[rakewell]

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When Phil makes the insurance bet at the end, he says he's insuring against a J or 9, giving Eli 8 wins out of 44 and him 6. He uses these numbers to make the deal, saying that he is insuring against a J or 9 hitting the river. Then, when river comes Q, he says, "chop pot no one pays insurance". It seems like with the specific "no J no 9" bet he made he should have lost the insurance bet and had to pay, regardless of the fact that the pot was chopped.

Or am I wrong?

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That seems right to me, since he didn't specify that a Q would mean no payment either way. Or perhaps in such deals it's understood that no money goes either way if it's a chop.

But I was more curious about Phil's math. He was admirably quick, but way off, I believe.

Here's the situation: Phil has K7 against Eli's K9 on a board of 10-Q-K-7, no flushes possible. Q splits the pot. Eli wins with a 9 or a J.

Phil says that Eli has 8 outs, which is his first mistake. There are only 7 (3 9s and 4 jacks). Assuming that the three remaining queens are out of the equation (because, apparently, Phil's understanding is that they're a wash on his insurance deal), there are 7 unknown cards that win for Eli and 41 for Phil. (I'm ignoring the cards seen by the hole cameras, since they're unknown to the people involved in the transaction--except that those offered the deal have slightly more information about mucked cards, which I'm going to disregard.Sammy folded a 9, which is the only relevant card we viewers got to see.) 41:7 is 5.86:1, but Phil says it's "36 to 8, 4 1/2 to 1."

Based on that, he asks for insurance at 4:1 (his $10,000 buys him $40,000 from Brandon Adams if a J or 9 hits on the river). He claims that since the actual odds are 4.5:1, and his insurance offer is 4:1, the insurer(s) are getting 12.5% juice. He's apparently figuring this as (4.5-4)/4 = 0.125.

But since the actual odds are 5.86:1, the "juice," calculated the same way, is actually a whopping 46.5%, because (5.86 - 4)/4 = 0.465. That is, Phil was off by a factor of almost 4.

It's even worse if you include the queens as wins for Phil, as he seems to imply in his "36 cards for me, 8 for Eli" comment. That would make the odds 44:7, or 6.29:1, which then means 57% "juice" by Phil's method of calculation.

Looks to me like Adams has an expected value of about $2700 on the offer. (Showing my work: If they ran it 48 times, Phil pays $10,000 41 of those, and collects $40,000 7 times, for a net loss of $130,000. $130,000/48 = $2708.) Hence Negreanu's question to Phil, "What is it about money that you hate?"

Adams took the deal, which apparently means that he's better at math than Hellmuth, less afraid of variance, or both. I'm thinking "both."

Anybody see the numbers any differently here?