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We have pawn on a board and we roll dice maximally two times. When we roll six we can roll dice again. We move pawn as many times as we threw dots. What's the expected value of move on the board.

Am i thinking correctly ?

$$E(X)= 1 \cdot \frac16 + 2 \cdot \frac16 + 3 \cdot \frac16 + 4 \cdot \frac16 + 5 \cdot \frac16 + 7 \cdot \frac1{36} + 8 \cdot \frac1{36} \\ \qquad + 9 \cdot \frac1{36} + 10 \cdot \frac1{36} + 11 \cdot \frac1{36} + 12 \cdot \frac1{36} $$

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Yes

Alternatively the expectation for the first die is $3.5$ and for the second (which may not be thrown) is $\frac16 \times {3.5}$ and you can add these together

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