Proportionality and Persistence of Perceptions

We hear a lot about the importance of “balance,” but it’s usually approached in a mathematical way. If we were playing against computers, this would certainly be the proper approach, but since we aren’t… it’s not.

What we are seeking isn’t balance, it’s the perception of balance, and these are not the same thing.

Humans remember some things while forgetting others. Some actions, like audacious bluffs, are more memorable, thus carry proportionally more weight than value bets, which are expected, thus easily forgotten. Actions that are memorable also have greater persistence simply by being more memorable.

Anyone who doubts this need merely read the “fairness debate” thread, which is full of anecdotal “evidence” that the site is rigged. Losing with AA 3 times in a row is more memorable than winning with aces 3 times in a row, so the perception is that aces get cracked more than they should.

In practice, this means we don’t have to bluff 50% of the time in order to give the appearance of bluffing 50% of the time. We don’t have to check half of our strong hands to give the appearance of checking strong hands half the time, and so on.

Strategically showing (or not showing) your hole cards is one of the ways we can take advantage of this idea of proportionality and persistence, but there are others too.

At the end of the day, it’s not what you are doing that’s important, it’s what your opponents think you are doing that counts. By controlling perceptions, we can weight our actions towards the desired results while apprearing to be perfectly balanced.


Well said. Cognitive biases exist and color our perceptions of reality. In most live games or casual online games without HUD’s, these perceptions can lead to massive errors in judgement over frequencies. There are people who pick up on frequency errors faster than others and these tend to be the more successful live players.

Balancing became more important when HUD’s and hand analysis software became more widely available. The human may miscalculate frequencies but the data reveals the truth. It may not matter as much for the vast majority of players but it does for the pool of regulars that face each other constantly.


Sure, but there you are more or less playing the computer. One can’t fool raw data, or at least not as easily.

I used range balancing as an example, but this idea has wider application too.