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by jessriedel 1612 days ago
Where is the variance-reduction technique discussed? I looked at this paper

https://www.science.org/doi/abs/10.1126/science.aay2400

https://par.nsf.gov/servlets/purl/10077416

and it just says

> Finally, we tested Libratus against top humans. In January 2017, Libratus played against a team of four top HUNL specialist professionals in a 120,000 hand Brains vs. AI challenge match over 20 days. The participants were Jason Les, Dong Kim, Daniel McCauley, and Jimmy Chou. A prize pool of $200,000 was allocated to the four humans in aggregate. Each human was guaranteed $20,000 of that pool. The remaining $120,000 was divided among them based on how much better the human did against Libratus than the worstperforming of the four humans. Libratus decisively defeated the humans by a margin of 147 mbb/hand, with 99.98% statistical significance and a p-value of 0.0002 (if the hands are treated as independent and identically distributed), see Fig. 3 (57). It also beat each of the humans individually.

2 comments

>The remaining $120,000 was divided among them based on how much better the human did against Libratus than the worstperforming of the four humans.

Surely the correct strategy here is for the human players to collude to give as much money as possible to a single player and then split the money afterwords, no?

Also, the fact that they players can only gain money without losing anything likely changes their play somewhat. By default I'd assume (and have generally observed) that most players on a freeroll (or better than a freeroll really) tend to undervalue their position and gamble more than is usually wise.

I'd definitely be interested in seeing a "real" game where the humans are betting their own money.

The four humans were getting $120,000 between them. Their share of that was dependent on how much better they did than the other humans. That means there was no incentive to collude.

Top pro poker players understand the value of money. They weren't treating it as a freeroll and anyone that has seen the hand histories can confirm that.

It's in the supplementary material of the 2019 paper: http://www.cs.cmu.edu/~noamb/papers/19-Science-Superhuman_Su... . Look at the "Variance reduction via AIVAT" section.