This week, ‘Poker After Dark’ is running what they are calling a “Rail Heaven” cash game. Blinds are $200/$400, and the players assembled are veritable who’s who of poker heavyweights: Phil Ivey, Tom “Durrrr” Dwan, Phil Hellmuth, Patrick Antonius, Daniel Negreanu, and Gus Hansen round out the rail-worthy six. Combined that’s 6 WPT titles, 22 WSOP bracelets, and untold fortunes won on the cash game felt.

When this episode was filmed last year, much of the talk centred around the first hand the group played: all-in blind, $100,000 a man. Well the hand in question finally aired last night (in the second episode of the week, for some reason), and it is as entertaining a poker hand as one could find, baring in mind that none of the players made any decisions (besides the very first reckless one).

Here’s how it all went down:

So since 5 of the 6 players put up $100,000, with Hellmuth opting to blind-fold for the cost of a $100 ante, we have $500,100 in the pot preflop. I thought it would be interesting to see, mathematically, just how much equity each player had at each point in the hand.

Preflop:

Player, Equity% {hand}, $EV
Tom Dwan, 17.674% { 5d4d }, -$11,612.33
Phil Ivey, 14.354% { 9d8h }, -$28,215.65
Gus Hansen, 27.123% { Tc9c }, $35,642.12
Daniel Negreanu, 11.494% { Ts6h }, -$42,518.51
Patrick Antonius, 29.355% { Ah5h }, $46,804.35

At this point, Patrick is in the best shape. His hand is expected to win 29.355% of the time, so his equity is $146,804.36 ($500,100 x 29.355%). Which means that he should profit, on average, $46,804.36 from this hand . Gus is in good shape with $35,642.12. Daniel, the last one into the bet, has the worst equity. He should expect to lose $42,518.51.

This actually is very instructive, in terms of evaluating preflop equity in No Limit Hold ‘Em. You can see quite clearly how Daniel’s hand, which is dominated in almost every way (he has a spade draw, basically, and can hit a miracle six), is not that far behind the other, more connected hands.

Flop:

Board: 5s 7s Jd

Player, Equity% {hand}, $EV
Tom Dwan, 11.606% { 5d4d }, -$41,958.39
Phil Ivey, 20.175% { 9d8h }, $895.18
Gus Hansen, 18.893% { Tc9c }, -$5,516.11
Daniel Negreanu, 7.895% { Ts6h }, -$60,517.11
Patrick Antonius, 41.430% { Ah5h }, $107,191.43

Obviously the flop goes a long way towards deciding just who has a chance to scoop this pot. Patrick improves to $107,191.43 average profit with his lowly pair of fives. Gus lost a lot of his equity by almost completely missing his draws; he can hit an 8 for a gutshot, but that’s unlikely seeing as one of his eights is in his Phil’s hand. Ivey, for his part, makes great gains, picking up a double-gutshot. Any 6 or 10 will make him a straight. But 3 of those outs are gone, so it’s not all rosy. Dwan hit his five, but is in rough shape, being outkicked by Patrick. He can only really hit a 4, or pick up a draw on the turn. Daniel, still, is floundering. His 6 is no good, because it fills Ivey’s straight. Basically he’s looking for running spades to hit the flush.

Turn:

Board: 5s 7s Jd 3h

Player, Equity% {hand}, $EV
Tom Dwan, 00.000% { 5d4d }, -$100,000.00
Phil Ivey, 13.158% { 9d8h }, -$34,196.84
Gus Hansen, 13.158% { Tc9c }, -$34,196.84
Daniel Negreanu, 7.895% { Ts6h }, -$60,517.11
Patrick Antonius, 65.789% { Ah5h }, $229,010.79

Dwan is now drawing dead. His 4 is no good, because it gives Daniel a straight. If he makes a straight with a 6, it would give Phil higher straight. Tom’s succinct summary of his predicament is the highlight of the video. Daniel is drawing to the three 4’s left in the deck for his straight. Phil and Gus both have five outs a piece: Phil can make a straight with one of two 10’s or one of three 6’s; Gus can pair one of two 9’s, or fill his gutshot with one of three 8’s. That leaves Patrick and his pair of fives, still in the lead, and looking to dodge 13 outs. He is the only one, at this point, who can expect to show an average profit from the hand, with a whopping $229,010.79.

River:

Jack of spades, shipping Patrick the pot with… a pair of fives!

Patrick came out ahead, in this spot, profiting $400,100 from the hand (plus additional sidebets). The other four players who went all-in blind each lost $100,000. And Phil Hellmuth, for once, came out looking like a genius, only losing his $100 ante (note: he folded Kd2c; if he had put up the $100k and played, he would’ve been in worse shape than even Daniel… good fold, Phil!).

Update: Oops, they did it again! This time, y’all can do the math yourselves. I’m just going to watch the carnage:

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