass wrote:

My goal was to come up with a paytable that a) paid 100% (or close to
it), and b) closely represented the relative probabilities of each
item. I accomplished that. If you have other goals in mind, feel free
to explore them :slight_smile:

Understood, and I apologize if it appeared I made light of your result.

I merely meant to suggest that one interesting aspect is that if you
extend the work to arrive at a "standard" vp paytable, the result is
something that is akin to All American.

- H.

#27

It seems to me that a coin-in requirement by itself is not sufficient to
determine a strategy; at least one additional parameter is needed. For
example, are you trying to minimize the time required to hit a coin-in
amount? (answer: avoid winning hands!?!) Minimize risk for that coin-in?
(answer: regular min-risk strategy) Maximize EV? (answer: regular max-ev
strategy). So it seems that coin-in becomes an irrelevant part of the
equation. Please correct me if I'm wrong.

The strategy that I'm developing maximizes the probability that the
player's bankroll will survive long enough to meet a fixed coin-in
requirement. The only other consideration that comes into play is
the payoff schedule.

···

On Sunday 23 July 2006 12:51 pm, John Douglass wrote:

Steve Jacobs <jacobs@xmission.com> wrote: Someone here recently asked
about getting the best shot at reaching a fixed coin-in requirement, as
their definition of "success". This leads to a complex strategy that has
some interesting characteristics, so I'm trying to find some time to
explore that goal in more detail.

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#28

I look forward to your results. For low rollers such as myself, I
think this fits my needs pretty well. I have a limited session
bankroll, limited time, and some limited choices for games. I would
like to find the game/denomination that give me the best chance of
reaching some desired coin-in.

- John

···

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

The strategy that I'm developing maximizes the probability that the
player's bankroll will survive long enough to meet a fixed coin-in
requirement. The only other consideration that comes into play is
the payoff schedule.

#29

Harry, I always appreciate your posts and didn't feel you made light of mine. I was just saying that I had accomplished what I set out to do. Interesting point about AA....I haven't played it but the similar payouts for s/f/fh are interesting, and as we found out, more realistic.

Harry Porter <harry.porter@verizon.net> wrote: Understood, and I apologize if it appeared I made light of your result.

I merely meant to suggest that one interesting aspect is that if you
extend the work to arrive at a "standard" vp paytable, the result is
something that is akin to All American.

···

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#30

Steve, interesting...let us know what you come up with.

Steve Jacobs <jacobs@xmission.com> wrote: The strategy that I'm developing maximizes the probability that the
player's bankroll will survive long enough to meet a fixed coin-in
requirement. The only other consideration that comes into play is
the payoff schedule.

···

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#31

IMHO, this is something that I would find quite helpful in reaching some short term goal,
like for instance, wanting to "qualify" for a buffet, or making DIAD, or having enough
money to "last" through a trip.

I have used Dunbar's software to "define" the bankroll that I would need to attain some
such goal, for instance to "define" the bankroll I would need for a "trip", estimating that I
would like to play some number of hands (10,000, say) of this particular game (NSUD) at
this particular level ($1) over the course of the trip. For the case cited, $5,000 was what
popped up. This is something that I could live with and it gives me a good idea as to what
I could or could not do, during the course of a trip.

.....bl

···

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

The strategy that I'm developing maximizes the probability that the
player's bankroll will survive long enough to meet a fixed coin-in
requirement. The only other consideration that comes into play is
the payoff schedule.

#32

Steve,

  Thanks for the explanation. It definitely helps me understand it all a
little bit more. In other words, when the game is viewed from the
perspective of these virtual payoffs, it appears that we are playing a
breakeven game.
  Hmmmm....(light going on)....the max-royal strategy also was based on a
break-even paytable.....Does this mean that all of the alternate strategies
you've outlined are based on paytables that treat the game *AS IF* it were
break-even?

Yes. However, this isn't as amazing as it might seem. If you take a payoff
schedule for any real machine, and multiply all of the payoffs by the same
number, then the scaled payoff schedule will still give the same max-EV
strategy. So, any payoff schedule can be scaled so that the virtual payoffs
give a breakeven game, or scaled in an infinite number of other ways which
still produce the same playing strategies. Still, there are some aspects of
breakeven that seem almost magical.

I.E. the sum of the probabilities of all of the paytable
entries equals 1.

That's not quite what breakeven means. The probabilities multiplied
by the payoffs sum to 1.

  I've often wondered what the 9/6 JoB paytable would look like if the
paytable was adjusted to reflect actual probability of hitting each entry,
and such that the game would be break-even. For example, it seems that
straight flushes should pay much more than 250 for how rare they are.

They are rare because the playing strategy makes them rare. Whenever an
optimal playing strategy is found based on a given game and some objective
that is optimized, the strategy strikes a perfect balance for that objective.
If one kind of payoff happened "too often" then the optimization process
would alter the strategy in order to restore a perfect balance.

In
fact, I'm guessing that a royal should pay exactly 9 times more than a
straight flush, since there are 9 straight flushes (Ace-low through 9-low)
per suit for every royal (only one per suit).

Ah, but what a hand "should" pay depends on your objective. Using
max-EV as an example, you could get a fair game for 9/6 JoB by
increasing the royal payoff to 976 units. Then, all the payoffs would
be what they "should" be for the max-EV strategy, and that strategy
would be breakeven. But, you could just as easily construct a fair game
by increasing one of the other payoffs until the return was 100%. All
of these altered games would be "fair" in different ways.

···

On Sunday 23 July 2006 1:08 pm, John Douglass wrote:

#33

I didn't mean a "fair" paytable, i.e. one that returns 100%. I meant a paytable that was identical (or as close to identical as possible) to the relative occurrence of each entry. For example, if the royal occurs every 32,000 hands, then the payoff should be 32,000 coins. That's what I meant. See my other post for what I came up with for 9/6 JoB.

Steve Jacobs <jacobs@xmission.com> wrote: Ah, but what a hand "should" pay depends on your objective. Using
max-EV as an example, you could get a fair game for 9/6 JoB by
increasing the royal payoff to 976 units. Then, all the payoffs would
be what they "should" be for the max-EV strategy, and that strategy
would be breakeven. But, you could just as easily construct a fair game
by increasing one of the other payoffs until the return was 100%. All
of these altered games would be "fair" in different ways.

···

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#34

We have not received a digest from vpfree in weeks. I've checked
yahoo groups and we're still listed as members and there doesn't
appear to be a bounce problem. Can anyone shed any light on this?

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