# What are the odds I will hit my flush? [duplicate]

Possible Duplicate:
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?
• 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 '12 at 19:24
• 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 '12 at 19:30
• 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 '12 at 20:13
• This is not a duplicate - it is two cards to come - not odds in general – paparazzo Aug 16 '16 at 12:56

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).

• 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 '12 at 19:43
• 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 '16 at 21:56

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.

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! :)