Post Flop Probabilities in Poker 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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Post Flop Probabilities in Poker Part 1

Written by: Dave Colclough (2004-09-20 22:15:57)

The last couple of articles concerned pre-flop probabilities. These are most relevant to NLH tournament play. This is because most chip movement occurs pre-flop in NLH tourneys, whereas, with Limit Hold 'em and Pot Limit Omaha, most of the action takes place post flop. The next couple of articles discuss post flop odds and probabilities. These are equally interesting to the NLH player, but they will have less opportunity and situations to take advantage of this knowledge.

Possibly the most useful probabilities are those surrounding a flush draw. If you hold two cards of the same suit, you will flop a made flush slightly less than 1% of the time. If you are all-in before the flop, the chances of completing your flush with all five cards are somewhere around 6%. More useful though is the situation when you flop four to your flush: two hearts in your hand with two hearts on the flop, or one heart in your hand with three on the flop.

Many NLH players will commit their whole stack heads up in this situation, but the odds say that really you shouldn't. You will only complete the flush around 35% of the time. So if a player has moved all-in, in front of you, for a large bet of greater than pot size, the correct play is probably to pass. You are not getting good pot odds. You will often see players making bad calls in this situation. It is of course different if you move all-in first to speak. You may only win the pot a third of the time if someone calls, but of course you may win the pot 50% of the time, uncontested, if everyone should pass.

In Limit Hold 'em of course, you will rarely win the pot uncontested, but the pot odds will be different. In many ways Limit Hold 'em is much more complicated here. In a $2/$4 game, four players may have seen the flop. The player in front of you bets $2 on the flop, and you can easily justify the pot odds as you are now calling $2 against a $10 pot. However, there are variables to consider: how much more you may have to call to see the final two cards, and how much more can you win if you hit the flush. Firstly, a player may raise behind you and the original bettor may re-raise. Now you are risking $6 against $20. The odds aren't as good but are still favourable. But of course, the flush may not arrive on the turn, and you may have to call another $4. Now the risk is $10 against $28, or possibly $10 against$24 if play becomes heads up. You are in fact still getting pot odds, but only just. The second variable is of course when you hit the flush, how much will you get paid? If the player will call a $4 bet on the end, or better still, a two bet situation may emerge, then you are of course reaping the real benefits of your draw. Flush draw flops are usually a profitable venture in Limit Hold 'em.

Remembering all these situations and odds isn't as hard as it initially looks. You will constantly hear players refer to 'outs'. A flush draw is 9 outs. If you have an open ended straight draw, you have 8 outs. Most top players just count their outs, and know the probabilities of hitting these outs. Next weeks article will include the 'outs' table and further explanation.

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