# Win probability of a dice contest mid-game

Five people are playing a dice contest, scoring is as follows: each person rolls a single die ten times. The ten rolls are totaled, highest total wins. Players may roll at their own pace. At a point in the contest, here is the score:

John: has rolled 9 times, 1 roll left (dice rolls: 3+1+2+6+5+5+2+1+6=31)
Paul: has rolled 2 times, 8 rolls left (dice rolls: 6+6=12)
George: has rolled 7 times, 3 rolls left (dice rolls: 2+6+5+2+1+5+2=23)
Ringo: has rolled 6 times, 4 rolls left (dice rolls: 3+3+3+5+2+4=20)
Yoko: hasn't started, 10 rolls left


What is the probability of each person winning the contest at this point in the game?

• Please show what you did and where you are stuck. – Jean-François Gagnon Nov 5 '15 at 13:48
• Having a hard time getting started, not sure what to google to see an example of a problem like this - suggestions? Thank you. – WatsonCat Nov 5 '15 at 14:03
• You could condition on the highest score. – Jean-François Gagnon Nov 5 '15 at 14:24