Person A has 5 fair coins and Person B has 4 fair coins. Person A wins only if he flips more heads than B does. What is the probability of A winning?
When I initially thought about the problem, I thought of it as if both had 4 coins, then they would on average get the same number of heads. If Person A had one more coin, then it would be a 50/50 shot for Person A to have more each time. But the more I think about this, its making less sense to me as an explanation, or at least it is incomplete.
Logically as I think about it if you have 2 people with the same amount of coins, they both have the same chance of winning, although that percent is less than 50 for each person because of the chance of them tying. When you give a person an extra coin, that reduces the probability of tying by half (one half is tie when the guy flips tails with his extra and the other half is when the guy flips and gets heads and get an extra point). I'm not sure how to justify the thought that the original percentage of winning + the extra gain from the tie scenarios given by the extra coin = 50%.
I guess I'm just looking for any tips on how to think about this problem so I can more fully understand it.