Re: Craps puzzle
How about 4 on both? This makes the P(8) highest, while also decreasing p(7), since 4 is weighted higher while 3 is weighted lower on each die, so when one die hits 4, chance of 7 is reduced even further.
I did no calculations-- figured posting would prompt me to compute a little. I can see 2/2 (or 5/5) as also profitable, but then you'd win more perhaps by placing the 4 (10), instead of just pass line. I'll take a stab at seeing if the weighted dice make up for house edge on placing the 4... seems a harder problem to calculate if placing the 8 instead of pass line is more profitable in first case.
-Curtis
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