A Mod Math Challenge: The Famous 44 RGP Hand

[W. Deranged]

So I was reading the new edition of Roy Cooke's Real Poker II (which I recommend), and read the description of the following famous RGP thread. The controversy, which broke down between Mason Malmuth, Gary Carson, and Abdul Jalib on one side and Daniel Negreanu and others on the other, involved the following hand:

Mason, our Grand Poobah, has 44 in the CO.

Pre-flop: 4 limpers to Mason who limps, Button raises, both blinds come along, all the limpers call.

Flop (8 players, 16 sb): 9[img]/images/graemlins/diamond.gif[/img] 8[img]/images/graemlins/club.gif[/img] 3[img]/images/graemlins/diamond.gif[/img]

(suits might be slightly different, but there's a flush draw)

SB bets, BB calls, all four limpers call, Mason...?


So, Mason's getting 22-1, interestingly enough.

Roy Cooke explains the following dynamic: If Mason were 100% confident that the button would never raise, obviously calling is correct. If Mason were 100% sure the button would raise, calling is clearly incorrect. So this got me a-thinkin'.

THE CHALLENGE

Determine how often the button must raise for calling and folding to be equal EV.

I have no idea what the answer is, but I'm interested to see what sort of stuff you guys come up with.