Poker (Texas Holdem) odds.?

Question

What is the probability that the community cards may yield a Three of a Kind, Fours, Flush or a Straight or even a Full House? There are four different situations, 1. After the Deal, 2. After the Flop, 3. After Turn, 4. After River.
 The situation changes dramatically after the flop as you may turn up with 3 or 4 cards neccesary but will expect that to turn up during turn or river. 

However you need to give me hints for calculation for situation 1 & 2 only. I am arriving at very low probabilities as I am multiplying the probability factors for each subsequent cards. I also want to know the combined probability of any one of the above happening and again combined including Two Pairs.
 
I don't think you can add up the individual probabilities as there are many overlapping situations.
 
Thanking you and wishing luck in a hand of poker.

Divide By Zero · Accepted Answer

I might not fully understand the question.

For #1 the probability is zero for two reasons -- there are 0 community cards so far, and you can't make any of those hands with only 2 cards anyway. (Therefore I'm not sure what you need help with and I must be misinterpreting something.)

For #2, of the hands you listed, only three fours can come in the community cards since the Flop only has 3 cards. Chance of the flop being three fours = 4C3 / 52C3
Or if you know your hole cards are not fours, then it's 4C3 / 50C3

I won't keep writing when I don't know what's being asked. If you don't have a chance to edit this question, then I can tell you the general mathematical topic that might interest you is called Combinatorics. If you learn some combinatorics you'll be able to answer these questions.

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Poker (Texas Holdem) odds.?

1 Answer