3 Card Poker with Multiple Decks
tuttigym
As the (blocked) link you included says, all poker rules are based on the math for 1 deck.
Flush pairs and trips become possible in 4 deck games.
I'm certainly not a math expert, and I haven't run the numbers. I would expect that the standard rules and payouts would not be offered on a 4 deck variant, and any 4 deck variant would have a house edge that is significantly less beneficial to the player.
Sorry, I can't trivially calculate the 3CP House Edge for multiple decks.
Quote: raistaceHi! I was wondering if any mathematicians can help me with the following question: if you deal 3 card poker with standard rules and payouts but using 4 decks instead of 1, do the odds change (possibly in favor of the player?) I was reading this article about standard poker with two decks: /poker-basics/can-poker-be-played-with-2-decks/ and it does show that the odds change due to the number of outs for certain hands. I was thinking that since certain hands pay bonuses for the ante bet and pair plus, it could affect the odds overall, but wasn't sure.
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Welcome to the forum. And ignore tuttigym’s rude response. With multiple decks there will be more of the big hands like 3 of a kind, which helps the player.
I do not have the math skills to answer your question, but even if someone does, it is more of a ‘project’ than just a simple answer. If you tell the forum why you are interested someone may decide to help.
I am going to take a guess and predict a player edge of about 4% with 3 decks.
Yes 5/4/1.Quote: raistaceSuper interesting, and I really appreciate it. Is this for the standard 5/4/1 ante payout bonuses? It seems like it's then slightly worse for the player (and probably will be worse the more decks you add).
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I don't understand how going from a house edge to a player edge could be worse for the player. Maybe you don't fully understand the terminology.
The 4 deck game will provide the player an increment of 0.02255 in EV as compared to the 1 deck games.
The 4 deck game will have an extra return of 0.0245 due to Ante Bonus payouts on the Trips; however the straight and straight flushes are slightly less frequent in the 4 deck game, resulting in an EV impact of - 0.00197. The net advantage to the player from the Ante Bonus Table is thus 0.0245-0.00197 = 0.02255.
The other impact will be that the dealer does not qualify(DNQ) with a frequency of 0.3041 in the 1-deck game compared to DNQ with a frequency of 0.2909 in the 4 deck game. Calculation of the change in player EV due to this effect involves several subtleties so I won't try to estimate it. We'll just wait on T. Eliot for the answers from his looping code.
I guess the explanation is that the house gets the better hands just as often as the player, so the change in edge is due to frequency of bonus hands in the 1/4/5 pay schedule. You will get more trips, that's clear.
I was obviously way wrong about a 4% player edge. The days of my having good intuition appear to be long gone.
Quote: DieterYes, the odds change.
As the (blocked) link you included says, all poker rules are based on the math for 1 deck.
Flush pairs and trips become possible in 4 deck games.
I'm certainly not a math expert, and I haven't run the numbers. I would expect that the standard rules and payouts would not be offered on a 4 deck variant, and any 4 deck variant would have a house edge that is significantly less beneficial to the player.
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I wish to clarify the text I have emboldened:
If you find 4 deck 3 card poker in a casino, assume they have adjusted the payouts. Harshly.
As it stands, that you are dealing 4 deck 3 card with standard payouts, I await an invitation. I generally dislike house banked poker and don't even know how to play, but this has inspired me to try it out.
Quote: teliotI get a 2.192% house edge, with a basic strategy of Q43 or higher (not 100% sure about basic strategy here).
I guess the explanation is that the house gets the better hands just as often as the player, so the change in edge is due to frequency of bonus hands in the 1/4/5 pay schedule. You will get more trips, that's clear.
I was obviously way wrong about a 4% player edge. The days of my having good intuition appear to be long gone.
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Thanks for this analysis, super helpful. Sounds like 4 deck would likely still be house edge although it’d be close. Really appreciate it!
Quote: raistaceHi! I was wondering if any mathematicians can help me with the following question: if you deal 3 card poker with standard rules and payouts but using 4 decks instead of 1, do the odds change (possibly in favor of the player?) I was reading this article about standard poker with two decks: /poker-basics/can-poker-be-played-with-2-decks/ and it does show that the odds change due to the number of outs for certain hands. I was thinking that since certain hands pay bonuses for the ante bet and pair plus, it could affect the odds overall, but wasn't sure.
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I'm more interested in whether the cards are shuffled after each round?
Quote: ssho88
I'm more interested in whether the cards are shuffled after each round?
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Yes the cards are shuffled after each deck.
a) 4 Deck(Raise when Q74 or higher), house edge = -2.028180%
b) 3 Deck(Raise when Q74 or higher), house edge = -2.192176%
The proposed basic strategy is quite different, maybe I'm wrong, any comments or corrections would be much appreciated.
BTW, 4 deck game took about 15 minutes to run a strategy.
The problem with my program is that the hashing to store the score of every hand required more memory than I could allocate, and I didn't feel like figuring out the ulimit command on Cygwin. Hence the long time to run my program. But yes, your time would be about the same as my time in a better world.Quote: ssho88The following 3CP house edge are based on combination analysis (assuming the top 3 hands are remain unchanged, i.e Straight Flush, Three of a kind and Straight with ante bonus 5/4/1 respectively).
a) 4 Deck(Raise when Q74 or higher), house edge = -2.028180%
b) 3 Deck Raise when Q74 or higher), house edge = -2.192176%
The proposed basic strategy is quite different, maybe I'm wrong, any comments or corrections would be much appreciated.
BTW, 4 deck game took about 15 minutes to run a strategy.
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Glad we agreed on the h/a for 3 decks.
Quote: teliotThe problem with my program is that the hashing to store the score of every hand required more memory than I could allocate, and I didn't feel like figuring out the ulimit command on Cygwin. Hence the long time to run my program. But yes, your time would be about the same as my time in a better world.Quote: ssho88The following 3CP house edge are based on combination analysis (assuming the top 3 hands are remain unchanged, i.e Straight Flush, Three of a kind and Straight with ante bonus 5/4/1 respectively).
a) 4 Deck(Raise when Q74 or higher), house edge = -2.028180%
b) 3 Deck Raise when Q74 or higher), house edge = -2.192176%
The proposed basic strategy is quite different, maybe I'm wrong, any comments or corrections would be much appreciated.
BTW, 4 deck game took about 15 minutes to run a strategy.
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Glad we agreed on the h/a for 3 decks.
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Thank you both for answering this! This was great (and great to see the analyses aligned). I really appreciate it. Completely unnecessary, but mostly out of curiosity, is it easy to calculate the house advantage for the Pair Plus? I would imagine that it changes even more than the standard Ante because you're not dealing with the dealer equally getting better hands, you're just taking advantage of that fact.
