# A coin tossing game with two players

In a coin tossing game two fair coins are given to two persons X and Y each. The game proceeds until one (or both) of the following happens.

1. X wins the game if he gets consecutively two tails for the first time.

2. Y wins the game if he gets a tails immediately followed by a heads for the first time.

Who has the more probability of winning?

• Possible duplicate of Who has more probability of winning the game? – lulu Apr 9 '19 at 14:41
• Note: I have retracted my close vote because, on re-reading, the questions are not exact duplicates. In the linked question, the two players were working off a single coin. Here, with two coins, the problem is different. In particular, the answer is obviously not $\frac 12$ each since, if nothing else, there is a possibility of a tie. – lulu Apr 9 '19 at 14:49
• Nevertheless, the same techniques apply. Just describe the possible states of the game (there are not many) and look at the possible transitions between the states, – lulu Apr 9 '19 at 14:55
• Does each person have one coin or two? In the latter case, does only the last toss of the coins matter (assuming that the coins are tossed "consecutive")? – user Apr 9 '19 at 15:00

## 1 Answer

The sample space is (HHHH, HHTH, HHHT, HTHH, THHH, TTHH, HTTH, THHT, THTH, HTHT, HHTT, TTTH, HTTT, THTT, TTHT, TTTT). therefore each person has equal possibilities of winning i.e 2/7.