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Question odds of making a straight in Texas Holdem


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Hello All

Can anyone tell me the odds of making a straight by the flop, turn and river when holding starting cards of:

1. Connected cards

2. Single gaps

3. Double gap

4. Triple gap

I realise the odds will change for cards at the high and low end but if someone could show me how to work it out for the for middle cards I am happy do the work for the higher and lower ends.

Thanks in advance

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1. lets say you're hole cards are 7 8. Your preflop probability of flopping a straight could be calculated as follows:

There are 4 ways to flop a straight with 78. Flop could come 456, 569, 69T, or 9TJ. The probability of each of these are the same. So we will figure out the probability of flopping one of these options, then multiply this number by 4 to get our final answer.

The probability of the flop containing a 4, 5, and 6 is as follows: (12/50) x (8/49) x (4/48) = .003265

Since there are 4 ways to flop the straight, and all are equally probably, we multiply .003265 x 4 = .013061 = ~ 1.31%

The 12, 8, and 4 in that equation are derived as follows: The number 12 is derived from there being four 4's, four 5's, and four 6's in the deck. Any of which will work for the first card. After the first card is flopped, assuming it is a 4, 5, or 6, there are now only 8 total cards left in the deck that will be acceptable for the second flop card. Assuming the second flop card is one of the 8 that will work, there are now only 4 total cards left in the deck that will be acceptable for the third flopped card.

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Thanks Donkiman. Very Clear.

For the next part... How about when we add in the turn, and the river. I understand how to calculate depending on what cards hit on the flop, but I really want to know what the odds are of hitting a straight from hole cards to flop, turn and then the river. i.e. all variations to the river.

Trying to do it in a spreadsheet but giving me a headache. Going to clear up a lot of brain space when I get this worked out :o)

Thanks in advance.

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Got there!! Thanks for starting me off.

So to continue....

Taking the combination 4,5,6

for a straight by the turn (* is a blank)

4,5,6,* (Hitting on the river as you stated above) = (12/50) x (8/49) x (4/48) = .003265

*,4,5,6 = (12/49)*(8/48)*(4/47) = .003474

4,*,5,6 = (12/50)*(8/48)*(4/47) = .003404

4,5,*,6 = (12/50)*(8/49)*(4/47) = .003335

Total for 4,5,6 by the turn is 0.013478

Multiplied by four to include the other three combinations (5,6,9), (6,9,T), (9,T,J)


Does this fit with your math?

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