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FiveThirtyEight

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Last poker post. I promise. Then it’s back to “normal” around here.

I was eliminated from the World Series of Poker late yesterday evening after more than 15 hours of play over two days. The hand on which I managed to eliminate myself was oddly and almost emblematically reflective of the declaration I made earlier, which is that I was “willing to gamble chips in certain somewhat marginal situations that mostly boil down to luck.” But first, a note on how I got there — warning: nerdy, detailed poker content follows!

I started the second day with about 60,000 chips. I ran this total to as high as 105,000 about an hour or two after the start of play, as I picked up some decent hands early and won some medium-sized pots. But that number was grdually whittled down over the course of the afternoon — not in any one particularly dramatic fashion, but rather via a number of hands where I might put 5,000 or 10,000 into the pot as the aggressor and ran into opponents who either caught some kind of hand or were willing to pretend that they did. I don’t think I played these hands badly — if you raise before the flop with KQ (king-queen), get a caller or two, and the flop comes down something “dry” like A82, it is usually correct to put at least one more bet into the pot when checked to. Your opponents will have a very difficult time continuing unless they have an ace or a set (three of a kind) of 8’s or 2’s, and you will win the pot right there against both better and worse hands.

But sometimes your opponent will in fact have a decent ace or something stronger and this “good” gamble will turn out badly — this is just one of the hundreds of forms of bad luck in poker. Of course, matters can be complicated greatly if your opponents are willing to pretend that they have an ace even when they don’t — and I may have been running into a little bit of that too. From a ‘meta’ perspective, my play may have appeared to lack finesse and veer too much toward the tight and predictable side. This wasn’t entirely the case — in fact, I had in fact run a couple of moderately gutsy bluffs — the problem was that they were successful so my opponents never saw my hand. I could have showed the bluffs after my opponents folded, of course, which is usually a beginners’ move, but may have been correct in this instance. In any event, it’s one thing to say in the abstract that, say, “against opponents who are capable of bluffing, you sometimes have to re-bluff the bluffer”, and another thing to actually find the right time to apply that principle in any particular hand at the poker table — and another thing still for that play to work to your advantage later in the afternoon.

In any event, by the time I got to the elimination hand, I was down to slightly under 50,000 chips. I think the number was closer to 45,000, in fact, but we’ll call it 47,500 because it will make the math work out conveniently down below. I was not exactly a short stack, but was well below the average of about 80,000 chips and was going to be fairly happy to take an opportunity to gamble. This was especially so after a loose, extremely poor opponent to my right had been eliminated — I had been playing somewhat conservatively before that because I knew there was a decent chance of getting all my chips in against him as a heavy favorite.

The hand that I picked up was pair of red 9’s. A fairly loose opponent — a young kid with hairy arms and sunglasses — made a “standard” raise of about 2,500 chips ahead of me. I re-raised him to 7,500. I’d be happy to have this opponent either fold, in which case I’d pick up a few chips at no additional risk, or call, in which case I’d have position on him after the flop with a hand I felt pretty good about. The only thing I didn’t want to see was a re-raise, because my stack was short enough that I’d probably be making a decision for all my chips.

But Hairy Arms didn’t get a chance to re-raise. Instead a third opponent in late position did. This was not someone I wanted to see get involved in the hand — he was a good, fairly tight, respectful player with a big stack in late position. Moreover, with two other players already involved in the hand, both of whom had raised, it was unlikely that he was making some sort of squeeze play. This was in all probability some kind of very good to outstanding hand, and the amount of the raise was large enough as to effectively put me all-in. The hairy-armed kid folded, which left the decision up to me.

I knew I was behind the good player’s range of possible hands. The question was exactly how far behind, because the pot was offering me a bit of a discount. I had roughly 40,000 chips left. If I gambled those, I had a chance to win 60,000: the 47,500 the good player had committed to the pot, the 7,500 I’d bet earlier and could now only recover by remaining in the hand, the 2,500 that Hairy Arms had abandoned, and another roughly 2,500 in blinds and antes. That meant I only had to wind up with the best hand 40 percent of the time for a call to be correct from the standpoint of maximizing my chips.

Against a larger pair like kings, queens, or aces, I’d be a heavy underdog — winning the pot only the 20 percent of the time or so that I pulled one of the two remaining 9’s out of the deck (without his hand also improving). On the other hand, I was a slight (roughly 53-55 percent) favorite against any unpaired hand like ace-king, and it’s a lot easier to have an unpaired hand than a paired one. There was also a slight — although probably extremely slight — chance that he’d make this re-raise with a smaller pair like 88, in which case I’d be the 4:1 favorite.

The question is exactly how tight the tight player was. About the tightest I could imagine him being in this spot would be to re-raise with AA, KK, QQ, AK, and half the time with JJ and AQs (a “suited” ace queen). Against that range, I was only about 35 percent to win the pot — less than the 40 percent I needed. (You can run these numbers yourself by downloading this program). On the other hand, suppose that his range was just slightly looser, and consisted of all pairs 88 and higher, plus AK, AQ (whether suited or not) and a suited KQ. In that case, I’d win the hand 43 percent of the time and would probably want to continue with the hand.

I recognized immediately that the decision was very close — I needed 40 percent of the pot to play on, and had somewhere between 35-43 percent. There were a couple of additional things that I thought about. First, there is some information in the fact that the hairy-armed kid had initially raised, and then folded. Odds are that did this with a hand consisting of two unpaired high cards — like AJ or KQ. Suppose, for instance, that this player had flipped over AJ as he’d folded. This is excellent news for me — it means that the good opponent was only half as likely to have AA and JJ, two of the hands that I didn’t want to run into — and also, that if he had AK, he’d be less likely to hit an ace on the board and improve to beat my pair. Of course, we don’t know that the hairy-armed kid had *exactly* AJ. But overall, his range of hands is worth an extra point or two’s worth of equity for me by deadening my opponent’s cards.

The other, more important thing I started to think about was how much “life” in the tournament was worth to me. This isn’t like a cash game, where if you go bust, you can reach into to your wallet and buy more chips. Once you go broke, you have to wait a year to play again.

There are a lot of good players that would never take this sort of gamble — their philosophy is that so long as you have a chip and a chair, you have a chance to win, and that being good players, they’ll find better spots to get their money in than what is essentially a breakeven decision. There are a couple of others — Chris Ferguson, for instance — that treat tournament chips almost exactly as they would cash game chips and aren’t willing to sacrifice very much equity at all for survival.

If I folded and opted for guaranteed survival, I’d have 40,000 chips left — not a cripplingly low amount, but enough that I’d probably have to make another all-in decision fairly soon. There has been very little work done on the relative values of different stack sizes — is an 80,000-chip stack worth exactly twice as much as a 40,000-chip stack? Less than twice as much? More than twice as much? Most of the theory points toward the “less than” answer, and this is almost certainly the case late in a tournament once everyone is in the money. But we were far from the cash bubble, and there is a lot more work to be done on what it means at this stage. Having a smaller stack limits your options in certain ways, but there are also elements of zugzwang in poker where having a limited set of options is helpful.

What was a little more tangible is that if I folded the hand, it probably meant I’d have to come back on play on Friday (after an off-day today) since there was only half an hour to go before that evening’s session ended. There is an opportunity cost to my being out here in Vegas — the time I spend at the poker tables is time I can’t spend working on the blog, working on my book, or doing consulting projects, all of which are very demanding on my time. Moreover, the fact of the matter is that even in my off-time, it’s just harder for me to get work done here than it is back at home in New York. With roughly 40,000 in chips, which is what I’d have if I’d folded, I’d probably have to at least triple and probably quadruple my stack to get into the money at the end of Day 3 — which meant that odds were I’d wind up staying for two additional days with little tangible return to show for it.

So let’s say, for instance, that I’m 38.5 percent to win against my opponent’s actual range of hands when I need 40.0 percent to continue; that means my decision would be incorrect by about 1,500 tournament chips. The cash value of 1,500 tournament chips is about $500. If folding means, say, 10 additional hours of lost productivity on average, that is worth quite a bit more to me than $500.

However, it’s easy to poke holes in this logic. For one thing, playing in the tournament is fun — otherwise I would not be doing it in the first place. And while I value my time highly, it is worth nowhere near as that of some top-flight professionals like Phil Ivey, who can make literally thousands of dollars an hour on average playing cash games. For the vast majority of players, both professional and amateur, playing the tournament is more of a lifestyle decision than a cash decision.

But for better or for worse, I was thinking about these things. If things had been just slightly different — if I had another 10,000 chips (or 10,000 fewer!), if the bad player on my right hadn’t busted on the previous hand, if my hand were tens rather than nines, I wouldn’t have had to think about them — my decision would be (comparatively) easy. Maybe I was thinking about them wrongly and maybe I shouldn’t have been thinking about them. But I was.

After about two minutes of contemplation, I called and went all-in for my few remaining chips, instantly regretting it, hoping for the best but expecting the worst. My opponent flipped over pocket queens, the board bricked off, and I shook his hand and went to get a beer.

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