1 Vladimir Ulanowsky is playing Keith Smithson in a two-game chess match. Winning a game scores 1 match match is over 1/2 . Explain this anomalous result.
2 Dickie Hustler has $2 and is going to toss an unfair coin (probability .4 of heads) three times. Before each toss, he can bet any amount of money (up to what he now has). If heads comes up, Dickie wins the number of dollars he bets;
if tails comes up, he loses the number of dollars he bets.
Use dynamic programming to determine a strategy that maximizes Dickie’s probability of having at least $5 after the third coin toss.