The Problem With M

So on Wednesday I was writing about Arnold Snyder's view on how the tight style of play espoused by Dan Harrington's seminal books on Holdem tournament play actually is far too tight to give oneself the best possible chance in poker tournaments. Actually, first let me get to the comments I received.

I should not have to keep pointing this out, but this is my blog. It's a journal. I write whatever I am thinking about and want to write about with the game of poker, or otherwise. You don't have to read here if you don't like what I have to say, or if you don't think I know my ass from first base about the game, or if you don't like the mix of poker and non-poker topics I write about here. I can see that it is so difficult for some of you to stay away regardless of your feelings about what I have to say, but I will suggest that you read this blog for what it is: my thoughts on poker. It's not your thoughts; it's my thoughts. It's not my suggestions for how you play the game; it's just my thoughts about the game. So the next time you are tempted to spout off in the comments how stupid it would be for you play the way I'm writing about, please check yourself. No one ever said you should play the way I write about, or even believe what I'm saying at all. If you find it hard to think of what you read here in this way, perhaps you might want to take some time away from this blog and try to calm it down. Now that's a suggestion for how you act, one of the few times you'll get those little tidbits to live by here.

Oh I should also point out that Arnold Snyder makes a specific point -- and I agree with this statement as well -- that Dan Harrington himself is not a Harringbot. So pointing out the amount of Harrington's lifetime mtt cashes does not actually address the point Snyder makes about the style espoused in Harrington's books. Harrington's books espouse a tight style of play, that much is not debatable, and he does not advocate opening things up in his writings until one's M falls below 20 at any point in a tournament, regardless of the structure. An M above 20 puts you in the green zone, and while Harrington may support making a move here or there in particular when first in the pot, I hope it is obvious to those that have read his tournament books that the approach Harrington suggests is quite the tight style of play. For those who did not get that from Harrington's books, hmmmmmmm. I don't really know what to say about that I guess. But it is what the rest of the goddam free world I took from his books, and they are and I imagine always will be considered among the very best tournament holdem books ever written.

But, getting back to today's topic of my thoughts on my blog, Harrington's calculation of M does include a potentially very serious flaw. Harrington describes "M" again as "the number of rounds of the table that you can survive before being blinded off, assuming you play no pots in the meantime". Thus, if your M is 11, you can sit at the table for 11 more rounds of play without playing a hand and still survive. So at a 10-handed table, you would have approximately 110 hands of poker left to sit and not play a hand and still survive in the tournament. That's M, in a nutshell, using Harrington's own words from his books.

The flaw with M, as pointed out quite correctly by Arnold Snyder, is that is completely ignores the crucial aspect of tournament structure in making its calculation. A few sample tournament situations I think make this crystal clear. Again, keep in mind that on page 126 of HOH II, Harrington himself defines M as "the number of rounds of the table that you can survive before being blinded off, assuming you play no pots in the meantime". So let's assume for purposes of illustration that you are roughly halfway through the field in a 1000-person mtt. You have 30,000 in chips, and blinds are 500-1000 with no ante. Thus, according to Harrington's formula, the cost of one round of folding is 1500 chips, and thus your M equals 20. So according to Harrington, you could sit at this table for 20 more rounds -- 200 hands if you're playing 10-handed -- and still survive in the tournament.

But now let's think about the structure of our hypothetical tournament above. Let's say you're playing one of the deep-stack live tournaments out there -- let's just say it's the WSOP Main Event with its 120-minute blinds, and you're just at the beginning of the 500-1000 blinds round, so you've got the full 120 minutes left at this level. In 120 minutes -- let's call that 60 hands at 2 minutes per hand just for ease of calculation here -- the blinds will go up to 600-1200. Then in another 120 minutes (60 more hands) they will be 800-1600. 60 hands later they will go up to 1000-2000 with a 50-chip ante. So, in reality, in this 120-minute blind-round tournament, 200 hands is not actually "the number of rounds of the table that you can survive before being blinded off, assuming you play no pots in the meantime" (Harrington's exact words). In reality, assuming again you are right at the beginning of the latest round of blinds, after 60 hands you will have blinded away 6 rounds' worth of blinds at 1500 chips per round for a total of 9000 chips, so you're down to 21,000 when the blinds bump up to 600-1200. So, after hands 60-120, you blind away another 6 rounds worth at 1800 chips per round, subtracting another 10,800 chips from your stack and leaving you with just 10,200 chips remaining. Then starting with hand #121, the blinds go up to 800-1600, making the cost per round at your 10-handed table 2400 chips. This means that, with 10,200 chips at the start of this third round, you're barely going to last 4 more rounds, depending on your position at the beginning of the round. Let's just pick 40 hands (four full rounds) left of survival as a good average outcome there.

So, you can see what the tournament structure did to Harrington's analysis that with 30,000 chips and 500-1000 blinds, you could sit for 20 more rounds at that table without playing a pot and stil be alive in the tournament. In reality, factoring in the tournament structure, you could only actually survive without playing a pot for 60 hands at 500-1000, 60 hands at 600-1200, and then 40 hands at 800-1600. That's only 160 hands, not the 200 Harrington's M calculation indicated.

Now you may be sitting there thinking "So what?" Harrington's M calculation ends up being a little off as the blinds go up, big deal? And there's some validity in my view to that comment. But I purposefully started with the slowest tournament structure known to man up there -- the 120-minute blind rounds -- to illustrate the method Snyder uses to make his point. Now let's get a little more realistic, as probably 1% or less of you out there reading this have ever actually played in a tournament with 120-minute blinds. Let's take the more standard live casino tournament structure like what I've played several times in Atlantic City, with the blind rounds are much shorter, say at 30 minutes. Same situation otherwise -- halway through the field, 30,000 chips in your stack, blinds of 500-1000, with no ante until the 1000-2000 blind level. Again, Harrington's M formula indicates that you have an M of 20, and that thus you can sit without playing a pot for 200 hands and still survive in the tournament. But look -- after 30 minutes (15 hands), you've played an average of 1.5 rounds, and you've paid an average of 2250 in blinds (your chipstack is down to 27,750). Then the blinds then become 600-1200, where over the next 15 hands you will play another 1.5 rounds on average and ante another 2700 in chips on average, bringing your stack down to 25,050. Then another 15 hands of 800-1600 play, anteing an average of 3200 and bringing your stack down to 21,850. Then another 15 hands at 1000-2000 plus the 50-chip ante, costing 3500 chips at a 10-handed table, and leading to an average blinds + antes of 5250, dropping your stack down to 16,600. Then let's say the next round is 1200-2400 with a 100-chip ante, making the total cost per round 4600 chips and costing you an average of 6900 chips to fold through a round and a half for another 15 minutes. This leaves your chip stack down at 9700. Next 15 hands is 1500-3000 with a 150-chip ante, costing 6000 chips per round, and you are basically done after this round costs you an average of 9000 chips.

So let's count that up. You played 15 hands at 500-1000, 15 hands at 600-1200, 15 hands at 800-1600, 15 hands at 1000-2000-50, 15 hands at 1200-2400-100, and 15 hands at 1500-3000-150. Let's throw in another 5 hands or so to take up the last few chips you have in the following round, and how many total hands did you get to play in that 30-minute-blinds tournament? That my friends is 95 hands. A far cry from the 200 hands Harrington's M formula said you could sit and fold through. In fact, his number was more than 100% higher than the true number of hands you could sit and fold in.

And now let's kick it up a notch again, but not to anything unrealistic. Let's just look at the standard online tournament, like "the" nightly 28k for example. 10-minute blind rounds. Otherwise, same situation. At a hand a minute (quicker since it's online instead of live play), that is one orbit per blind round. This would be the same calculation for a live tournament with 20-minute blind rounds, just like the daily tournaments at the Taj Mahal and some other places in AC. Now you're playing only 10 hands per round (instead of 15 in the immediately preceding example), so you pay 1500 in chips at the 500-1000 level (down to 28,500 chips), you pay 1800 chips at the 600-1200 level (26,700 left), 2400 chips at the 800-1600 level (24,300 left), 3500 chips at the 1000-2000-50 level (20,800 left), 4600 chips at the 1200-2400-100 level (16,200 chips), 6000 chips at the 1500-3000-150 level (10,200 chips left), and then at then next level, let's call it 2000-4000 with a 200 ante, that's another 8000 chips again, leaving you with just 2,200 chips left and not even enough to put up the small blind when the next round begins. We can call that on average another 5 hands in the next round before you're out. So with the 10-minute online levels (or 20-minute live blind levels like at the Taj), you played 75 hands. An even further cry from the 200 hands Harrington's formula said you could sit and fold through while still surviving in the tournament.

And this is exactly the point made by Snyder all through his book. Harrington's approach as espoused in his books is about survival more than anything else. But the problem is, the survival numbers that Harrington's M formula calculates are in most cases more than twice as high as the actual number of rounds that a player can expect to survive by folding. This is why Harrington's strategies, including his general approach of not opening up one's game much with an M of more than 20, do not lead to many final table runs and big scores, but rather lead the Harringbots to pushing allin on medium to small stacks halfway through the field of the large-field mtts. Because when your M according to Harrington is 20, that doesn't really mean you have 20 more rounds to sit and fold. You typically have fewer than 10 rounds left or survival once you take into account the tournament's structure. The third example I gave above is sadly by far the most common and certainly the most realistic for anyone who likes to play online mtts. If you've played a lot of online mtts and haven't had the success you would like, and you're playing some form of Dan Harrington's strategy from his HOH books, then this could be why. When Harrington says your M is 20, your "Real M" is really more like 6 or 7 in most cases. And you don't even want to see the "Real M" calculations with the turbo tournaments or just the "regular" online mtts with blind rounds of less than 10 minutes, or the widely-prevalent live tournaments nowadays with 15-minute blind rounds. Then Harrington is overestimating your "Real M" by usually a factor of three or four, or more.

If you knew when your Harrington M was 20 that your "Real M" was 5 or 6, wouldn't you play a lot looser? Wouldn't you see your situation for what it is -- far more desperate than Harrington's "Green Zone" M of 20 indicates? This is one of the huge secrets that the world's great multi-table tournament players understand better than everyone else. And it's why the Harringbots -- which again, Dan Harrington himself is clearly not one of -- are usually such easy pickings for the guys who are playing big, opening up their games when their "Real M" is getting low, the guys muscling and bullying everyone at the table.

Chew on that one for the weekend, and I'll be back next week with more of my poker thoughts inspired by the great book The Poker Tournament Formula II.