According to my superior calculations the chances of white winning are:

..........beep........beep...........

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679

percent chance of winning 


Yum! Pie!


Seriously, it would be interesting to see how many moves white could last...

wow... how very technical of you.

but still black wins

LOL technically this is an illegal position, because Black's queens and pawns can't total more than nine, but even without the pawns, White still has some questions to answer...

Obviously Qxf2# is the immediate threat, so White needs to disrupt the c- and f-queens' mutual control of f2.

1.f3 Qgg3+ 2.hxg3 (forced), followed by 2...Qexg3#

1.Nh3 covering f2 is no help at all, because Black has the simple response 1...Qhxh3 !  Nothing much helps here, perhaps 2.f3 with a similar idea to the above line: 2...Qgg3+ 3.hxg3 Qexg3#

The more conventional Nf3 is my personal favorite, sacrificing the knight to lengthen the pawn shield on f3 by one move: 1. Nf3 Qhxf3 2.gxf3 Qdxf3 with 3...Qcxf2# to follow.  Black has sacrificed two of his queens on the same square for a knight and a pawn...luckily, he still has seven more to execute the mate with!