This challenge concerns a game for two players, played using one fair cubical die numbered 1 - 6. 

There are also two "winning rule" cards: on card A the rule is that the person with the card wins if the score is 2 or 4 and on card B, the person with the card wins if the score is odd. 

Our players are called Sasha and Tasha.

Cards A and B are given out so the players have one each. Sasha and Tasha take turns to throw the die, Sasha throws first. (It doesn't matter who throws the die, it's just fairer to take turns!) 

If the die shows a 6 at any point, then the players swap their "winning rule" cards and the die is thrown again.

Here's an example game:

Sasha gets card A and Tasha gets card B. Sasha throws first and gets a 6, so no-one wins but on the next go, after swapping cards A and B, Sasha will win if the score is odd and Tasha will win if it is 2 or 4.

Now Tasha throws the die, and gets a 6, so again no-one wins but having swapped the cards again, on the next go, Sasha will win if the score is 2 or 4 and Tasha will win if it is odd.

Next Sasha throws a 3, so Tasha wins.

Here's the question!

What is the probability that you will win this game if you start with card B?