Should/Could the Wizard do a project for the betterment of table games?
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 | 5 votes (27.77%) | ||
| | 14 votes (77.77%) |
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We - the gambling and playing public - have the worked out (and available to us all) the best Basic Strategy for Blackjack in all configurations, and best strategy for many poker-based table games, often done by Mike on his WizardofOdds.com site. But we do NOT have the proven best and definitive house way and player way for pai gow poker. I've done this work algebraicly for the Optimized casino house way, as well as for an optimized best player way, and I have kept private this optimized "best player" way that I use; there are actually two: a three-page player's way that's hard to remember, and a one-page easy-to-remember player way.
When I saw the work effort involved just for the Rainbow Logo attached to Mike's www.wizardofodds.com site, I figure something like this might warrant a reasonable effort to obtain this. Mike already links the various house ways that different casinos use on his site; why not include a best house way and a best player's way with a "this is it - it's been research" with it.
For Mike, it has some advantages:
1. No mathematician has done this before, certainly NOT the casino operators themselves - They get their house ways updated by some guy in a raincoat in the Palace Station parking lot once every 6 months, - or so it seems. It would be of great prestige and service to Mike and the industry to have this.
2. The "Player optimized" house way (which I use to slaughter bad house ways) would be of great player advantage service to the playing public, which is something that Mike personally espouses.
3. he would really get noticed by casino operators (hint: lucrative work potential and status among operators); they already know is name, true, but another feather in the cap is a good thing.
Rules for the strategies:
1. Must be One page (12 point, not microfiche), - and in plain English, as it must be playable and deal-able.
2. Mike defines all other criteria, if he wishes to do this. (up to him, he's the boss here.)
just a proposal.
Since we have finalized strategies for all other games, why not end the case with Pai Gow Poker?
Quote: PaigowdanThis is interesting because this is an area that has not been definitively solved in the casino industry, and it has not yet been done: There can pretty much be one definitive "best" house way, as well as one definitive "best" player way, for Pai Gow Poker. And No one knows what these are.
We - the gambling and playing public - have the worked out (and available to us all) the best Basic Strategy for Blackjack in all configurations, and best strategy for many poker-based table games, often done by Mike on his WizardofOdds.com site. But we do NOT have the proven best and definitive house way and player way for pai gow poker. I've done this work algebraicly for the Optimized casino house way, as well as for an optimized best player way, and I have kept private this optimized "best player" way that I use; there are actually two: a three-page player's way that's hard to remember, and a one-page easy-to-remember player way.
When I saw the work effort involved just for the Rainbow Logo attached to Mike's www.wizardofodds.com site, I figure something like this might warrant a reasonable effort to obtain this. Mike already links the various house ways that different casinos use on his site; why not include a best house way and a best player's way with a "this is it - it's been research" with it.
For Mike, it has some advantages:
1. No mathematician has done this before, certainly NOT the casino operators themselves - They get their house ways updated by some guy in a raincoat in the Palace Station parking lot once every 6 months, - or so it seems. It would be of great prestige and service to Mike and the industry to have this.
2. The "Player optimized" house way (which I use to slaughter bad house ways) would be of great player advantage service to the playing public, which is something that Mike personally espouses.
3. he would really get noticed by casino operators (hint: lucrative work potential and status among operators); they already know is name, true, but another feather in the cap is a good thing.
Rules for the strategies:
1. Must be One page (12 point, not microfiche), - and in plain English, as it must be playable and deal-able.
2. Mike defines all other criteria, if he wishes to do this. (up to him, he's the boss here.)
just a proposal.
Since we have finalized strategies for all other games, why not end the case with Pai Gow Poker?
How do you define (mathematically) "slaughter"?
Dan, think of it this way: why are you keeping you own best player ways to yourself?
Answer that and you'll understand Mike's reluctance.
Quote: WizardI have no plans to do that. My sites are supposed to be for the benefit of players. After getting the cold shoulder from most casinos in Vegas, I'm in no hurry to do them any favors.
In what way have you been given the cold shoulder?
nothing. They sure have no qualms about screwing
players.
Quote: EvenBobScrew the casinos, they're not called the Dark Side for
nothing. They sure have no qualms about screwing
players.
I'm with Bob on this one...don't give the casinos ANYTHING unless they pay dearly for it. I wouldn't even give away too much information here if I thought that the casino operators could use it to increase/maximize their advantage over the players. They have a house edge; we play against it knowingly. They change the rules against the players to increase their house edge; smart players avoid those games. If they pay the Wizard for something that is a different story but there is no way I would offer them squat for free.
Casinos have the advantage--there is no need to increase it!!
Dan, are you thinking that the HE could really be reduced quite a bit more if a player has a better house way yet to be determined, better than you have used and are keeping private, which the casino might ignore due to practicality?
(2) Should/Could the Paigowdan do a project for the betterment of table games? Why? The reasons may be obvious.
Quote: PaigowdanThis is interesting because this is an area that has not been definitively solved in the casino industry, and it has not yet been done: There can pretty much be one definitive "best" house way, as well as one definitive "best" player way, for Pai Gow Poker. And No one knows what these are.
That's not exactly right. First, some terms. Define H = the set of all possible house ways and S = the set of all possible player strategies. Define s_opt(h) as the optimal player strategy for a given house way h in H. Define EV(s(h)) as the player EV of player strategy s under house way h. Finally, define h_opt as the house way in H where EV(s_opt(h_opt)) <= EV(s(h_opt)) for all s in S other than s_opt. In English, h_opt is the house way which yields the greatest player disadvantage under the player's optimal strategy.
Given all that, there are two important points. First, finding h_opt is not straightforward. There's a chapter in Finding The Edge about how to do it but it's a reasonably complicated search algorithm. The problem is that each h is an array of strategy options for all 154M possible hands and making an adjustment to h (i.e. by changing one of the house plays) does not have an obvious impact on EV(s(h)). You have to calculate it each time and the relation is not monotonic. In other words, you can't just use a greedy search and guarantee you'll find the global optimum.
Second, even if you find h_opt, you may not be able to deal it with human dealers. Asking a dealer to memorize more than a few dozen generic rules is unworkable; asking a dealer to memorize hundreds of exceptional cases is totally unrealistic. The house ways listed by the Wizard on his Pai Gow Poker pages are around two dozen rules/exceptions long. h_opt is likely to be many times larger.
Now, if you mean something other than h_opt when you say "best", there's a discussion to be had there. I implemented the algorithm above when I searched for the optimal house way for my dominoes game Twist'em. It took a really, really long time to run. And you know what? The h_opt it found was totally unworkable for a human dealer, even though it had a strong house edge (>3% under optimal play). As a new game, I decided that dealability was far more important than having a house edge that strong, so I threw out h_opt and simplified. The current house way for Twist'em is a single line long (always play the strongest possible hand in the back) and therefore requires no complicated dealer training. It's much weaker -- the optimal player strategy yields 0.9% house edge in one variation, 1.9% in another -- but that's much more important than not being able to spread the game at all because you can't train the dealers properly.
I don't have a pai gow analyzer right now, but here's an interesting question: what would be the optimal edge (for a non-banking player) under the house way "always make the strongest possible back hand"? What about the house way "always make the strongest possible (legal) front hand?"
In any event, you really need to define what you mean by "best" before going further. You alluded to one page, playable/dealable, so you can't actually mean the mathematically optimal house way h_opt. So what are your other criteria for "best"?
If you give one side a perceived advantage, the other will find ways to neutralize it. Pai Gow Poker becomes a game of differential strengths. I answered Dan's Ultimate House Way thread, since I have retired from gaming as a Player, and am not and have not been a House Employee: I don't intend to be one either.
The best answer I can come up with is Play your way after learning the strengths and weaknesses by reading a little Wong, checking in with the Odds site, and believe it or not check out Wikipedia for a few new ideas... the links too. Printing it here might help the House... it might not. Many people with various strategies is why the House plays to general rulings, when the players wins a bit too much, the house way changes. I've never seen it as more than that. That 5% vig on a winner ain't leaving anytime soon, otherwise PGP is about 1.3% HE by House Way in most establishments. Without the Vig, PGP becomes THE Cat and Mouse game.
JMH pair of Shield pennies.
98Clubs
Quote: odiousgambitI was thinking casinos have to modify the "best" house ways to something the dealers can really handle, something simpler
Dan, are you thinking that the HE could really be reduced quite a bit more if a player has a better house way yet to be determined, better than you have used and are keeping private, which the casino might ignore due to practicality?
Yes, and I use it; it factors in the copy effect on the two-card side. I also have an optimized casino/Banker house way that is super-easy to deal, that was developed for Pai Gow poker when I developed EZ Pai Gow. But most house-ways are "just good enough" - and require no dealer retraining expenses.
Make it easy to make a sale, - and you make a sale.
Quote: 98Clubs
The best answer I can come up with is Play your way after learning the strengths and weaknesses by reading a little Wong,
Yes - Stanford Wong's Optimal strategy for Pai Gow poker, Pee Yee Press.
Quote: 98Clucbs...checking in with the Odds site, and believe it or not check out Wikipedia for a few new ideas... the links too. Printing it here might help the House... it might not.
I disagree - Casino management makes intelligent changes at a galacial pace, though some are trying...
Quote: 98clubsMany people with various strategies is why the House plays to general rulings, when the players wins a bit too much, the house way changes. I've never seen it as more than that. That 5% vig on a winner ain't leaving anytime soon,
It may - EZ Pai Gow is making very serious inroads -
Quote: 98clubs... otherwise PGP is about 1.3% HE by House Way in most establishments. Without the Vig, PGP becomes THE Cat and Mouse game.
JMH pair of Shield pennies.
98Clubs
Quote: MathExtremistThat's not exactly right. First, some terms. Define H = the set of all possible house ways and S = the set of all possible player strategies. Define s_opt(h) as the optimal player strategy for a given house way h in H. Define EV(s(h)) as the player EV of player strategy s under house way h. Finally, define h_opt as the house way in H where EV(s_opt(h_opt)) <= EV(s(h_opt)) for all s in S other than s_opt. In English, h_opt is the house way which yields the greatest player disadvantage under the player's optimal strategy.
Given all that, there are two important points. First, finding h_opt is not straightforward. There's a chapter in Finding The Edge about how to do it but it's a reasonably complicated search algorithm. The problem is that each h is an array of strategy options for all 154M possible hands and making an adjustment to h (i.e. by changing one of the house plays) does not have an obvious impact on EV(s(h)). You have to calculate it each time and the relation is not monotonic. In other words, you can't just use a greedy search and guarantee you'll find the global optimum.
The playing public adopts unwittingly to fully incorporate the house way at the casinos they play at. They learn the house way of the most visited casino the way we learn a language - and a specific dialect even, by exposure. You will NOT see a few dozen different and perfected strategies from the playing public as much as you will simply see bad play.
Quote: MathExtremistSecond, even if you find h_opt, you may not be able to deal it with human dealers. Asking a dealer to memorize more than a few dozen generic rules is unworkable; asking a dealer to memorize hundreds of exceptional cases is totally unrealistic. The house ways listed by the Wizard on his Pai Gow Poker pages are around two dozen rules/exceptions long. h_opt is likely to be many times larger.
Trust us, we know this. The real main ingredient in making a short and clear house way much stronger is to use the best, optimized cut-off points as when to break up a hand - for example, when to split pairs or to keep AQ up; when to use the two-pair rule (- instead of using it 100% of the time if two-pairs are present) or when keep the straight and play the AK up. A Tiny fix - if accurate - can make a huge improvement.
Adding the single and easy-to-deal clause 'Play as straight or flush instead of two pairs if the straight or flush can be played with an AK up" creates an undefeatable improvement to the house way, - and it is easy to deal. The hand AAKKQJ10 is ALWAYS better played as AK/AKQJ10 than as KK/AAQJ10, (63% ev with a straight and AK) versus about 59% playing it as AA/KKxxx - and both are very good. Adding the dealer's or banker's copy advantage on the AK two-card side only makes it even stronger. There is NO strategy play to defeat this hand, as even a player splitting 3322876 for a push in this case leaves him statistically open to be clobbered by more common two pair hands that are split by an opponent, causing a weaker effective strategy when trying to adjust for it.
So does keeping ALL two pairs hands together if an AK can be played on top by the banker or dealer. NO player's variant of play can defeat these improvements; in other words, these simple changes increase the house advantage with NO recourse by the player using ANY modified strategy whatsoever. A LOT can be done, but has not been done, primarily because of casino management inertia.
When you add that it is better for a house dealer (who faces many players) to push 4 hands and win two, than to win 4 hands and lose 2 hands back - for the same net 2 wins - then there is additional income and merit to such a strategy. The Casino house does not make much money winning a hand only to lose it right back, it is better to quickly skip ahead to next next winner without any wasted transactions.
Because the hands that occur in Pai Gow poker are statistically defined, (as all pai gow hands will occur at their established frequencies in 7-card hands), and because there are very limited choices even in multi-path hands (only in two-pair hands and above do you have multiple ways of setting a hand, and that less than one-third of the time), I think a best, easy-to-deal example of such a house way or player way can be produced - and the example at the top of this thread is a very hard to beat example, - for a banker/dealer house way. And it is about two-third of one page - shorter than most house ways.
Quote: MathExtremistI don't have a pai gow analyzer right now, but here's an interesting question: what would be the optimal edge (for a non-banking player) under the house way "always make the strongest possible back hand"? What about the house way "always make the strongest possible (legal) front hand?"
That's a damn good question, and it gives us the good starting point of outlier examples to find the "sweet-zone" optimal middle, which should be the goal here.
And my point is is when we find that optimal middle where any defensive play adjustments are minimized or nullified in their effects (and I think I came pretty close), then we have our optimal strategy. This is where ANY counter-strategy that favors unbalancing - in an attempt to compensate - can become only weaker in facing that optimal strategy point.
The ONLY thing I think that can be done is to:
1. is to see which strategy, given a handful of starting strategies - does best in facing other strategies, with each examined strategy trying it hand as "best dealer/banker" house way against the others in simulated play (5M hands +).
2. Then tweak the best strategy to become an optimal "player's strategy," by reducing the trigger point to split a multi-path by the amount of the copy factor (e.g., If the player's hand AK/QQJJ3 performs worse than JJ/QQAK3 when NOT banking in dealer mode, the JJ/QQAK3 is the optimal player's strategy for that hand; therefore then also try AKQQ 10 10 3, and AKQQ993, AKQQ883, etc.)
3. What CAN be done to reduce computer-run simulation time is to evaluate the strategies algebraicly with Wong's Power Ranking table or M.S.'s Power Ranking tables, or to write a strategy from scratch based on the power ranking tables, and reduce it to one page. My original strategy had two pairs and straights/flushes broken down by Top two-card side, and it looked like this:
Top: Two Pair Split action to take
AK: split no two pairs with AK for the top, except Q’s with 8+’s.
AQ: split King’s with 5’s or better only.
AJ: split K’s with 3’s and better, and Q’s with 6’s and better, keep lower
A-low: split all K’s, Q’s w 4’s+, J’s w 6’s+, 10’s or 9’s w 8’s+, keep lower
KQ: split all two pair jacks and better, 10’s w 3’s+, 9’s w 4’s +, 8’s w/ 6’s (you would actually play 101022KQ3 as KQ/1010223)
KJ: split all two pair 9’s and higher, 8’s w 3’s+, 7’s with 5’s+
K-low: split all two pair 9’s and better, 8’s w 3’s+, 7’s w 4’s+, keep all lower
QJ-: split 7’s with 2’s or better, and 6’s w/ 4’s+, keep all lower two pairs
- along with corresponding tables for straights, flushes, full houses, four-of-a-kind, etc. My Widdle Head hurts!!
But this is too long and complex for a casino house dealer, and to get back to your last definition, Stacy:
Quote: mathExtremistIn any event, you really need to define what you mean by "best" before going further. You alluded to one page, playable/dealable, so you can't actually mean the mathematically optimal house way h_opt. So what are your other criteria for "best"?
1. Final Strategy is One Page, 12-point type, in plain English - so that it is usuable!
2. Performs best when simulated against other best strategies, using either an "everyone-faces-all" evaluation, or a "playoff team" type methodology to say:
"Okay - strategy #7 over here seems to be the best of them all against one another."
2A. You can also use a reasonable "favor five-card side" based strategy and a "favor two-card side" based strategy as the extreme outlier strategies:
- Five card favoring strategy changes outlier #1 :
a) Keep all two pairs together unless they are 10's and less AND you have an AK/AQ for the top.
b) Play two pairs with a flush or straight as a flush/straight, unless the straight or flush has a jack or less top.
c) Keep all full houses together with a King or better for the top.
d) Keep all four of a kinds together.
- Split-Happy strategy - outlier #2:
a) Split all two pairs unless 6's and less with an ace for the top
b) Play ALL straights and flushes with two pairs as two pairs always.
c) Split ALL full houses.
d) split all four of a kinds, unless 6's or less with an ace for the top.
3. then develop an optimal player strategy against the optimal house strategy found.
4. Then run the same group of house way strategies against the best player strategy.
The pai gow (tiles) house way is even worse, with entirely too many exceptions. It also balances entirely too much. Instead of trying to achieve a high-3 in the low, it should strive for a 5, otherwise maximize the high.
It is sad they cling to these antiquated strategies, created before the ability to test them with computers, which can show how bad they really are.
Mike, let me ask you this: since you are adverse to supplying a good casino house way for free, - would you be interested in working on/reviewing an optimized player advantage strategy - as much as could be done?
When you consider that fine-tuning the cut-off points, AND avoiding the dealer's two-side copy-trap can make a big improvement in a Pai Gow Poker player's AP play, would this interest you?
