If A plays first and the one who rolls a 5 first wins: If A wins, B gets fewer rolls than A. If B wins, A gets the same number of rolls as B. So the game is unfair (in favor of A) and [prob A winning]>[prob B winning]. There is also the possibility that there is no winner within these 5 rounds of rolls.

- roll 1:
win A= 1/6win B= (5/6)*(1/6)no win= 1-(11/36)- roll 2:
win A= (1/6)*(25/36)win B= (5/6)*(1/6)*(25/36)no win= 1-(275/1296)- roll 3:
win A= (1/6)*(1021/1296)win B= (5/6)*(1/6)*(1021/1296)no win= 1-(11231/46656)- roll 4:
win A= (1/6)*(35425/46656)win B= (5/6)*(1/6)*(35425/46656)no win= 1-(389675/1679616)- roll 5:
win A= (1/6)*(1289941/1679616)win B= (5/6)*(1/6)*(1289941/1679616)no win= 1-(14189351/60466176)

Totals:

win A= (40406838/60466176)/5= 0.133651044841995630747345424986028552558045013463 3948win B= (33672365/60466176)/5= 0.111375870701663025622787854155023793798370844552 8290no win= (168361825/60466176)/5= 0.754973084456341343629866720858947653643584141983 7761