Why do solvers sometimes play unprofitable hands?
Dara O'Kearney uses Holdem Resources Calculator to show why a losing hand is necessary to make the rest of our range priofitable.
I was recently asked about why solvers sometimes play hands that are unprofitable. Occasionally at the bottom of the range, there will be a hand that will lose money for the range.
For example this shoving range from Holdem Resources Calculator. As you can see, 55 is in the range (it is played 28% of the time) but it loses us 0.01BBs on average.
There are also some breakeven hands in the range like 66, 77, and A2s. Most people can understand why breakeven hands are in there, but why voluntarily play a hand that loses us money?
Unprofitable hands make our big hands more profitable
The first thing to say is that the sim is correct. Tools like HRC have a margin of error built in, so we do see things like this on the margins.
The reason 55 is still a shove here is that without it, the other hands in the range become less profitable. Our opponent is more likely to call us when they know we are capable of having a weak hand like 55, which means our Aces get more action.
Indeed, check out the range when I 'node lock' and manually take 55 out of the range:
The range is essentially the same, but all of our big hands are slightly less profitable. KK makes 1.29BBs in the first example and 1.27BBs, on average, in this new example. Some hands become more profitable like QJs, for example. All of this is because of how the opponent's calling range tightens in response to our tighter range.
Curiously 55 is profitable now, which means it is profitable against the new calling ranges, but it won't be if we reintroduced it to our range, because the calling ranges would adjust.
In practice, the way I recommend interpreting solver results like this is you want to shove the clearly profitable ones, not shove the clearly unprofitable ones, and it doesn’t really matter what you do with the slightly plus or minus ones. They are so close to break even then your gut will likely tell you what to do based on whether it seems like your opponents are overcalling or overfolding.
We play unprofitable hands sometimes because it makes the rest of our range more profitable. We covered this when we wrote about bluffs being overrated. The point is that bluffs in a vacuum do not make us much money compared to value bets, their purpose is to get value bets called more often.
Dara O'Kearney's book on this topic Endgame Poker Strategy: The ICM Book is out now.
