Continuing the thought process from this thread:

http://forumserver.twoplustwo.com/18...takes-1665210/

- When playing a tournament, how do you estimate your % edge over the field?
- What is the real-world maximum possible edge?
- Let's say you know your ROI (which for live tournaments seems very difficult to get because it's just not possible to play tons and tons of live tournaments like you can online), how do you figure out where exactly that ROI comes from? We could start by discussing how you determine this online and then transition to how you would do it for live.

In terms of analyzing where the edge comes from, let's start with the simplest measure and then get more complex:

1. Does Hero cash in MTTs at a greater than random rate? That's easy to calculate online or with rudimentary live record-keeping. Keep track of tournaments that pay 10% of the field, 12%, 15% or whatever. See if Hero's cash rate for each type of tournament is higher or lower. This lets us know if the edge comes via a high survival rate early on.

2. When Hero cashes, does he come away with more or less money, on average, than random chance would suggest? (i.e. 500 people pay $100 each to play in an MTT, and the top 50 cash, with 10% taken out for the house, there's $45,000 to be won by 50 people, or an average $900/player.) This lets us know if the edge comes from winning play in the late stages leading up to the final table.

Beyond that, it would be nice to know if Hero clears various thresholds with more or fewer chips than the average surviving player. If Hero is usually the big stack halfway through, that suggests that crushing weak players fast is a major part of the edge. If Hero ramps up more slowly, that tells you that survival and opportunistic play later on is the source of the edge.

* * *

In terms of maximum achievable win rate, I'll nominate Phil Hellmuth as the right specimen for our lab study, even if we can argue about where exactly he ranks among the pros. The reason: Hellmuth for two decades has been systematically playing a ton of WSOP events every year. It's been well-known that he will do so, and it's easy to gather data on his performance, without worrying that we are accidentally catching a loaded sample that we belatedly got steered in a way that's very non-random.

Even if Hellmuth doesn't play as well outside the WSOP format, it's a big enough part of the poker tour that how he does there is a fine proxy for success in any player's most effective setting.

We don't know for sure how many events Hellmuth enters, because the WSOP doesn't publicize names of players who don't cash. But let's assume that he plays everything except the women's events, the casino dealers' events, and a few where he's traveled so deep in an earlier tournament that he can't get clear to register in the next one.

Some guy at Upswing Poker called Ryan has taken a first shot at the math, and has decided that if Hellmuth enters 40+ WSOP events every year, he has been achieving a 250% ROI. That's quite good. More detail is here: https://www.upswingpoker.com/how-goo...llmuth-really/

I'd been told years ago by tournament organizers that strong pros can achieve 100% ROI. This would suggest that 100% is not the ceiling.

This is a good starting point, but the sample size is still small. The times have also changed from say 2006 to now. How much? I'm not sure. Would be interesting if we could piece this together for a bunch of the top-earners; the trick is figuring out how many tournaments they actually played.

Nice answer RD.

It's important to make a distinction between your ROI/edge expectations in different types of tournaments and at different BIs, but I guess that's self evident.

One thing I've found interesting is that my ROI is lowest in low buy in events. The reasons are (i) I don't take them as seriously as I should (ii) other players are far more likely to take risks and it's hard to win five flips in a row even as fav, or to win while card-dead against calling stations.

Final point I'd make is that ROI changes as your table and opponents change throughout an event. I've had monstrous table draws and fought for my life an entire day, only to look at the next table to see people routinely stealing and restealing blinds, folding to single cbets etc.

I like to look at my BB/100 hands win rate, possibly in different buy-in ranges. Best would be to also have categories based on stack depth or tournament advancement (early vs late stages).
I know it's more of a cash game statistic, but mtts are just so high variance that I still think it would take multiple lives worth of online multitabling to determine a vague approximation of your edge based on cash results.
Sure, ITM percentage is an indication, but how much you actually cash just can't be.
You can be the best player in the world, play perfectly but still lose your 70/30 flip at 15th place like 10 times and be losing a lot of money over a significant period of time.
BB/100 will show you how much you actually win over the field, you'd need to adjust to icm situations though obviously in the different stages of the tournament.

oldsilver, I have the same results than you regarding lower ROI on low buy in events. But while I considered it being because of a certain lack of focus in these tournaments as well, I do think it can also be greatly impacted by "luck" and variance, especially since the low buy in events I will play will have even bigger fields, thus introduce even bigger variance. For example, I do have a higher BB/100 hands win rate in these tournaments.
Making Top3 of a 10'000 players tournament (top 3 usually is what will radically change your ROI) demands so much luck that variance will play a huge factor.

Edit: Of course, BB/100 hands does not translate well at all to live tournament poker, because it's just impossible to keep track of... But continuing on my high variance argument, to me it is just impossible to evaluate any approximation of your edge over a live field, because the variance is just too high. It can be argumented in this context that this is why live players with the most smallball strategy and putting high value in survival are posting the most consistent results, like D. Negreanu or P. Helmuth (I'm not talking about best results necessarily, but their consistency over a long period of time can't be argued with). Their play tends to lessen the variance aspect, so they probably lose some short-term value (or edge), but their remaining edge is enough for them to post good results more consistently.

This one is fascinating but tricky. Hero can run up a good score by taking down a few pots early (20BB at 10/20 is just 400 chips), and then playing listless/tight to no effect until the blinds get steep. Bust out before the bubble on a 7BB shove that doesn't work, and you'll still look like a winner when you aren't.

To get value out of this one, I think you need BB/100 broken into different stages. The march to the bubble would be the most interesting one to me. Early stage winrate not so much.

Such a severe run of bad luck is a pretty remote 0.028 probability. But let's think about the more realistic probability of losing 7 of 10, which will hurt your numbers. Yeah, that level of variance is frustrating, but I'll submit that the strongest MTT players seldom put their whole stacks at risk.

Sometimes the only way to win a tournament is to win a lot of flips; other times it's the middle stacks who never go broke that glide through traffic better than anyone else. Or they become big stacks so gradually that it's perplexing how it happened. I remember reading a Mike Matusow interview a few years ago, where he talked about what you can do when you're card dead, including a day at the WSOP main event where he added a net $1 million to his stack "without ever having a single good hand." I'd love to know more about how they do it.

Agree with both of you that this is tricky territory. If the blinds go up slowly enough, these tournaments can be very juicy. If the blinds go up fast, though, a few lucky LAGs/maniacs are going to emerge as big stacks just at the point that rising blinds start to make the game very shallow for the rest of us. It's hard to make headway in such situations without playing double-or-nothing several times within 20 hands. And unless the deck is being very kind, we're not going to be a big favorite in each of those.

Which gets me wondering . . .
. . . Is there anything to be learned from what percentage of BB wins come from premium hands vs. non-premium hands? Over time, is there an optimal ratio? Clearly nits that hardly ever play anything else are hurting themselves (If 90% of cash is won on AK+/QQ+, there must be huge missed opportunities elsewhere.) Do the best MTT players get 40% of their money from blind steals with junk, big-blind specials and small pairs/suited connectors that work out? More? Less? That would be interesting to know.

Also interesting . . . what percentage of BB/100 wins come from uncontested pots vs. showdowns? Do the best players have different ratios than the not-so-good ones?

Some good thoughts here!

Well, that's actually the spirit! Say your win rate is something like 3BB/100 hands in middle and late stages of a tournament (saying that to make sure that we're not the type of player who starts playing bad later on). If you play big fields only, you could still be a massively losing player in MTTs due to variance. But technically, you're a winning player! And if you are good enough with icm notions, you should win in the long run.
Which is why it's very relevant in my opinion.

Yes, that would be better indeed!


Yes, I understand you breaking down the numbers of my example, but I think my point is still relevant. The example was extreme in order to show that you don't need to get it in bad to lose.

And in a big field, while I understand the idea of not putting your whole stack at risk being nice, I do not think it's ever possible, even if you have the skills of Helmuth and Ivey combined!... You need some insane situational luck for you not to be forced to regularly put your stack at risk or you are just hugely missing out on opportunities, which leads you to have to put your stack at risk later on...

A middling stack will still have to take risks at some points. With 30BB you can avoid getting it in somehow, but there are times where it doesn't work and you're down to 20BB. And unless it's 2005, chances are you will have to get it in at some point.




Some interesting points here!
Crunching out numbers with hands other than the top 15% and where you VPIP'ed seems interesting for example!
Regarding showdowns vs uncontested, I think that depends a lot on the type of tournament you're playing! (buy-in, knockouts, turbos)

Let's dig deeper on this one, because it is an important issue. If we collect a really big sample, variance should start to shrink. Comparing two players that have been through 10 life-or-death flips is clearly way too small. You might win four; I'd win six, and even though you're a better player, I've got better results.

What if we got our sample size big enough that we could be 99% confident that both of us were within 1% of the true statistical mean for the risks we took? To make the math simple, let's assume that we're talking about 50/50 flips every time. We want an outcome where you always win at least 49% of them; I never win more than 51% of them.

With a sufficiently big sample, the last vestiges of my luck edge will linger on, but they shouldn't cloud the picture much. I might be artificially two percentage points ahead of you, which means 2/51st of my win rate would be bogus, or about 4 percentage points. It shouldn't get any more egregious. Worst case, I've got a 6% ROI; you've got a 4% ROI, but our true strengths are reversed.

Playing around with Raosoft (http://www.raosoft.com/samplesize.html), I learn that a sample size of about 16,000 flip situations will get us there.

Let's assume that in each MTT, our fate depends on how we do in five high-stakes flip situations. (We'll be playing more than that, but most of them will be for small enough stakes that they won't seal our fate.) If you'd rather assume a different frequency, it's totally okay to rework the math that follows. We'll get to a similar place either way.

So, if we each play 3,200 tournaments with five flip situations, we're there. That's a lot of tournaments.

If you're willing to live with 95% accuracy and a variance of two percentage points in either direction, we need only 480 tournaments, with about five flip situations each. (Note: the Hellmuth WSOP sample size is about that big.)

Bear in mind that our results won't be distributed evenly across specific hand-to-hand clashes. You may be frustrated that you've had AA cracked four times in a row. I may be annoyed that AK v. JJ has gone against me repeatedly, no matter which side I'm on. Most of those examples of luck average out.

On a larger scale, luck might have make-or-break implications 20 times in a tournament. Frequencies of AA/KK vary greatly. Success at set-mining does, too. But if we believe that the cards are random, the more abundant such luck events are in a tournament, the more everyone's overall luck quotient should eventually cluster around the mean. High incidences of events create large sample sizes ... which are our friend.