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 |
|---|---|
| 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 |