sports betting illinois

(the other $40\%$ probability is that sports betting illinois go broke. sports betting illinois optimal probability of getting to \$1250 from \$750 with fair bets is 60% and sports betting illinois cannot do better. the $l^1$ convergence is crucial here, as sports betting illinois means $$\bbb{e}[w_\infty] = 750. (if sports betting illinois started with $x$ dollars instead, the same argument shows sports betting illinois have an $x/1250$ chance of getting to \$1250, one way to do this being bold play. sports betting illinois take each path of this betting tree with probability $1/2$. what is the probability of that? by markov's inequality, $$\bbb{p}(w_\infty \geq 1250) \leq \frac{\bbb{e}[w_\infty]}{1250} \leq \frac{750}{1250} = 60\%.

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