gordonm888
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gordonm888
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April 27th, 2022 at 3:45:46 PM permalink
Redgarding the 5-4-1 Ante Bonus Table:

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.
Last edited by: gordonm888 on Apr 27, 2022
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
teliot
teliot
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April 27th, 2022 at 3:49:57 PM permalink
I 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.
Last edited by: teliot on Apr 27, 2022
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Dieter
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Dieter
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April 27th, 2022 at 5:29:41 PM permalink
Quote: Dieter

Yes, 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.
link to original post



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.

I generally pay about $3 for a new deck of cards. I think you'll recoup the investment in 1 night. Don't deal poker out of a shoe.
May the cards fall in your favor.
raistace
raistace
Joined: Apr 27, 2022
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April 27th, 2022 at 6:21:08 PM permalink
Quote: teliot

I 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.
link to original post



Thanks for this analysis, super helpful. Sounds like 4 deck would likely still be house edge although itd be close. Really appreciate it!
ssho88
ssho88
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April 27th, 2022 at 8:28:30 PM permalink
Quote: raistace

Hi! 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?
raistace
raistace
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April 28th, 2022 at 6:21:11 AM permalink
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.
ssho88
ssho88
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Thanks for this post from:
teliotraistace
April 28th, 2022 at 6:54:14 AM permalink
The 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.

Last edited by: ssho88 on Apr 28, 2022
teliot
teliot
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April 28th, 2022 at 7:00:56 AM permalink
Quote: ssho88

The 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.
link to original post

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.

Glad we agreed on the h/a for 3 decks.
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raistace
raistace
Joined: Apr 27, 2022
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April 28th, 2022 at 11:23:27 AM permalink
Quote: teliot

Quote: ssho88

The 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.
link to original post

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.

Glad we agreed on the h/a for 3 decks.
link to original post



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.

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