Michael grabs a marble from a bag. There are 5 green marbles and 1 red marble. If he grabs the red marble he loses everything he bet on. The marbles are not put back into the bag. The max amount of times Michael can bet on the same game is 4. If he bets 300 and wins 578 (having 278 as winnings), he has the choice to bet again with everything he earned for 682. Then he has the choice to do so again for 945, then 1312 at max. At what point in the game should Michael stop playing to gain the most given the percent of risk of losing the game? What point in the game is the least beneficial for Michael's gains?
First bet (300 -> 578)
Second bet (578 -> 682)
Third bet (682 -> 945)
Fourth bet (945 -> 1312)
If Michael wins every round he would go from 300 to 1312. If he loses, he doesn't gain any of the rewards and is 300 in debt.
