Bust on Ten | PuzzledQuant

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New on YouTube: This HRT Quant Interview Question Has a One-Line Answer - Watch now

⚡ Build the skills to land top-paying quant jobs. Offer ends in 25d 09h 51m 13s25 days 9 hours 51 minutes 13 seconds.

A player repeatedly rolls a fair ten-sided die (faces 1 through 10).

If the player rolls a 10, the game ends immediately and the player wins nothing.
After any other roll, the player may either stop and collect a payout equal to that roll's value, or roll again under the same rules.

Assuming the player plays to maximise expected winnings, what is the expected payout of the game (in the same units as the die values)?

A player repeatedly rolls a fair ten-sided die (faces 1 through 10).

If the player rolls a 10, the game ends immediately and the player wins nothing.
After any other roll, the player may either stop and collect a payout equal to that roll's value, or roll again under the same rules.

Assuming the player plays to maximise expected winnings, what is the expected payout of the game (in the same units as the die values)?