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/images/graemlins/diamond.gif 8/images/graemlins/club.gif 3/images/graemlins/diamond.gif

(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.

[milesdyson]

im not about to do this, but if i were going to i would want to know if we held the 4 of flush

[hobbsmann]

it is very important to know if MM has the 4/images/graemlins/diamond.gif

[W. Deranged]

Oh...yeah yeah yeah... I'm sorry I forgot that.

Mason DOES hold the 4/images/graemlins/diamond.gif.

In my opinion, without it, I think it's probably at least a marginal fold even if the button never raises.

[hobbsmann]

assumptions:

-the button will never fold so the times he doesn't raise we will be getting 23:1
-the times button raises sb never 3-bets and everybody else calls in which case we will effectively be getting 15:1 on our call.
-we will assume that our implied odds of hitting our set and the reverse implied odds of being up against a higher set effectively cancel.

Given these assumptions we need button to call more than or equal to 62.5% to be getting 20:1 on our call.

We will assume button is a solid TAG and thus will be raising a lot of suited connectors and large aces on the button as well as mid to large pairs. I would guess that less than 40% of this range warrents a raise on this flop and thus MM should be ok to call here, but I'll leave it to somebody else to come up a with a percentage of a hand range that will raise this flop.