Congratulations! You have just hit a $4,000 royal flush jackpot on a $1 video poker machine in Las Vegas. The machine is now offering you the chance to double your jackpot. If you accept, you and the house will each be dealt one card at random. If your card is higher, your jackpot doubles to $8,000, but if your card is lower, you win nothing. (If you tie, you and the house each get another card until someone wins.) The odds of doubling your jackpot would therefore be exactly 50 percent. If you behave as a risk averter...