Difficult Pai Gow math question

This may be a difficult question to answer because of a lot of variables such as house way and player strategy, but here goes.

What are the odds of a five-card pai gow hand beating a seven-card pai gow hand? The five-card hand is split into a two-card hand and a three-card hand which compares against the dealer's five-card hand. The best possible three card hand is three of a kind. Straights and flushes don't count in the three-card hand.

Alternatively, how about a six-card hand, split 4 and 2. Straights and flushes still don't count, but now two pair and quads are possible.

How much odds would a win have to pay to be a reasonably fair game?

Quote: Deucekies

This may be a difficult question to answer because of a lot of variables such as house way and player strategy, but here goes.

What are the odds of a five-card pai gow hand beating a seven-card pai gow hand? The five-card hand is split into a two-card hand and a three-card hand which compares against the dealer's five-card hand. The best possible three card hand is three of a kind. Straights and flushes don't count in the three-card hand.

Alternatively, how about a six-card hand, split 4 and 2. Straights and flushes still don't count, but now two pair and quads are possible.

How much odds would a win have to pay to be a reasonably fair game?

You might find the beginnings of the contrast between the two here. This page is so useful to me I have it bookmarked. lol...

Quote: Deucekies

This may be a difficult question to answer because of a lot of variables such as house way and player strategy, but here goes.

What are the odds of a five-card pai gow hand beating a seven-card pai gow hand? The five-card hand is split into a two-card hand and a three-card hand which compares against the dealer's five-card hand. The best possible three card hand is three of a kind. Straights and flushes don't count in the three-card hand.

Alternatively, how about a six-card hand, split 4 and 2. Straights and flushes still don't count, but now two pair and quads are possible.

How much odds would a win have to pay to be a reasonably fair game?

how can you compare oranges and apples?
at least you have to define which one ranks higher? a 3 card 3-of-a-kind or 5 card straight.

Quote: andysif

how can you compare oranges and apples?
at least you have to define which one ranks higher? a 3 card 3-of-a-kind or 5 card straight.

All hands are compared apples to apples. A 3 card 3-of-a-kind is just as good as a 5 card 3-of-a-kind. A 3 card 7-7-7 still loses to a 5 card 8-8-8-4-2. This is why winning bets would be paid odds, not even money.

Quote: Deucekies

All hands are compared apples to apples. A 3 card 3-of-a-kind is just as good as a 5 card 3-of-a-kind. A 3 card 7-7-7 still loses to a 5 card 8-8-8-4-2. This is why winning bets would be paid odds, not even money.

it's not apples to apples. A 3 card 3-of-a-kind is NOT the same as a 5 card 3-of-a-kind
According to this
https://wizardofodds.com/games/poker/
the probability of a 5 card 3-of-a-kind (which you would use to make your 3 card 3-of-a-kind) is 0.02112845
the probability of a 7 card 3-of-a-kind (which you would use to make your 5 card 3-of-a-kind) is 0.04829870

A 3 card 7-7-7 loses to a 5 card 8-8-8-4-2 would be unfair.

that is why he is stating it as if it was a handicap. if you really want 7 cards vs 7 cards, reread it this way. you have a 7 card hand with 2 "dead cards" (can not be used to make hands, and is the lowest possible kicker) that must go into your 5 card hand. what is the odds that it beats the 7 card hand with no dead cards.

Quote: andysif

it's not apples to apples. A 3 card 3-of-a-kind is NOT the same as a 5 card 3-of-a-kind
According to this
https://wizardofodds.com/games/poker/
the probability of a 5 card 3-of-a-kind (which you would use to make your 3 card 3-of-a-kind) is 0.02112845
the probability of a 7 card 3-of-a-kind (which you would use to make your 5 card 3-of-a-kind) is 0.04829870

A 3 card 7-7-7 loses to a 5 card 8-8-8-4-2 would be unfair.

Doesn't matter, if he says the rules are X, then the rules are X. Once the rules are known, you can do the math. (Not for free, the OP should expect to pay for the analysis.) But there are lots of different ranking schemes for card games and many of them involve paying more money for more frequent (rather than less frequent) awards due to historical or other game design considerations. It's not unfair if the same rules apply to everyone, even if they're not traditional. E.g., in Bonus Video Poker, quad 4s pays more than quad 5s, but in normal poker the latter outranks the former.

It's an interesting idea to give players less cards but this allows for payouts better than evens. There are a few games that give the dealer more cards ( https://wizardofodds.com/games/four-card-poker/ ). If you've stumbled across other threads on getting games certified, these poker-like games are very hard to analyse, and hence expensive to have the maths done on them.

If you're thinking of such a game with a significant number of cards involved, one thing going for you is there seem to be no decision points, thus it may be easier for you to develop a program to go through all the combinations.

Personally I have never looked at poker-like ideas when thinking of games because of the complexity the calculations. As has been said you may be to find someone to do this, but this will cost. Another alternative might be to look to a large distributor, who have the expertise to do the maths, on a profit sharing deal.

Quote: GamerMan

that is why he is stating it as if it was a handicap. if you really want 7 cards vs 7 cards, reread it this way. you have a 7 card hand with 2 "dead cards" (can not be used to make hands, and is the lowest possible kicker) that must go into your 5 card hand. what is the odds that it beats the 7 card hand with no dead cards.

Thanks. This is what I was going for.