Hi. I could not follow your calculation with the graph. But I'll calculate the probabilities that A or B wins in two ways.Originally Posted by Dartgen
If i interpret the rules correctly, A wins if an odd product occurs in any of the first three rolls. B wins otherwise. That's the same as saying B wins if an even product occurs in each of the first three rolls. The game never goes beyond 3 rolls.
So B wins if an even product occurs 3 times in a row. The probability is as you say The probability that A wins is
To calculate this in another way, use A wins if an odd product occurs in any of the first three rolls. This probability is
the same as above.
I hope that helps.