An Unwanted PotHero finds himself in the big blind with . The CO opens to 2BB and the SB calls. Hero gladly tosses in his one additional big blind to see the flop, which comes down . Check check check and an turn falls. Once again, all three players check and the river is the . Small blind checks a third time and the action is on Hero with his pathetic 9-high, which has about a 0% chance of winning at showdown. Let's do some hand reading and figure out what is going on here.
The CO is unlikely to have a Jack too often, at least not a good Jack, after he checks behind on the flop in a situation where top pair would want to build the pot and deny the opponents a free card. The SB could have a Jack but will probably not call too many Jx hands in this position pre-flop unless thy are suited. His Ax would likely have attempted a value bet on the river so we can discount that. CO is very unlikely to hold Ax after his turn check. The majority of the time, then, each player holds something weaker than second pair. Now onto the math of bluffing.
The Math of BluffingIf we bet two thirds of the pot here in an attempt to fold out all hands worse than Jx, we will be risking 2 units to win 3 units. Our required fold equity percentage, meaning the amount of the time we will need both players to fold in order to break even on a bluff, is found by with the following equation:
Required Fold Equity = (Risk / Risk + Reward)
In this case: Required Fold Equity = 4BB / (4BB + 6BB) = 40%
If both opponents combined fold 40% of the time, we shall not lose any money of a bluff here; if they fold any more than this, we begin to profit.
For both opponents to fold 40% of the time, we need each of them to be folding around 63% of the time. This seems very reasonable indeed. In fact, I would estimate that each individual opponent is likely to be folding upwards of 70% here. Bluffing should make a lot of money.
Show Restraint with Showdown ValueHaving showdown value means being able to win the pot a reasonable amount of the time unimproved at showdown. In order for this to be true on the checked down board, we will need to have some kind of pair. Let's imagine that we get to this same spot, but instead of the , we hold . We have showdown value with this hand, and quite a lot of it.
In the previous example, we were going to lose the pot all of the time by checking. This meant that the EV (expected value) of checking was 0. Therefore, if betting was in anyway positive EV, we preferred it to checking; and we found that it likely was positive since we were likely to meet the required fold equity target of 40% for making a two-thirds pot-sized bet.
When we hold the , however, we expect to win the pot a good amount of the time by checking. We might have the best hand here about 50% of the time. In this case, the EV of checking could be as much as 50% of the pot, or +3BB. This is now the target that we should try to exceed when we consider betting. Are we going to make more than 3BB by betting? The answer is certainly not. Actually, we are going to make less. Why is this the case?
With , when we are called by either player, we expect to lose almost always, just like when we had the . If we are to suppose that we get each player to fold 70% of the time, they will both fold 0.70 x 0.70 = 0.49 or 49% of the time. Let's round this up and call it 50% for simplicity. When we bet the for two thirds of the pot, we win 6BB 50% of the time when both players fold, and lose 4BB (our bet) 50% of the time when someone calls. The EV of betting is, therefore, 6BB + -4BB = +2BB.
Checking is worth a whole big blind more than betting, if these assumptions are largely correct. This analysis demonstrates the importance of refraining from bluffing when you have showdown value – your bet might be profitable, but checking is more profitable.
- Small multiway pots are often neglected. Be the one to take them down if you cannot win at showdown.
- Do not try to win pots by bluffing if you are going to win at showdown any way against the hands your opponents would fold.
- Our goal is not just to take a +EV line, but to take the highest EV line. Checking might be even better than making a profitable bet.
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