A and B each put 10 coins in the pot. A then takes a coin from the pot and tosses it, while B calls heads or tails. If B’s call is correct, he takes the coin and keeps it; otherwise, A keeps the coin. B then takes a coin from the remaining pot and tosses it while A calls heads or tails.

The play continues in this way until one player has accumulated 10 coins, whereupon he wins the game and takes all the coins remaining in the pot. At one point in the play, A has six coins, while B has only four. What is A’s probability of winning?

When the situation occurs in a game such that one player has won six coins while his opponent has won four coins, what is the expected value of the winnings (net number of coins) of the player with six coins?