### Probability to win Einstein forum

2 replies. Last post: 2013-09-05

Probability to win
• Carroll ★ at 2006-03-14

Suppose both player have probability q to win on next move, and otherwise, after one move each, situation has about same probabilities :
P(1st player win)=1/(2-q) P(2nd player win)=(1-q)/(2-q)

If q (1st player) and r (2nd player) are different, it is a bit more complicated: P(1st player)=1/(1+r/q r).

Here is a short table with q and r from 1/6 to 5/6

`  | r\q | 1/6  2/6  3/6  4/6   5/6  |  +----+--------------------------+  | 1/6 | 6/11 3/4  6/7 12/13 30/31 |  | 2/6 | 3/8  3/5  3/4  6/7  15/16 |  | 3/6 | 2/7  1/2  2/3  4/5  10/11 |  | 4/6 | 3/13 3/7  3/5  3/4  15/17 |  | 5/6 | 6/31 3/8  6/11 12/17 6/7  |  ---------------------------------So it is interesting to note that if both have 1/6 to win in one, 1st player has better chances with 6/11, and the same if you have a piece which moves with 1/2 to win next move against a piece of your opponent which has 5/6 !`

• Carroll ★ at 2013-09-05

As textile eated my formating, I repost the formula for probability of q (1st player) to win:

1/(1+r/q-r)

... well it was back in 2006 3,14