three card poker math problem> do i have the edge???!!!
May 16th, 2011 at 9:49:52 AM
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Hi, The game is three card poker. I know a casino where you can play one on one with the dealer in my mind i cannot help but think that i am infact the favourite over an extended peroid of time...these are the facts regarding the table
-dealer must have q-8 to qualify
-high card pays! 1-1 flush 1-1 straight 4-1 three of a kind 30-1 and im not worried about the rest
-cards are shuffled by hand no machines in operation...
my thoughts are if i play one on one only ante/bet every hand no matter what it is i have the edge over an extended period of time ...would this be correct??? can someone give me some mathematical feedback on this so i can go and destroy this casino :p thanks
-dealer must have q-8 to qualify
-high card pays! 1-1 flush 1-1 straight 4-1 three of a kind 30-1 and im not worried about the rest
-cards are shuffled by hand no machines in operation...
my thoughts are if i play one on one only ante/bet every hand no matter what it is i have the edge over an extended period of time ...would this be correct??? can someone give me some mathematical feedback on this so i can go and destroy this casino :p thanks
June 16th, 2011 at 9:05:38 AM
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No you do not have an edge
June 16th, 2011 at 1:40:21 PM
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lol, very funny post..
Yeah go ahead and destroy them. That's why any casino offers the game, right?
Yeah go ahead and destroy them. That's why any casino offers the game, right?
June 21st, 2011 at 7:10:56 PM
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Firstly with 3-card poker there's two types of bets. However I've generalized the answer as the same logic applies to any similar game, assuming it's a fair game with proper shuffling and no ability to peek at the dealer's cards.
(i) The sucker bets are where you bet on what your hand will be without regard to the whether the dealer beats you or not. Almost by definition these have a built-in house advantage, since there is no skill, you either get a good hand or don't.
(ii) The play bet is slightly different. In most similar games there's an Ante and a subsequent choice whether to add more money (Raise) or give in. If the dealer doesn't qualify the Ante (or in some games Raise) pays. If the dealer does qualify then the better hand wins.
You usually have two choices, whether to raise all hands or only hands that exceed a cutoff. In the former you win (+1 instead of -1) if both you and the dealer have a bad hand, but lose out (-2/-3 instead of -1) if you have a bad hand and the dealer qualifies. The qualifying rules usually make it better to fold very bad hands (i.e. in 3-card >66.67% chance of qualifying, in 5-card >50% chance of qualifying).
Assuming you decide to fold very bad hands, similar logic to blackjack applies
(i) if you both qualify it's evens who has the best hand
(ii) if one has a bad hand and the other a good one, it's evens whether you had the bad hand and lost or good hand and won
(iii) if both have a bad hand - the dealer wins; it is this bit that gives the house an edge.
Without adding bonuses, the house edge would be approximately P(bad hand) squared.
In blackjack the "bonus" is seeing the dealer's card, doubling, BJ paying 3-2 etc.
In poker the "bonus" is (a) being paid more than evens for good hands (b) being able to fold marginal hands (c.f. Q64 not Q32), the threshold for the player is usually higher than that of the dealer (AK432, Q32) (c) seeing one of the dealer's cards (in 5-card).
If you found a table that
(a) played excessive hands (e.g. in 5-card dealer only needing K-high) then this means your good hands would be paid out too often
(b) played too few hands (e.g. in 5-card needing a pair) then this means you might as well play every hand regardless.
either of these might eventually give the player an advantage.
As in 3-card the bonuses are paid regardless, it makes no difference whether the dealer plays Q32, Q64 or Q82. The disadvantage is being paid less often (i.e. only Ante not the Raise) for hands that exceed Q82. The advantage is that since the chance of the dealer qualifying is less than 2/3, you probably play everything.
Quickly it looks as if
(i) what you're gaining is -1 (would have folded) is now (by playing blind, say) -.96344 for (J73) for all bad hands (i.e. about 1%)
(ii) what you're losing is +1 (Ante paid) for about 4% of the time (i.e. dealer has Q32 to Q76 and doesn't qualify) where you have a good hand (2/3 time).
So I think you lose more than you gain.
Academically (on 3-card without bonuses) if the dealer only qualified 50% of the time (e.g. K65), it would be (nearly) a no house-edge game (1/2 time you win 1 when dealer had bad hand, 1/4 time you lose 2 when you have bad hand and dealer qualifies, 1/4 time it's evens who has a good hand.)
Another thing to check is that the bonuses are at least 1-1, 4-1 and 5-1.
(i) The sucker bets are where you bet on what your hand will be without regard to the whether the dealer beats you or not. Almost by definition these have a built-in house advantage, since there is no skill, you either get a good hand or don't.
(ii) The play bet is slightly different. In most similar games there's an Ante and a subsequent choice whether to add more money (Raise) or give in. If the dealer doesn't qualify the Ante (or in some games Raise) pays. If the dealer does qualify then the better hand wins.
You usually have two choices, whether to raise all hands or only hands that exceed a cutoff. In the former you win (+1 instead of -1) if both you and the dealer have a bad hand, but lose out (-2/-3 instead of -1) if you have a bad hand and the dealer qualifies. The qualifying rules usually make it better to fold very bad hands (i.e. in 3-card >66.67% chance of qualifying, in 5-card >50% chance of qualifying).
Assuming you decide to fold very bad hands, similar logic to blackjack applies
(i) if you both qualify it's evens who has the best hand
(ii) if one has a bad hand and the other a good one, it's evens whether you had the bad hand and lost or good hand and won
(iii) if both have a bad hand - the dealer wins; it is this bit that gives the house an edge.
Without adding bonuses, the house edge would be approximately P(bad hand) squared.
In blackjack the "bonus" is seeing the dealer's card, doubling, BJ paying 3-2 etc.
In poker the "bonus" is (a) being paid more than evens for good hands (b) being able to fold marginal hands (c.f. Q64 not Q32), the threshold for the player is usually higher than that of the dealer (AK432, Q32) (c) seeing one of the dealer's cards (in 5-card).
If you found a table that
(a) played excessive hands (e.g. in 5-card dealer only needing K-high) then this means your good hands would be paid out too often
(b) played too few hands (e.g. in 5-card needing a pair) then this means you might as well play every hand regardless.
either of these might eventually give the player an advantage.
As in 3-card the bonuses are paid regardless, it makes no difference whether the dealer plays Q32, Q64 or Q82. The disadvantage is being paid less often (i.e. only Ante not the Raise) for hands that exceed Q82. The advantage is that since the chance of the dealer qualifying is less than 2/3, you probably play everything.
Quickly it looks as if
(i) what you're gaining is -1 (would have folded) is now (by playing blind, say) -.96344 for (J73) for all bad hands (i.e. about 1%)
(ii) what you're losing is +1 (Ante paid) for about 4% of the time (i.e. dealer has Q32 to Q76 and doesn't qualify) where you have a good hand (2/3 time).
So I think you lose more than you gain.
Academically (on 3-card without bonuses) if the dealer only qualified 50% of the time (e.g. K65), it would be (nearly) a no house-edge game (1/2 time you win 1 when dealer had bad hand, 1/4 time you lose 2 when you have bad hand and dealer qualifies, 1/4 time it's evens who has a good hand.)
Another thing to check is that the bonuses are at least 1-1, 4-1 and 5-1.
