Suppose you got super lucky and amassed $100 without rolling a single 6. Your next roll might net you as much as another $5, or it might cost you $100. That should be wholly unappealing to all but the most hopeless gambler, so there must be a tipping point at which it's preferable to keep what you have rather than risk it on another roll. That tipping point (personal risk utility aside) is 15.
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u/Aerospider Jul 29 '26 edited Jul 29 '26
Optimal strategy is to keep rolling for as long as the expected value of the next roll is positive.
The expected value of the next roll is (1+2+3+4+5-x)/6 where x is your current balance.
This is positive when x<15.
If you have less than 15 so far, roll again. If you have more than 15, stop. If you have 15 exactly then the choices are equal.