If I am playing a game, and I'm trying to decide whether to choose option A or option B for my next move (neither option has a 100% success rate), given the following probabilities, what is the minimum success probability in order to choose option B?
Option A Success Probability: 70%
Win Probability after option A is successful: 56%
- Win Probability after option A is unsuccessful: 45%
- Win Probability after option B is successful: 60%
- Win Probability after option B is unsuccessful: 46%
I was thinking that the total probability of winning given option A would be calculated with:
(0.56*0.7) + (0.45*0.3) = 0.527
And then, try and solve for the success probability of option B by doing the following:
(0.6*x) + (0.46*(1-x)) = 0.528 (having a total win rate higher than option A)
0.6x + 0.46 - 0.46x = 0.528
0.14x = 0.068
x = 0.486
However, I'm not entirely confident this is the correct answer and would like to see if anyone had any other thoughts.