http://en.wikipedia.org/wiki/Walter_Penney
Here is a graph I made for this. To make it a fair game, instead of flipping coins until you reach a given state, throw 3 coins as one single event.
the arrows mean: ‘beats this choice’
from wikipedia:
| 1st player’s choice | 2nd player’s choice | Odds in favour of 2nd player |
|---|---|---|
| HHH | THH | 7 to 1 |
| HHT | THH | 3 to 1 |
| HTH | HHT | 2 to 1 |
| HTT | HHT | 2 to 1 |
| THH | TTH | 2 to 1 |
| THT | TTH | 2 to 1 |
| TTH | HTT | 3 to 1 |
| TTT | HTT | 7 to 1 |
