Payout from blue beating red by three before a tie

A red and a blue fair ten-sided die (faces $1$–$10$) are rolled together repeatedly. When the two match, the game stops. Otherwise, if blue exceeds red by $3$ or more you earn $1, and in every non-matching case you roll again. What is your expected total winnings?

$14/5$. Per round, a tie has probability $\tfrac1{10}$ and a paying outcome $\tfrac{28}{100}$ (red $=k$ allows $8-k$ blue values, $k\le7$). The number of rounds is geometric, so expected earnings are $\tfrac{0.28}{0.1}=2.8$.