Probabilistic game Suppose a rich person offers you $\$1000$ and says that you can participate in $1000$ rounds of this game:
In each round a coin is flipped and you get a $50$% return on the portion of your money that you risked if it lands on heads, or get a $40$% loss if it lands on tails. For example if you choose to risk all of your money in round one, then you'll either have $1500$ or $600$ dollars for rounds two. If you only risk half of it, then you'll either have $1250$ ($500+500*1.5$) or $800$($500+500*0.6$) dollars.
What is your best strategy ?

The expected value of your game is positive ($E[X]=0.5\alpha-0.4\alpha\ge 0$, where $\alpha$ is the amount of money bet) so the more you bet, the more you'll earn.  
Moreover, betting all your money doesn't prevent you playing the $1000$ games since the result only affect a percentage of your bet, so the best strategy is to bet everything you have in the $1000$ rounds.
EDIT : I assume the coin is a fair coin.
