Folding Kings?

I don’t usually write about spots that come up infrequently but recently I witnessed this hand I thought was uniquely instructive. Everyone started with about 150 big blinds. Player A in 1^st position raised to 3 big blinds, Player B, a good tight aggressive kid in 2^ndposition, reraised to 8 big blinds and Player C, a mediocre loose aggressive kid in 3^rdposition, 4-bet to 22 big blinds. Player A folded then Player B 5-bet to 42 big blinds. Player C elected to 6-bet to 68 big blinds only to watch as Player B decided to go all-in. Fun stuff! Player C, who was currently getting 3.7:1 pot odds, meaning he needs to win 27% of the time, proudly flipped his K-K face up and folded.

While I am all for making big folds when they make sense, in this situation, even though Player B will have A-A a huge amount of the time, folding K-K is a fairly large error unless you know for a fact that Player B will only go all-in with A-A. The problem with this hand is that Player B is certainly aware that Player C is a loose aggressive player. Because of this, Player B could easily have a wider range than only A-A.

Suppose Player B’s range is A-A and K-K. Notice there is only one combination of K-K remaining, meaning he will have A-A 86% of the time and K-K 14% of the time. Player C will win the hand 22% of the time, making a call an error as he needs to win 27% of the time to break even. If Player B would go all-in with A-A, K-K and Q-Q, Player C would win 50% of the time. If Player B would push with A-A, K-K, Q-Q and A-K, Player C would win 57% of the time. If Player B is ever bluffing, Player C’s equity skyrockets.

The way I look at these situations, especially when I do not know my opponent’s exact range, is to average the ranges I think make sense. I imagine the equation for calculating Player C’s equity in this spot looks something like this:

EV = .3(.18) + .4(.22) + .2(.5) + .1(.57) = 30%

Clearly I do not do this math at the table. I have studied the game away from the table enough to know how this situation typically looks and how to react if I am ever in this spot. What this equation represents is 30% of the time Player B will have A-A, 40% of the time he will have A-A or K-K, 20% of the time he will have A-A, K-K or Q-Q, and 10% of the time he will have A-A, K-K, Q-Q or A-K.  Given the numbers, it would be a small error to fold as Player C will win 30% of the time, on average, and he needs to win 27% of the time to break even. Since 30% is larger than 27%, he should call.

As always, one simple equation is not the end of the story. Notice I did not add any total bluffs to Player B’s range. If Player B is bluffing around 10% of the time and he has A-A 10% less often, Player C’s equity jumps to 35%, making a fold a clear error. However, there is always value in surviving in a tournament, especially if you think you are much better than your opponents. Assuming Player C is good, which he obviously isn’t because he folded K-K face up, he should lean toward folding, especially if he thinks the situation is nearly break even. If Player C is a bad player, significantly worse than his opponents, he should actually be much more prone to call as he can get all of his money in with around neutral equity, which is probably much better than he will do later in the tournament.

In my opinion, Player C made a large error by 5-betting to 22 big blinds. If he called, he could take a flop and likely see a somewhat cheap showdown. While he would still lose a large pot if his opponent had A-A, he would force his opponent to take a flop with all of his worse hands as well. Assuming you are a good player, you rarely want to get all-in preflop when extremely deep stacked. You are much better off winning lots of small pots, slowly grinding up your stack. By putting in the 5-bet, Player C set himself up for failure if Player B decided to go all-in.

As Player B mucked, he flashed his As-3s. I liked it.

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Be sure to check back next week for another educational blog post! Thanks for reading and good luck in your games!