Finding rhythm in the madness (a theory)

[Irieguy]

I think we all often wonder exactly how beatable the SNGs are. What's the best we can do? Well, for what it's worth... here's what I think. The following pertains to PP single table SNGs (using the $11 limit as an example):

Since poker is a zero-sum game, we can only play well to the extent that our opponents play poorly. In the context of a 50-60 minute SNG, there is a limit to how poorly somebody can possibly play; and therefore, a limit to how much we can possibly win. I think the best place to start is to consider the worst error you can possibly make in a tournament: calling.

When you call, you give yourself no chance to win the pot right then, and you surrender betting impetus to your opponent, making it more difficult to win the pot later. You also surrender chips with the play (a very limited resource). So it's pretty bad to call. The more chips you call off, the worse the mistake is, and the earlier in a SNG you call, the worse you are playing. So specifically, the willingness to call all-in in the first level of a SNG is the single biggest mistake you can make. Fortunately, there is a limitless supply of people willing to call all-in with hands like A-4s, K-10, 66, etc. So, if you are unwilling to call all-in early, you will gain an advantage. Experience has shown me that you should be able to finish in 10th place about 3% of the time, 9th place about 5% of the time, and 8th place about 7% of the time. I think this is as good as you can do, and as bad as you can hope that others will play.

As you move out of the first 3 levels and down to the last 5-7 players, the biggest mistake you can make other than calling too much, is raising too infrequently. If you don't change gears, you will not find big hands often enough to keep up with the blinds, and you will be chronically short-stacked, which degrades your betting leverage and makes it very difficult to make the money without getting lucky. By raising more during these levels, you should finish 5th-7th a much greater percentage of the time than you should 8th-10th, but still less often than your opponents who are not raising enough. Experience leads me to think that the best you can do here with correct strategy is about 8%,9%, and 10% respectively. (More on the 10% number below)

Now the bubble. The difference in net monetary outcome between 4th and 3rd place is bigger than the difference between any other adjacent spots. So, if you are going broke in 4th place too often, you are making a huge mistake. It gets tricky here, because sometimes your opponents are playing too tight, and sometimes they are raising too much. But more importantly, they are almost always too willing to call. So, if you call even less frequently than you think you should, you are probably making money. Even though a 4th place percentage of 12% seems bad since it's worse than the average of 10%, a SNG strategy up to that point that stresses survival more than anything else is likely to land you in 4th place quite a bit. I think that is the right way to play, and I don't think you can do much better than 12% 4ths for those reasons.

So, if you add up all of those theoretically optimal percentages, you get 54%. That means the best In-The-Money (ITM%) percentage you can hope to accomplish at the $11 level is 46%.

Once you get into the money, the blinds are high, your opponents, on average, are better, and you will be short stacked quite frequently due to your survival-oriented/calling-averse (and correct) strategy. I don't think that under these circumstances you can hope to do better than an equal proportion of finishes in 1st-3rd. In fact, I suspect that optimal SNG strategy will result in end-game situations involving shortest-stack play so frequently that the best you can hope for is a preponderance of 2nd place finishes. In any case, the best way to estimate the limits of possibility for Return on Investment (ROI) is probably to assume an equal proportion of finishes 1st-3rd.

So, if the best ITM% you can hope for is 46%, your ROI will be 39% if you assume an equal percentage of finishes 1st-3rd.

That's my story for the $11 SNGs and I'm sticking with it.

At the $22 and $33 levels, you will see slightly fewer opponents willing to make the above mistakes, so the limits of possibility for success will adjust downward a percentage point or two each time you move up.

At the $55 level and up, the skill level continues to improve AND you get more chips. Those considerations require much more complex mid-game adjustments in strategy than you would have to contend with at the lower levels. I think the above theory would have to be modified quite a bit to come up with reasonably accurate estimates for the limits of profitability at those levels. Maybe somebody else would like to tackle that.

Comments and criticisms welcome, please.

Play the right way,
Irieguy