# It's a toss-up ....

A game is played with a fair coin where you are asked to toss the coin $$10$$ times. If you make it through the $$10$$ tosses without tossing a sequence of either $$3$$ (or more) consecutive heads or $$3$$ (or more) consecutive tails in a row then you win $$5$$, otherwise you pay $$1$$.

Your expected monetary return, (in dollars), after playing this game $$100$$ times is $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. Find $$a + b$$.

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