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Just wondering, what's the rationale behind the first equation?

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I think I can explain this one:

Just as the second equation stems from determining player B's cutoff based on player A's cutoff, the first equation stems from player A's cutoff based on player B's cutoff.

If A draws, B will draw with anything <0.5, and stand with anything >0.5. So, if A draws, then 50% of the time, when B draws, A will win 1/2 the time, while the other 50% of the time, when B stays, B will on average have 0.75, so A will win 1/4 of the time. So when A draws, he can expect to win (0.5)*(1/2)+(0.5)*(1/4) = 3/8 of the time.

When A stands, his expectation is simply X*y (since A will lose whenever Y>y, and will have expectation X when B draws, which he will do fraction y of the time.

So A's cutoff is related to B's cutoff by x*y = 3/8.