Post Flop Probabilities - Part 2

Written by: Dave Colclough (2004-10-04 18:10:20)

The following table refers to the number of outs, and the probability of one of these outs appearing. If you have an open ended straight draw, you have 8 outs.

You hold 10,J on a three-suited flop of 2,8,9. You know that you can win the pot with the four 7s or the four Qs. In Omaha, you may hold 7,10,J,Q so have 16 outs to give you the nuts : four 6s, three 7s, three 10s, three Js and three Qs. You are a favourite ! Should there be two hearts on the flop, and you have 10,J of hearts in your hand, then you can also add the A,K,3,4 and 5 of hearts, making 21 outs. The danger here though, is that an opponent may have a nut flush draw, which changes the hand from being a favourite, to an underdog. So be careful when counting outs. Don't get carried away. Many of them may not be sure winners. Paying for a draw in poker, that turns out to be a losing draw, is possibly the biggest crime you can commit. Don't do it.

The table shows the percentage chances of improvement after the flop has been dealt in a Hold 'em game. The first column shows the chances of improving with the next 'turn' card. The second column shows the chances of improving in the final two cards. Column 3 indicates the chances of improvement after 4 communal cards have been dealt, and only the final 'river' card is to come. There are slight differences between the first and last columns because the number of unknown cards in the pack is one less (you can see four on the flop as opposed to three). In Hold 'em should you have a flush draw, you have 9 winners from 47 cards in the pack after the flop. You have 9 winners out of 46 after the 'turn' card.

Outs	Improve On Turn	Improve In 2 Cards	Improve On River
1	2.1%	4.3%	2.2%
2	4.2%	8.4%	4.3%
3	6.4%	12.5%	6.5%
4	8.5%	16.5%	8.7%
5	10.7%	20.3%	10.9%
6	12.8%	24.1%	13.0%
7	14.9%	27.8%	15.2%
8	17.0%	31.5%	17.4%
9	19.1%	35.0%	19.6%
10	21.2%	38.4%	21.7%
11	23.4%	41.7%	24.0%
12	25.6%	45.0%	26.1%
13	27.7%	48.1%	28.3%
14	29.8%	51.2%	30.4%
15	31.9%	54.1%	32.6%
16	34.0%	57.0%	34.8%
17	36.2%	59.8%	37.0%
18	38.3%	62.4%	39.1%
19	40.4%	65.0%	41.3%
20	42.6%	67.5%	43.5%

I would suggest that it may be worth printing this odds sheet and sticking it on your computer desk next to your screen.

Note that these are Hold 'em percentages. When playing Omaha the odds are different because you have 4 cards in your hand. The number of unknowns after the flop is no longer 47 cards, but 45. In Omaha, it is also much easier to put opponents on exact hands. For example some opponents will only ever raise with top set. Therefore, you know two more cards, and can discount them from the 45 unknowns. So now your flush draw is 9 out of 43, but not all 9 are winners.

Finally, just to re-iterate the above warning. These are odds on 'improvement'. They are not necessarily odds on winning the pot. Should your opponent have 'a set' (three of a kind) on the flop when you are chasing your flush draw, you are in bad shape. At least 1 of your flush draw cards also gives your opponent a full house. So you don't actually have 9 'winners'. Secondly, once you have hit your flush on the turn, your opponent will have 10 cards to improve (a 21.7% chance) of making a bigger hand on the river. So in reality, your flush draw will not win 35% of the time, and not even 25% of the time, in this case!

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