Probability Puzzles

1. Alice had some unknown number of unbiased coins with her (say x). And Bob has one more coin with him than Alice. Alice flips all her coins in one go and observes the number of heads and so does Bob. What is the probability that Alice has more number of heads than Bob? (Courtesy Romil Goyal)

2. Bothra and Tiwari are playing a fair game repeated for one paise each game. That is both put one paise in the game, and the winner takes back two paise.

If originally Bothra had A paise and Tiwari had B paise, what is the chances of Bothra winning all of Tiwari's money, assuming that they will play until one person has lost all of his money.

Sorry for the delay in posting the solutions to the earlier puzzles. I will try doing that today. Have fun!