Optimal Strategy for Pai Gow Poker

aka23

Dormant account
I am working on an optimal strategy calculator for Pai Gow. It decides on how to split cards by adding up EVs for all the valid splits and selecting the highest one. My working test version is at
.

The calc is showing slight differences in a few situations from the most commonly recommended strategy. An example is 4 of a Kind. The standard B&M strategy for 4 of a kind is:

2 through 6: Always keep together.
7 through 10: Split unless a king or better can be played in front.
Jack through king: Split unless an ace can be played in front.
Aces: Always split.

My calc suggests:
2 through 5: Play the four of a kind
6 through 9: Split into two pairs unless 2-card hand contains a king or better
10 through Queen: Split into two pairs unless 2-card hand contains an ace
King: Split into two pairs unless 2-card hand contains ace, then split KKK / AK
Ace: Split into two pairs

I believe my math is correct, so I am uncertain about the reasons for the slight difference. It does not relate to optimizing for player vs banker, as I have checked. It might related to recommended strategy optimizing for KJ or AJ + 4 of a kind, rather than K9 or A9. I suppose, you'd want to optimize for A10 or K10, given that there are 2 cards left, which is right on the borderline between the two strategies listed above. It might also relate to optimizing for different dealer play strategies.

Does anyone know of optimal strategy tables for Pai Gow that were determined via computer simulation, rather than following dealer statagies? This would be helpful for verifying results.

bridgehajen

Dormant account
Does anyone know of optimal strategy tables for Pai Gow that were determined via computer simulation, rather than following dealer statagies? This would be helpful for verifying results.
I'm quite certain the The Wizard Of Odds uses computer simulations. His conclusions on Pai Gow poker seem similar to yours as far as I can tell by a quick glance:

As far as I understand, it's impractical to describe the perfect strategy for splitting in Pai Gow poker, because of the vast number of hands; any practical strategy would have to cut a few corners. My guess is that if your strategy differs slightly from that of thw Wizard, it's because you choose to cut different corners.

aka23

Dormant account
I'm quite certain the The Wizard Of Odds uses computer simulations. His conclusions on Pai Gow poker seem similar to yours as far as I can tell by a quick glance:

The page you linked to talks about optimal strategy for splitting two pairs. I don't see an optimal strategy for general play based on computer simulations. Instead, the strategy used by dealers at a good number of land-based casinos is listed.

As far as I understand, it's impractical to describe the perfect strategy for splitting in Pai Gow poker, because of the vast number of hands; any practical strategy would have to cut a few corners. My guess is that if your strategy differs slightly from that of thw Wizard, it's because you choose to cut different corners.
It's sort of like Video Poker strategy tables. You can print more and more complex tables and get very close to optimal strategy, but at a certain point the complexity is not worth the benefit. This is especially true with live Pai Gow in B&M casinos where you cannot look at a cheat sheet. The rules list above was such a simplified summary. For example, I could have said "10/10/10/10 -- Split unless rest of hand is KJ or higher, rather than just rounding to A. However my calc is not a simplified summary according to programmed rules that cuts corners (in a typical way). It adds up EVs to select decisions, rather than using a rules list.

spearmaster

RIP Ted
I think if you look at the Wizard's site, you will see that there really is no standard for house way. Different casinos follow different rules.

In any case, the optimal strategies for 4oak - especially Aces - must necessarily differ based on the remainder of your hand.

If your hand was 4 aces plus a pair of kings and one other card, why in the world would you split your aces? For that matter, any pair of 10s or higher, it seems pretty damn silly to split your aces. Yeah, you might increase your chances of losing the front since house wins ties, but a pair of aces in back is far from safe. Or two pair if you split the aces, then put two pair in back - might be reasonable under some circumstances but not with 10s or higher as the pair.

aka23

Dormant account
I think if you look at the Wizard's site, you will see that there really is no standard for house way. Different casinos follow different rules.
That is true. However, if you look at the list on Wizard of Odds, you will find that there are some situations where the majority of the listed strategies are the same. For 4 of a kind, there seem to be two common sets of rules.

In any case, the optimal strategies for 4oak - especially Aces - must necessarily differ based on the remainder of your hand.

If your hand was 4 aces plus a pair of kings and one other card, why in the world would you split your aces? For that matter, any pair of 10s or higher, it seems pretty damn silly to split your aces. Yeah, you might increase your chances of losing the front since house wins ties, but a pair of aces in back is far from safe. Or two pair if you split the aces, then put two pair in back - might be reasonable under some circumstances but not with 10s or higher as the pair.
My calc suggests in the case of 4 Aces + a pair, you'd split the aces with a pair of 3s or less, and keep the 4 aces with a pair of 4s or greater. I did not include 4 of a kind + pair in the results summary above to reduce complexity and to be consistent with the format of the Trump Plaza house way rules above it. It is likely not included in various other rule summaries for similar reasons.

To confirm calc results, I'm look for a strategy table (generated via computer sim), calc, or similar with this level of complexity... one that goes into which pairs with the 4 of a kinds. I believe Stanford Wong wrote a book that covers such topics, but I don't care about this enough to buy it.

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spearmaster

RIP Ted
Even were you to combine some of the information which will be similar across all house ways, there are enough variants which would make a single optimal strategy way too complex. Of course, if we're talking about a version for use in online Pai Gow Poker, it might not be quite so bad.

aka23

Dormant account
Even were you to combine some of the information which will be similar across all house ways, there are enough variants which would make a single optimal strategy way too complex. Of course, if we're talking about a version for use in online Pai Gow Poker, it might not be quite so bad.
Yes, there would be slight differences in the close calls depending on house way used by the dealer. You'd have to optimize for different sets of house ways, sort of like slight differences in blackjack strategy depending on rules used by the dealer (hit/stand soft 17, peak for bj, etc.). This is a practical goal for online use, as the house way should be the same across a particular software, likely across multiple SWs. This difference in house ways may explain the slight differences in strategy mentioned in my first post.

Having said that, when playing without a house way button, you need some kind of default strategy to use. I expect that the calc would produce a significantly lower house edge than a generic strategy table due to covering complex situations that may be simplified in the table, like the 4Aces + pair situation discussed above.

KasinoKing

WebMeister & Slotaholic..
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PABnonaccred
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Having said that, when playing without a house way button, you need some kind of default strategy to use. I expect that the calc would produce a significantly lower house edge than a generic strategy table due to covering complex situations that may be simplified in the table, like the 4Aces + pair situation discussed above.
PaiGow is one of my favorite games, and I like it best at Crypto casinos precisely because there is NO house-way button!
This lazy tool takes all the fun out of playing the game for me.
I guess some Video Poker players would say the same about auto-hold!

A 'perfect strategy' for PaiGow would be very difficult to create & very tedious to follow due to the numerous complex choices with some of the hands you get. This is why I like it so much; when I split a way which I know isn't best strategy, but then win a hand I would have otherwise lost or drawn.

I think you can over-analyse these things - just playing what you feel is best at the time is much more fun!
KK

aka23

Dormant account
I think you can over-analyse these things - just playing what you feel is best at the time is much more fun!
KK
My ex-girlfriend (the one mentioned in my journal on this site) had a similar philosophy for blackjack play. She played according to what felt like the best decision, which usually minimized the impact of the dealer upcard. For example, she'd be shocked to see me stand on 12 vs 6 because 12 is a low sum; or hit on 16 vs 7 because 16 is a high sum. It's a different style of play for different goals.

With strategy games like BJ Switch, Pai Gow, and Video Poker I play most hands without a strategy/switch table. But every now and then, I'll be unsure about a hand and like to have an optimal strategy table/calc to fall back on.

spearmaster

RIP Ted
As a matter of course, when I play online, I always click the house way button if it does not automatically set the cards and play the hand. If I don't agree with the house way, I set the cards myself.

Unfortunately, with some online software programs, clicking house way ends the decision-making process and the result is calculated. In these situations I fully agree that clicking the house way button is not good.

As for an optimal strategy, again it depends a lot on what you are trying to achieve. For some people, they want to take the most aggressive route; for others, the safest route, particularly in situations where one is trying to achieve playthrough requirements.

Me, I generally play the aggressive route, with only a few exceptions. But then again I've been playing since the game was invented, so it comes pretty naturally to me. And more often than not I disagree with the house way.

Scooter7

Meister Member
As for an optimal strategy, again it depends a lot on what you are trying to achieve. For some people, they want to take the most aggressive route; for others, the safest route, particularly in situations where one is trying to achieve playthrough requirements.

And more often than not I disagree with the house way.

The house way being offered to the players as a convenience is a reasonable customer service effort, but one should always remember that the house way is not the optimum strategy to have the best chance to beat hand 'x'. It is the best strategy for the house to maximize its chance to win against hands x, y, z, etc.

Your goal in setting the hand is different from the house's goal.

spearmaster

RIP Ted
The house way being offered to the players as a convenience is a reasonable customer service effort, but one should always remember that the house way is not the optimum strategy to have the best chance to beat hand 'x'. It is the best strategy for the house to maximize its chance to win against hands x, y, z, etc.
The house cannot know the composition of hands beforehand, so it too must use a strategy. House way does not always mean maximizing win - it can also mean minimizing loss.

Keep in mind that the house is NOT there to gamble - it is there to benefit from a house edge.

Your goal in setting the hand is different from the house's goal.
Maybe. I play to gamble - and this is almost always when I differ with the house way. If I wanted to play safe all the time, house way usually agrees.

lojo

Banned User - repetitive violations of <a href="ht
The house way being offered to the players as a convenience is a reasonable customer service effort, but one should always remember that the house way is not the optimum strategy to have the best chance to beat hand 'x'. It is the best strategy for the house to maximize its chance to win against hands x, y, z, etc.

Your goal in setting the hand is different from the house's goal.
Couldn't Microgaming say the same with the VP 10 question? Oh yeah, I forgot, they don't say anything.