I’ve now bothered to read how those in the philosophy departments handle this and found this post, which is good walk through:
Some of us, not me are “causal decision theory” (CDT) people. Others are in my “evidence decision theory” (EDT) camp. But there are others too!
It even includes a detailed analysis of the coin flip strategy @dprk and says the best is a slightly unfair coin that comes up one box slightly more often
At , the predictor leaves Box B empty and you average $510. At , the predictor fills Box B and you average $1,000,490. A 2% shift in coin bias produces a $999,980 jump in expected payoff.
The optimal mixed strategy is just above : one-box slightly more than half the time. This earns approximately $1,000,500, which beats pure one-boxing ($1,000,000) by $500. You get the million (the predictor fills Box B because you’re majority one-box) while occasionally grabbing the extra $1,000 when the coin lands on two-box …
For those us who have gotten intrigued by the strength of positions held it is a good read!