An interesting hypergammon programming project
Posted By: Timothy Chow
Date: Thursday, 4 September 2014, at 2:24 a.m.
I've always been curious how much equity can be gained by exploiting known opponent weaknesses. This question seems difficult to answer for regular backgammon, but the recent discussion about hypergammon got me thinking that perhaps one can get some answers in that case because the game is so much simpler.
The idea would be this. Design a weak hypergammon player (the "fish") that plays a very simple strategy. Maybe something like this: first priority is to bear off maximally, second priority is to hit, third priority is to minimize shots, otherwise choose randomly among the shot-minimizing options. For the cube, perhaps always drop a little too quickly and double a little too late. The details don't matter too much as long as the strategy is halfway plausible and extremely easy to compute.
Now re-solve hypergammon, but armed with the knowledge that your opponent will play the above weak strategy. This will give a strategy (the "shark") that is specifically tuned to maximally exploit the weakness of the fish. The question I'm interested in is, how much more equity does the shark get against the fish, compared to the "perfect" player against the fish?
I suspect that the answer will be larger than most people expect.
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