Quote:
Originally Posted by Faustfan
So I saw this problem in two different books now and both times with the same explanation I think is wrong. Since i dont know how to upload a diagram i will explain the situation, which is pretty simple.
both sides have only two checkers left, both on the 2point (23point)
now it says, that the player to move should double, which obviously is correct. but then it says, the other player should take, because the first player will win only 26/36th of the time, which is wrong.
true, the player to move will win immediately with 26 out of 36 throws. but even if he misses, he will win 10/36 of the remaining time, making him a 80% favorite to win.
I did the complete EV-calculation for this scenario and the fact, that player 2 will redouble and player 1 has to take turns it into a take with an EV of -0.95.
but the explanation really threw me off, because it was obvious to me, that player 2 had a chance smaller than 25% to win.
is the total winning percantage irrelevant if there is still the possibility to redouble? I am having trouble to fully understand the mathematics of these situations.
Your analysis is correct. I wrestled with including the complete explanation when I wrote the book, but decided to leave it in its very simplified (but technically incorrect form) because the book's audience was complete beginners, and I didn't want to lose them. I figured the potentially interested players who saw the real problem could figure out the math for themselves.
And so you did!