Dicey Probability

Satvik and Agnishom are playing a game with 22 standard dice. Both the dice are rolled together and the total is counted.

Satvik says that a total of 22 will be rolled first.

Agnishom, whereas, says that two Consecutive totals of 7s7's will be rolled first.

They keep rolling the dice till one of them wins!

The probability that Satvik wins the game can be expressed as ab\dfrac{a}{b} where aa and bb are co-prime positive integers.

Find the value of a+ba+b.

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