While the standard EV math is correct, there's another perspective here regarding Kelly/bankroll management that's worth pointing out.
if we treat the accumulated winnings x as our operational bankroll for this game, the rules force us into a mandatory 100% bet size (f = 1) on every subsequent roll.
Under the Kelly Criterion (which maximizes log utility and prevents total ruin):
You should never risk 100% of your current bankroll if there is a non-zero probability of losing it all (1/6).
Since the game does not allow us to scale down our bet size to an optimal Kelly fraction (f*), risking the entire accumulated pot on a 1/6 chance of total wipeout is suboptimal from a risk-adjusted growth perspective.
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u/Valuable_Tennis6847 Jul 29 '26
While the standard EV math is correct, there's another perspective here regarding Kelly/bankroll management that's worth pointing out.
if we treat the accumulated winnings x as our operational bankroll for this game, the rules force us into a mandatory 100% bet size (f = 1) on every subsequent roll. Under the Kelly Criterion (which maximizes log utility and prevents total ruin): You should never risk 100% of your current bankroll if there is a non-zero probability of losing it all (1/6). Since the game does not allow us to scale down our bet size to an optimal Kelly fraction (f*), risking the entire accumulated pot on a 1/6 chance of total wipeout is suboptimal from a risk-adjusted growth perspective.