Win the biggest pot, not the most pots

Barry Carter shares some wisdom from Phil Galfond then takes to the solvers to prove his point.

When Phil Galfond tweets (which is a lot these days) you should always pay attention, and this recent one caught my attention. 

The "Take it Down" Bias:

Most players cbet too often because it leads to a higher frequency of emotionally positive outcomes (winning the pot).

Your goal in poker is to win more money. Not more pots.

— Phil Galfond (@PhilGalfond) January 24, 2023

This one hit a nerve with me because I think it is a leak of my own and something I am paying attention to a lot. As luck would have it, Dara O'Kearney and I are working on our next book and a hand came up that summed this up perfectly. 

We were looking at exploits and what a solver does when you 'node lock' to say a player overfolds on the river. In this spot we told the solver to fold anything less than two pair to a river shove. If you had this read on your opponent, how would you play the nuts? 

Most people would answer that they would bet smaller with the nuts to 'milk' a call out of their opponent with a top pair type hand. That is also what we thought. The actual answer is the opposite, the solver shoved every hand including the nuts. 

The main reason was that with such a tight folding range, bluffing was very profitable. We have written before in GTO world that bluffing is overrated, but in these spots, it is printing money. In the GTO version of our sim bluffing with 88 made 4.5BBs, but in the node-locked version it made 48BBs. 

Get over the frequency bias

That might make intuitive sense, but why do we shove strong hands like the nuts too? The answer was simply that it still made the most money overall the few times it got a call than a smaller milking bet that gets called more often. The nuts was AA for top set in this example and we used a simple calculation to work out why it was the best option. 

You multiply your bet size by the percentage of time you think your opponent will call. In this case, the effective stacks were 68.1BBs. The math went something like this:

• If we shove 68.1 bbs with the nuts and they call 20% of the time, the EV of the shove is 13.62 bbs
• If we bet 60% pot, which is 38.46BBs, and they call 33% of the time, the EV of bet is 12.69BBs
• If we bet 25% pot, which is 16.03bbs, and they call 75% of time, the EV of the bet is 12.02 BBs.

As you can see, shoving is still the most profitable option. Getting max value 20% of the time is worth more than getting some value 75% of the time. Most players struggle to get their head around this, they prioritize getting something for their hand all the time rather than trying to win the biggest pot.

We have a frequency bias where spots like this are concerned because our shove gets folds 80% of the time we think it is a mistake, but the 20% of times we get called more than makes up for it. Think about that the next time you flop Quads and get tricky checking back flop and turn. 

Do you have this leak too? Let us know in the comments: