Joe Dalton desperately wants to raise his bankroll of $600 to $1,000 in order to pay his debts before midnight. He enters a casino to play European roulette. He decides to bet on red each time using bold play, that is, Joe bets either his entire bankroll or the amount needed to reach the target bankroll, whichever is smaller (a bet on red is won with probability 19). Thus the stake is $200 if his bankroll is $200 or $800 and the stake is $400 if his bankroll is $400 or $600. What is the probability that Joe will reach his goal? What is the expected number of bets of Joe?

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