3 Card Poker

In 3 Card Poker, I know that Q/6/4 is the mathematically optimal strategy, but what affect might there be on the house edge if you get to see other players hands?

For example, if you can see that multiple players have a queen in their hand then it surely reduces the chance that the dealer will have one when making the decision about a marginal play of your own?

Thanks in advance!

Quote: mtjyoung

In 3 Card Poker, I know that Q/6/4 is the mathematically optimal strategy, but what affect might there be on the house edge if you get to see other players hands?

For example, if you can see that multiple players have a queen in their hand then it surely reduces the chance that the dealer will have one when making the decision about a marginal play of your own?

Thanks in advance!

There is some info you can use. A simple example. You see 12 cards of other players and they are all the 2's, 3's and 4's in the deck. Would you play with a Q 6 5? Of course not!

Your question is not specific enough. Did the other players have zero kings or aces? How many cards in total did you see? Etc.....

And welcome to the forum! I'm not expert, but there is a search function that will likely help you find this topic previously discussed here.

If you can see one other card and it's a Queen then you play Q43 and some Q42 (depending on suits). I'm not sure what happens if (say) you can see 9 cards and a few Queens.

The key issue on marginal hands is what the probabilities are that the Dealer will Qualify or Not Qualify.

Seeing Aces, Kings and Queens are all important because the presence of those cards in other player hands makes it more likely that the dealer will not qualify. Obviously, the absence of those cards in other player hands means that "all the low cards are out" and the dealer is more likely to have a qualifying hand.

According to some calculations I did about 10 years ago, here are the minimum 3CP hands that you can bet (as I remember them), as a function of the number of high cards that you see in two other player hands (6 cards total seen.)

Definition: Low Cards = 2-J; High Cards = Q - A

You see: NO Q,K,A (6 low cards)_____Q75
You see: A or K + 5 low cards_____Q53
You see: Q + 5 low cards_____Q63
You see: Any 2 High cards (Q,K, or A) + 4 low cards_____ Q32
You see: 3,4,5 or 6 high cards______532 (Bet all hands)

So, if you see exactly one Ace or King in 6 cards, you can bet an A53 or higher. If you see 3 or more high cards in the 6 cards (which would be rare), then you should never fold because the dealers probability of Not Qualifying are greater than 33.333% and thus a Bet on any hand will have a higher EV than folding.

As I remember, I think the incremental reduction you can achieve in House Edge by seeing 2 hands (6 cards) and using the strategy above is less than 0.2%. Since the House Edge in 3CP is 3.3% or higher, lowering the house edge by 0.2% is not a big deal.

I am told (by others) that even if you had perfect knowledge of every card in every players' hand at a 6 player table and you used that knowledge to play computer-perfect strategy, you cannot come close to overcoming the 3.3% house edge of 3CP. So, collusion is not a threat to 3CP.

Quote: gordonm888

I am told (by others) that even if you had perfect knowledge of every card in every players' hand at a 6 player table and you used that knowledge to play computer-perfect strategy, you cannot come close to overcoming the 3.3% house edge of 3CP. So, collusion is not a threat to 3CP.

going on memory here, but I did this analysis a few years ago myself, I believe perfect knowledge and perfect play gives a house edge of 2.7%. awaiting correction if my memory is faulty.

deleted

Quote: charliepatrick

If you can see one other card and it's a Queen then you play Q43 and some Q42 (depending on suits). I'm not sure what happens if (say) you can see 9 cards and a few Queens.

If you see one dealer Q, raise if you have Q92 and above !

Quote: teliot

going on memory here, but I did this analysis a few years ago myself, I believe perfect knowledge and perfect play gives a house edge of 2.7%. awaiting correction if my memory is faulty.

If you had knowledge of 18 cards(6 players), you can reduce house edge to -2.63%.

Quote: ssho88

If you see one Q, raise if you have Q92 and above !

he means a queen in a player hand not a dealer hole card.

Quote: teliot

he means a queen in a player hand not a dealer hole card.

oops, my bad.

Q + 5 low cards(player at your left and right, not included your own cards), raise if Q63 or higher.

You can beat the game(1/4/6/30/40) if you had knowledge of 36 cards and adjust your strategy accordingly ! LOL

Quote: gordonm888

The key issue on marginal hands is what the probabilities are that the Dealer will Qualify or Not Qualify.

Seeing Aces, Kings and Queens are all important because the presence of those cards in other player hands makes it more likely that the dealer will not qualify. Obviously, the absence of those cards in other player hands means that "all the low cards are out" and the dealer is more likely to have a qualifying hand.

According to some calculations I did about 10 years ago, here are the minimum 3CP hands that you can bet (as I remember them), as a function of the number of high cards that you see in two other player hands (6 cards total seen.)

Definition: Low Cards = 2-J; High Cards = Q - A

You see: NO Q,K,A (6 low cards)_____Q75
You see: A or K + 5 low cards_____Q53
You see: Q + 5 low cards_____Q63
You see: Any 2 High cards (Q,K, or A) + 4 low cards_____ Q32
You see: 3,4,5 or 6 high cards______532 (Bet all hands)

So, if you see exactly one Ace or King in 6 cards, you can bet an A53 or higher. If you see 3 or more high cards in the 6 cards (which would be rare), then you should never fold because the dealers probability of Not Qualifying are greater than 33.333% and thus a Bet on any hand will have a higher EV than folding.

As I remember, I think the incremental reduction you can achieve in House Edge by seeing 2 hands (6 cards) and using the strategy above is less than 0.2%. Since the House Edge in 3CP is 3.3% or higher, lowering the house edge by 0.2% is not a big deal.

I am told (by others) that even if you had perfect knowledge of every card in every players' hand at a 6 player table and you used that knowledge to play computer-perfect strategy, you cannot come close to overcoming the 3.3% house edge of 3CP. So, collusion is not a threat to 3CP.

1)RANDOMLY Remove a Q and 5 low cards(2 - J) from the deck, dealt 3 cards each to PLAYER and DEALER from the remaining deck and record the outcome

2) Return all cards and repeat 1) for 1 billions rounds

3) The EV for each scenarios(1 billion rounds simulation each) below :-


a) Raise when >= Q62, EV=-2.743%
b) Raise when >= Q63, EV=-2.730%
c) Raise when >= Q64, EV=-2.719%
d) Raise when >= Q65, EV=-2.709%
e) Raise when >= Q72, EV=-2.701%
f) Raise when >= Q73, EV=-2.693%
g) Raise when >= Q74, EV=-2.688%
h) Raise when >= Q75, EV=-2.684%
i) Raise when >= Q76, EV=-2.688%
j) Raise when >= Q82, EV=-2.688%
k) Raise when >= Q83, EV=-2.689%
l) Raise when >= Q84, EV=-2.691%
m) Raise when >= Q85, EV=-2.695%
n) Raise when >= Q86, EV=-2.701%


So the simulations shown that, if your left and right player holding a Q + 5 low cards, the optimum strategy is raise when >= Q75.

Am I missing something ?