POST FLOP PROBABILITIES
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.