A bit of flop math

Poker Strategy
#1

Continuation betting is a key part of poker (it is a postflop bet made by the original raiser, so raise preflop!). C-betting can be great part of your game even if your hand does not directly hit the flop. If you think betting when you don’t have a pair is an immoral form of lying then I recommend you quit poker and take up ice dancing, though that sport has also been subject to controversy. Here is a bit of math that shows why c-betting works so well.

Let’s say the pot after your preflop raise and one opponent calls is 1000 chips. If you bet 500 chips, and you NEVER have the best hand by the river, your bet will be positive expected value if your opponent folds 33% of the time. That means if you have 27o and the flop comes AAQ, if you think your opponent will fold 1/3 of the time, it is still a positive play to bet half pot. If you have AA in the same situation, you still have the opportunity to win those 500 chips if your opponent does call. By c-betting you are able to win pots with your good hands, drawing hands, semi-bluffs, and even complete bluffs.

Now, let’s say you have an inside straight draw and a backdoor flush draw (8h7h on a JcTh2d flop). Let’s say your outs give you a 15% chance to win by the river (realistically it could be more like 20-25%), if you bet 500 chips, you only need your opponent to fold more than 17% of the time for your bet to be profitable.

Looking at it another way, if you bet 500 and your hand has 25% equity against your opponent’s range, you break even if your opponent never folds. Granted, these situations are not as simple as I am presenting them because you do not get to realize all of your equity until the river and the equity equation on the river becomes binary because there are no more cards to hit. But, even if your opponent calls you on the flop you have a chance to improve or apply pressure with another bet. This math shows how being the bettor provides a way to win that does not always involve showing down the best hand.

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#2

To diagnose my play, I keep track of my key stats, which includes PFR% (pre-flop raise) and c-bet frequencies and the win% attached to each of these statistics. The key lesson I have learned from this exercise is basically the essence of what JoeDirk has laid bare – aggression pays. Poker favours the pre-flop aggressor, and I rarely limp in or flat call, because the latter (at least for me) is generally a strategy for losing chips. Of course, knowing when to c-bet and when to check the flop requires careful observation and an understanding of your fold equity in a given situation.

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#3

I’d add a little to this to include all the available options villain has - If your opponent will only call or fold, then the c-bet numbers work out as you indicated. However, if you include the option for villain to check-raise, things get more complicated in a hurry. In many (most) cases, your bluffs on the flop have significant equity. By opening the betting action up again through a c-bet (vs checking and seeing a free card), you risk getting blown off that equity by a check-raise.

Its also worth noting that there are many instances where you don’t know if you are actually bluffing with your c-bet. If the flop comes KT3 and you bet with Q9 vs the BB caller, are you bluffing or not? Vs his A-high or small pairs, yes you are, though you have chances to improve. Vs his 6/5s, no you aren’t because you have the best hand by far. Conversely, there are plenty of times we think we are betting for value when we are beat. This is a game of incomplete information after all.

Your overall point is one of the most important concepts in poker. The idea of betting for value vs betting as a bluff has been replaced by betting your equity or betting to deny your opponent’s equity. This is the entire game in a nutshell. Also, in tournament poker the effects of fold equity get magnified as stacks get shorter. Anyone who does not understand the concept of fold equity + actual equity (if called) will not succeed vs even modestly competent fields.

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#4

I’d also mention that the math here applies not just to c-betting, but to bluffs in general, and that it is not actually necessary to raise pre-flop to avail yourself of the power of betting.

If anything, you’ll find check raising the flop generates rather more folds than a c-bet against competent opposition, and so the same bet sizing relative to the pot is likely to have more fold equity. Of course, your opponent’s opening range is important here: if they raise 0.5% of their hands, then they may tend to get quite sticky post flop.

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