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Comment by xapata | Hacker News Reader

I suspect Libratus' overbet frequency is overfit to this particular reduced-variance game format. In a normal game, the opponent doesn't take chips off the table after winning a hand and might stand up at any moment.

It's hard to know how much that affected the strategy, but in the Reddit thread, the human players said the overbet frequency was what they were most surprised by.

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Maybe overbetting is better EV and humans just don't know it yet. It will be interesting to see if this changes the game at the higher stakes Heads Up tables

Yes, but expected value isn't everything. A good investor considers the ratio of expected return to variance of return. In a normal game, the variance on an overbet is enormous and therefore the denominator of its Sharpe ratio [0] is large and drives the value (or should I say "score" so as not to get confused with "expected value"?) of that action down.

You'd happily go all-in pre-flop AA vs KK. On the other hand if you got 4-bet pre-flop by a 22 and you're holding AK, you might ask, "Check it down?" This is assuming the opponent really likes small pocket pairs and will call an all-in, etc.

[0] https://en.wikipedia.org/wiki/Sharpe_ratio

> you might ask, "Check it down?"

In a heads up game? Really? "Check it down?" ???

The example applies more to a ring game, where you might be going after a particular fish and don't want to get involved with a better player. Still, I think it illustrates the principle of trying to keep the variance down.

Also, if you're first to act on the next round, it might be worth asking, even if you don't think they'll agree.

That's collusion and it's not cool. No top pro would ever seriously ask to 'check it down'

Kelly's criterion and the sharpe ratio is not relevant for the format played in these human-AI heads up games. They play with an unlimited bankroll.

I'm not talking about a tournament. And yes, it could indicate collusion. But most of the time, it's just a friendly low- or mid-stakes game and the players are tired of thinking.

My point exactly about the unlimited bankroll. The experimenters may not have realized that an unlimited bankroll would significantly affect the strategy.

Theoretically the best way to maximize an edge is to just wager larger amounts at all times. This has a beneficial side effect of deviating from 'standard' human play which can be further exploited, although I doubt this the intention of the AI.

Maximum expected value is not always optimal. Bets are an investment with uncertain returns. In normal circumstances, portfolio theory helps us optimize our investments. This reduced-variance format removed the budget constraint and made portfolio theory irrelevant. Overbets made sense to the bot who had only trained in this particular format, but not to the humans who have trained for years with a budget.

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