Aaron offers Berenice to play a game of dice with him. Aaron explains the game to Berenice as follows:

"We each get one die, the highest one wins. If we tie, I win, but since you always lose when you roll a one, if you roll a one you can roll it again. If you get a one the second time you have to keep it."

What is each person's probability of winning? What are the probabilities of winning if Berenice can keep rolling until she gets something besides a one?

For what it's worth, my sim started working and likewise confirmed.

lord@rabbit 12785 % dice             
  predictions A B
  0.513888896      0.486111104    
 sim A B, 10^6 rounds
 game            1
  0.513759613      0.486240387    
 game            2
  0.499957293      0.500042677    

Edited on November 14, 2022, 5:22 pm

Posted by Steven Lord on 2022-11-14 17:09:23