1st player rolls a pair of fair dice and if they jointly display 7 or 11 he wins, if not the 2nd player tries his luck and they take turns untill one of the goals is reached.
Since it clear to both of them that 1st player has higher chances to win than the second - the one that started becomes the second and they always play an even number of rounds.
Oney day A suggested the following modification:
1st player is one of us for the whole day, but while for
each of his wins he will get 10 bucks - for 2nd player's winning the reward will be 16 ...
Your choice today, be 1st or second !
What is your (the solver’s) advice?
