Sunday, June 17, 2007

Canada Cal's Coach's Corner: Blinds Progression and Payout Structures in the End Game

Canada Cal here, still on temporary duty for Haley, on convalescent leave---

Today we'll look at a common situation for the discerning online player, that being arriving in the end stages of a smallish online tournament with a stack that might seem healthy, but when compared to the size of the blinds and antes, really isn't.

All tournaments devolve into 'pushfests' in their last stages. That's what tournaments are designed to do, after all, with their ever-increasing blinds: to force those chips into the middle, produce some action, and declare a winner.

However, the blind structures from one tourmanent to the next are often not just different, but are in fact radically different. The same goes for payouts. Some structures are comparatively flat, with not much of a jump from one spot to the next, while others climb sharply higher with each successive knockout. Because of this, there are situations that occur where what might seem an obvious play in one circumstance might be a questionable play in another, even though the setup looks the same. It's the blinds, baby, (and the payouts) and those blinds are gonna eat you up, sooner or later. But how soon is too soon or too late, when trying to optimize your payday, in terms of reacting to that pressure?

Managing a short stack properly in a tournament's end stages is essential to bankroll accumulation. Let's look an example to illustrate the problem.

The setup: Five players remaining in a smallish online tournament. The blinds are 3,000/6,000 with 300 antes. You have about 52,000 chips, about tied with another player for third place, with one player down to about 30,000, and the two leaders close to 150,000 each. You're already deep in the money, and the payouts for the top five spots go something like this, from the next one out up to the top:

5th: $600
4th: $700
3rd: $900
2nd: $1,800
1st: $2,700

You've already got the $600 guaranteed; it's the worst you're going to do. The spots below fifth were $500, $400 and $300, so this is an example of a very flat payout structure, with --- except for those two spots right at the top --- not a lot of relative difference between most spots.

Let's return to that poker scenario. Your "M" (as popularized by Dan Harrington, though he didn't invent it), is looking pretty sad. For five players, that's computed by dividing your total chips (52,000), by the sum of all the blinds and antes, which looks like this:

52,000 / [3,000 + 6,000 + (5 * 300)] =

52,000 / 10,500 =

= 4.95

That's an unhealthy M, but even the leader of the event has an M of only about 15. In other words, welcome to the end game.

Let's toss in one more little quirk, right from the example where this occurred. You're in the under-the-gun seat, and only seconds remain before the next level is scheduled to begin. That level will be 4,000/8,000 with 400 antes. In one hand, assuming you fold here, your M will shrink from 4.95 to this:

51,700 / [4,000 + 8,000 + (5 * 400)] =

51,700 / 14,000 =

= 3.69

But it's even less than that, because you'll be in the big blind on that next hand, meaning that 8,400 of your remaining 51,700 is already in the pot, leaving you only 43,300 with which to choose your play.

It's still 3,000/6,000, though, and you in the UTG seat discover you've been dealt... a pair of deuces. Given the scenario above, this is an auto-push. The reasons for pushing here are:

(a) You might capture the blinds and antes, bumping your M by about one and allowing you at least another round to wake up with a hand or at least find yourself in a better positional spot;

(b) Even though deuces are almost never ahead by much and in fact might be way behind, the odds are that you've got the best hand at the moment. The odds that a player has a pocket pair on any given hand are 1 in 17, or about 5.8%, and if they do have a pocket pair, it's almost 99% that it's not the other pair of deuces. (There are some minor clustering effects that also change the odds just slighty, but do not affect the point of this rough calculation in any meaningful way.) Anyhow, 5.8% * 4 (the other remaining players) = 23.2%, and it's actually about 23% that you're behind with your deuces at the moment. The other 77% of the time, you're ahead.

There are some factors that weigh against making a move from the UTG spot with a pair of deuces or some similar baby pair, in general terms. Those are:

(a) Savvier players would quite rightly be expecting you to steal in this spot, and they would be more likely to look you up with anything reasonable. 'Anything reasonable' from any player other than the short stack might be an ace, or K-Q or K-J suited, in general a fairly loose range that includes lots of other hands;

(b) You could always try to fold and move up a spot, or even two. Backing up the final-table board is a time-honored tradition.

Except here. This one isn't even close to a coin-flip judgment; you must push and hope for the best. In the circumstances described, the next two spots don't pay out much more (in percentage terms) than the fifth place you'd snag by exiting right here, as happened to me in this instance. The big stack to my left found A-J, thought it over... and made the call. I finished in fifth, with the other two shorter stacks assured of one more spot in pay due to my demise.

But, if I were to have any chance at all to win this thing, then I needed to make a move when I had the chance. I needed chips, and I needed chips at that moment.

Think about all the factors that came into play. Had fourth place been $900 instread of $700 with the fifth-place spot still being $600, then I'd have a much higher incentive to hope someone else could knock the shortest stack out. Likewise, too, if I'd had 20,000 or 30,000 more chips, I could have have assessed the likelihood of a call (and potential elimination of me) in a slightly different light. Every bit of increase in M allows for more leeway in decisions, but down in those low single digits, there's really little true choice to be made.

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