Tie to Win | PuzzledQuant

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 53m 09s25 days 9 hours 53 minutes 9 seconds.

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 53m 09s25 days 9 hours 53 minutes 9 seconds.

Zoe and Liam each have a fair 8-sided die (faces 1 to 8). They roll at the same time.

If the two dice show the same value, Liam wins.
If Liam rolls a strictly larger value than Zoe, Zoe wins.
If Zoe rolls a strictly larger value than Liam, nobody wins that round and they both roll again, repeating until one of the other two outcomes occurs.

What is the probability that Liam wins the game? Give an exact fraction.

Zoe and Liam each have a fair 8-sided die (faces 1 to 8). They roll at the same time.

If the two dice show the same value, Liam wins.
If Liam rolls a strictly larger value than Zoe, Zoe wins.
If Zoe rolls a strictly larger value than Liam, nobody wins that round and they both roll again, repeating until one of the other two outcomes occurs.

What is the probability that Liam wins the game? Give an exact fraction.