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What can I do to calculate my odds in a hand?

If I have 2 cards of the same suit in the hole, and 2 board cards with those suits on the flop, what are the chances that I will hit my flush:

  1. On the turn?
  2. By the end of the hand?
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  • If you're holding two, say, Spades, and there are two more on the board along with one other card, that leaves (52-5) = 47 other cards, of which (13-4) = 9 are Spades. Your chance of hitting the flush on the turn is 9/47 = 19.15% (about 1 in 5). If you don't hit on the turn, your change of hitting the river is 9/46 = 19.57%. Your overall chances are 19.15% + (19.57% * (1-0.1915)) = almost exactly 35%.
    – voraciti
    Jan 10, 2012 at 19:24
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    Another trick that some people use to estimate your odds of hitting a single draw card in any situation: going into the turn, multiply your number of outs (in this case, 9 Spades) by 4 to get approximate odds (i.e. 9 * 4 = 36%, which is close to the 35% we calculated above). Going into the river, multiply by 2 (9 * 2 = 18%, close to the 19% we calculated above). For example, if you have an outside straight draw with 8 outs going into the turn, you have about a 8 * 4 = 32% chance of hitting it by the river (actual chance is 31.4%, so it's close again). Some people call this the "2-4 rule".
    – voraciti
    Jan 10, 2012 at 19:30
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    We should avoid such basic questions during private beta. It's important to attract experts by avoiding easy questions and thinking like an expert.
    – Michael McGowan
    Jan 10, 2012 at 20:13
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    This is not a duplicate - it is two cards to come - not odds in general
    – paparazzo
    Aug 16, 2016 at 12:56

2 Answers 2

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After the flop you've seen 4 cards of your suit, and 1 of another suit. This leaves 9 cards of your suit, and 38 of a different suit; your odds of completing your flush on the turn are thus 9/47, or 19.14%.

If the turn hasn't completed your flush, your odds of completing it on the river are 9/46, or 19.5%.

This means that the total odds for completing a flush - which should matter for example if you're going all in after the flop - are (19.14%) + (19.5%*(1-19.14%)) = 34.96% (the odds of completing on the turn, plus the odds of completing on the river times the odds of not completing on the turn).

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    It would be useful to explain how you came up with the 34.96 number for people who don't understand dependent events.
    – Nick Larsen
    Jan 10, 2012 at 19:43
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    This answer is mathematically correct. It's worth mentioning that there is an additional (19.4% * 17.4%) = 3.33% chance of completing the flush on the turn and seeing another flush card on the river. Because players going all-in for a flush draw after the flop usually have near the nuts, this 3.33% outcome means the pot odds calculation depends on how high your flush is.
    – Heath Hunnicutt
    Jan 16, 2016 at 21:56
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A good rule of thumb I always use for a flush draw is multiply outs(13 spades - 4 spades) with 4 on the flop and 2 on the turn. This ways it's much easier to remember and you aren't that far away from the correct percentage.

That is:

On the flop = number of flush outs x 4 = (13-4)x 4 = 36%

On the turn = number of flush outs x 2 = (13-4)x 2 = 18%

Obviously a "naked" flush draw is not a very good hand to move all-in with on the flop since you are most likely to be up against a much stronger hand if your opponent raises you. However, if you are holding a flush draw as well as two cards that are higher than the cards on the flop, this is a much stronger hand since you are drawing to a higher pair versus a potential top pair on the flop.

example: s = spade.

AsKs vs 88

flop: 4s 7h 2s

here you have 9 outs for the flush + 3 aces and 3 kings to hit against his pair of eights. This works out to a total of 9+3+3 = 15 outs => 15 x 4 = 60% .. although the correct answer is a bit smaller.. so 55% is more accurate.

My conclusion is that if you really "have to" move all-in with a flush draw, you should do it with two high cards of the same suit! :)

Here is a nice tool called pro poker tools.com to help you calculate your chances!

propokertools.com

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  • It may seem that the rule I just wrote only applies to flush draws.. I hope you understood that it works the same in any other situation as well! just find how many cards you need to hit to make your hand, and that is how many "outs" you have.
    – Duffman1985
    Jan 10, 2012 at 20:00
  • +1: This is known as the "Rule of 2 and 4"
    – John Dibling
    Jan 10, 2012 at 20:12
  • that's true! I think you will find it in the Harrington on holdem book
    – Duffman1985
    Jan 10, 2012 at 20:16
  • It may be in Harrington, but it has been known by this name since long before that. Harrington did not pioneer this knowledge, nor the moniker for it.
    – John Dibling
    Jan 10, 2012 at 20:22
  • Good to know. Doesn't really matter though..and I am not even sure if Harrington mentioned it or not.
    – Duffman1985
    Jan 10, 2012 at 20:30

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