Abstract
It is shown that if a gamble γ stakes positive amounts on infinitely many holes of a subfair roulette-table, then for every e{open}>0, there is a gamble γ * with positive stakes on only a finite number of holes, such that γQ≦γ*Q+ε for every nondecreasing function Q bounded above by 1 on [0, ∞]. It is deduced from this proposition that a gambler who wishes to maximize his chances to increase his current fortune by a specified amount, has no advantage in ever placing positive stakes on more than a finite number of holes on any single spin. This result settles a question left open in [1].
Original language | English |
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Pages (from-to) | 282-285 |
Number of pages | 4 |
Journal | Israel Journal of Mathematics |
Volume | 24 |
Issue number | 3-4 |
DOIs | |
State | Published - Dec 1976 |
Externally published | Yes |