poker question?

Question

Suppose that i want to compute the probabilities of winning at poker.
I compute, for example, the probability of winning one pair and then for two pairs.
I can see that winning one pair is more probable. But this is not the real probability of winning since, even if is less probable, you have a better chance to win with two pairs.
Question is : how i compute the real probability?

My original question was like this. Suppose i play hold'em poker and the last card (the fifth) should be discarded.
I have already a pair. I computed the probability that last card to give me 2 pairs( 2/46) and to give me 3 of a kind (3/46). I can conclude that i can with (2+3)/46 = 5/46 probability. But this is not real since 3 of a kind gives me more chances to win after all cards are dealt. So I thought to add some coefficients like 2/46*a+3/46*b, but i think now this depends of what the others could have or how many they are, so a and b become too complicated . My question is not very clear even for me so it's more like a discussion. Thanks

Answer 1

During a game you need to watch other players' reactions to cards and their betting patterns. Play conservatively until you get the drift of how people bet and play. Then, during each hand, calculate your odds of winning the hand based on predicted behavior of opponents.

Answer 2

I'm not sure of the question, but if we are talking pure statistics with no draw, no folding, just cards dealt and then compared for highest hand, the probability of you winning in a two hand game is .5. Each person has equal probability of winning any one hand.

If you are talking about calculating the probability of winning once the cards are dealt, then the higher scoring the hand, which means the least probable the hand you have after dealing, is the most likely to win. The reason 3 of a kind beats 2 pair is because it is less probable and so it goes for all the ranking.

Answer 3

This is not a simple problem. I will just sketch out a few thoughts.

Let's assume it is just you and a second player.

You need to know what is the probability of each winning hand, and then for each winning hand the probability you have it and the second player has a lesser hand.

If you are just interested in the answer, find a website with poker probabilities.

If you are interested in the mathematics, find a website that discusses "Combinations" in mathematics, such as 52C5 is the number of possible five-card combinations out of 52 cards, which equals 52!/(47!x5!). For each winning hand, calculate the combinations, and divide by the total possible combinations above.

Answer 4

the probability of getting apair is 1/17
" " 2 pairs is 3/833
" "4 of a kind 13/270725
trust me i aced stat

Answer 5

since every poker game is different, you would have to calculate the probability of different hands, also taking the amount of hands drawn and number of players. Sounds like an incredible feat.

I'll stick to the probability of dealing different hands.

Answer 6

Got any money?