(This is a follow-up to this post. You probably want to read that first if you haven’t already.)
My previous post about the variance in MTTs got some interest and plenty of criticism, so I thought I’d follow up with a (slightly) less sloppy post that considered some criticism. In future posts, I plan to look at various forms of cash games, STTs, and DoNs. (If you’d like to share your data for any of these things, please get in contact with me.)
First of all, I should clarify something: Some people are definitely better off playing large-field MTTs than other games. I’ll make an argument below that almost no small/mid-stakes players fit into this category in the current climate. For mid/high-stakes player: If you’re insanely good at MTTs and you’re down to put in lots of volume, then play them. If you really enjoy large-field MTTs and you’re willing and able to deal with their ridiculous variance, then play them. If you’ve got a really sweet backing deal, then play them. If for whatever other reason you think you’d like to play them, I won’t pretend to know what’s best for you. But, make sure you seriously consider the extreme variance that’s involved. Before this, I haven’t seen anyone present this information correctly. Thus these posts. (I have seen people use the normal approximation to look into this, but as I showed here, that method doesn’t actually work.)
Anyway, there’s lots of fun stuff that I didn’t do with Shaun’s data that I’d like to do with my shiny new data set (see the section at the bottom for more about this sexy piece of data). For example, varying buy-in sizes obviously increases variance. For Shaun’s data, I looked at buy-ins between $55 and $216, i.e. with a max buy-in about 4x his min buy-in. But what if we don’t vary the buy-ins at all? Here’s the data for that:
Large-Field Tourneys with No Variation in Buy-In
| ROI | Tourneys Played | Chance of Loss | Chance <0.5x EV | Chance > 1.5x EV | Chance >2x EV |
| 20% | 100 | 59.7% | 62.7% | 32.4% | 29.4% |
| 20% | 500 | 43.5% | 51.1% | 36.2% | 31.0% |
| 20% | 1000 | 35.4% | 45.2% | 36.2% | 28.4% |
| 20% | 2000 | 25.1% | 38.7% | 33.2% | 22.3% |
| 20% | 5000 | 12.5% | 30.1% | 27.6% | 13.0% |
| 40% | 100 | 55.1% | 60.9% | 31.1% | 26.8% |
| 40% | 500 | 30.7% | 45.2% | 32.0% | 23.5% |
| 40% | 1000 | 20.1% | 37.3% | 29.4% | 18.3% |
| 40% | 2000 | 9.9% | 28.4% | 24.8% | 11.5% |
| 40% | 5000 | 1.4% | 16.7% | 16.8% | 3.5% |
| 60% | 100 | 51.0% | 59.3% | 28.7% | 22.9% |
| 60% | 500 | 21.5% | 41.0% | 28.9% | 19.0% |
| 60% | 1000 | 10.8% | 31.6% | 25.3% | 12.8% |
| 60% | 2000 | 3.4% | 22.2% | 20.0% | 6.7% |
| 60% | 5000 | 0.1% | 9.6% | 10.6% | 1.0% |
| 80% | 100 | 46.9% | 58.2% | 27.5% | 21.3% |
| 80% | 500 | 15.7% | 37.1% | 27.2% | 16.4% |
| 80% | 1000 | 5.8% | 27.3% | 22.5% | 10.0% |
| 80% | 2000 | 1.1% | 17.5% | 16.7% | 4.2% |
| 80% | 5000 | 0.0% | 5.4% | 7.2% | 0.4% |
| 100% | 100 | 42.8% | 56.5% | 26.9% | 20.6% |
| 100% | 500 | 10.9% | 34.7% | 25.2% | 14.2% |
| 100% | 1000 | 3.2% | 24.1% | 20.9% | 7.9% |
| 100% | 2000 | 0.4% | 13.6% | 14.2% | 2.9% |
| 100% | 5000 | 0.0% | 3.5% | 5.6% | 0.1% |
If you compare this to the data from my previous post, you’ll see that the situation is actually quite a bit better in some spots. For example, for a 20% ROI player, the chance of losing over 5k tournaments goes from 20% to 13%. For a 60% ROI player, it goes from 6% to 1.4% over 5k tourneys and from 20% to 11% over 1k tourneys. The difference is less impressive in some other situations, but I think in general it’s pretty clear that varying your buy-ins increases variance by quite a significant amount (more than I expected). The numbers are still pretty ugly–Even a very good player with a 40% ROI has a 10% chance of losing over 2k tourneys and 20% over 1k tourneys–but they’re clearly much more tolerable.
However, for most serious large-field MTT players, it’s completely impractical to play only one buy-in. Many players vary their buy-ins a lot more than I assumed in my previous post (Shaun grinds everything from $10ks to $33s, for example, but I only considered $55s to $216s), and of course there are players who do everything in between. To consider this, I’ll hold ROI constant at 40% and vary the range of buy-ins. I’ll assume that buy-ins vary by powers of two (e.g. $50, $100, $200, $400, etc) and players invest the same amount of money at each level (e.g. they might play 4 $50s, 2 $100s, and 1 $200):
40% ROI Player in Large-Field Tourneys
| Max/Min | Tourneys Played | Chance of Loss | Chance <0.5x EV | Chance > 1.5x EV | Chance >2x EV |
| 1 | 100 | 56.3% | 61.5% | 30.6% | 26.4% |
| 1 | 500 | 31.3% | 45.1% | 31.6% | 23.6% |
| 1 | 1000 | 19.6% | 37.1% | 29.5% | 18.3% |
| 1 | 2000 | 10.1% | 29.0% | 25.6% | 11.7% |
| 1 | 5000 | 1.6% | 17.2% | 16.9% | 3.8% |
| 2 | 100 | 56.5% | 62.2% | 28.1% | 24.3% |
| 2 | 500 | 32.4% | 46.0% | 31.2% | 23.0% |
| 2 | 1000 | 21.5% | 39.0% | 29.5% | 18.7% |
| 2 | 2000 | 11.3% | 31.0% | 26.1% | 13.0% |
| 2 | 5000 | 2.2% | 18.0% | 17.4% | 4.4% |
| 8 | 100 | 59.3% | 65.6% | 24.8% | 21.3% |
| 8 | 500 | 38.1% | 50.9% | 29.8% | 22.6% |
| 8 | 1000 | 27.3% | 43.9% | 28.8% | 20.3% |
| 8 | 2000 | 16.7% | 36.3% | 27.0% | 16.1% |
| 8 | 5000 | 4.4% | 24.6% | 21.3% | 8.6% |
| 32 | 100 | 64.2% | 70.7% | 21.0% | 18.5% |
| 32 | 500 | 46.7% | 58.6% | 25.5% | 20.3% |
| 32 | 1000 | 36.4% | 52.0% | 27.0% | 20.3% |
| 32 | 2000 | 25.2% | 45.1% | 26.6% | 18.0% |
| 32 | 5000 | 10.5% | 32.9% | 24.1% | 13.2% |
As you can see, there’s almost no difference between playing at just one stake and playing two stakes (e.g. $55s and $109s). Not surprisingly, it gets more extreme as the spread increases. For example, if you have a 8x spread (e.g. $12s to $109s) and a 40% ROI, you have a 27.3% chance of losing over 1,000 tourneys and 4.4% over 5,000 tournaments. If you have a 32x spread (still just 1/10 of Shaun’s…), even with a 40% ROI over 5,000 tourneys, you have a 10.5% chance of losing. This doesn’t even consider the fact that your ROI almost certainly goes down as stakes increase, which makes the negative side of variance even worse.
Some people criticized my previous post because I removed tourneys with 180 or fewer entrants. I’d intended to separate those games from larger-field MTTs because, from a variance perspective, they’re quite different. But, many people pointed out to me that most serious MTT players play both, so I’ll look at them here. Since 180s are by far the most common small-field tourneys, I’ll consider those. I’ll look at $12 turbos, but the results are essentially the same and only slightly better for non-turbos. Here are the numbers:
180s with No Buy-In Spread ($12 buy-in used):
| ROI | Tourneys Played | Expectation | Chance of Loss | Chance <0.5x EV | Chance > 1.5x EV | Chance >2x EV |
| 10% | 500 | $600 | 35.8% | 44.2% | 39.3% | 31.7% |
| 10% | 1000 | $1,200 | 27.5% | 38.6% | 37.7% | 27.5% |
| 10% | 2000 | $2,400 | 20.4% | 34.6% | 33.2% | 20.5% |
| 10% | 5000 | $6,000 | 8.9% | 26.0% | 24.5% | 9.3% |
| 10% | 10000 | $12,000 | 2.8% | 17.5% | 17.8% | 3.6% |
| 15% | 500 | $900 | 28.5% | 39.6% | 37.4% | 27.4% |
| 15% | 1000 | $1,800 | 20.0% | 35.0% | 32.1% | 19.5% |
| 15% | 2000 | $3,600 | 11.0% | 28.0% | 27.2% | 11.6% |
| 15% | 5000 | $9,000 | 2.3% | 16.2% | 17.0% | 3.1% |
| 15% | 10000 | $18,000 | 0.3% | 8.6% | 9.3% | 0.3% |
| 20% | 500 | $1,200 | 23.0% | 37.4% | 33.7% | 21.3% |
| 20% | 1000 | $2,400 | 13.4% | 30.3% | 29.1% | 14.0% |
| 20% | 2000 | $4,800 | 5.4% | 22.1% | 21.4% | 6.6% |
| 20% | 5000 | $12,000 | 0.6% | 10.6% | 11.6% | 1.0% |
| 20% | 10000 | $24,000 | 0.0% | 3.9% | 4.8% | 0.1% |
| 25% | 500 | $1,500 | 18.2% | 33.6% | 30.4% | 17.5% |
| 25% | 1000 | $3,000 | 9.1% | 26.1% | 25.0% | 9.8% |
| 25% | 2000 | $6,000 | 2.8% | 17.1% | 18.1% | 4.1% |
| 25% | 5000 | $15,000 | 0.1% | 7.5% | 7.3% | 0.2% |
| 25% | 10000 | $30,000 | 0.0% | 1.6% | 2.2% | 0.0% |
| 30% | 500 | $1,800 | 13.8% | 30.2% | 28.6% | 14.8% |
| 30% | 1000 | $3,600 | 6.3% | 23.5% | 21.9% | 7.0% |
| 30% | 2000 | $7,200 | 1.3% | 14.8% | 14.4% | 2.1% |
| 30% | 5000 | $18,000 | 0.0% | 4.3% | 5.2% | 0.1% |
| 30% | 10000 | $36,000 | 0.0% | 0.7% | 1.0% | 0.0% |
The picture is indeed much nicer for small-field tourneys. Obviously ROIs are going to be much lower and samples will tend to be larger (as is reflected in the table), so comparison between large-field MTTs and small-field MTTs is a bit difficult. But, if you consider two situations that are roughly equivalent like, say, a 20% ROI 180-man player playing 2,000 tourneys and a 40% ROI large-field player playing 1,000 tourneys with an 8x spread, you’ll see that the situation is indeed much better for the 180-man player. Both players have the same equity, but the smaller-field player has only a 5.4% chance of losing, while the large-field player has a 27.3% chance of losing. (Even if the large-field player plays 2,000 MTTs, he still has a 16.7% chance of losing.) Indeed, because of this much lower variance, you also need a significantly smaller bankroll to play 180s: Bankroll requirements only need to be about one third as high for 180s as they are for large-field MTTs if your ROI in the 180s is half your large-field ROI. (See here for a rough explanation of how I got that number.)
This is pretty damning. If you’re a low/mid-stakes tournament player, it’s much much easier to play 2,000 180s than it is to play 1,000 large-field MTTs. So, you can achieve the same exact equity faster, with essentially the same skill-set, and with much less variance. If you play low stakes large-field MTTs, you can even move up a bit when you switch to 180s because of the lower bankroll requirements and have an even higher equity. 180s also offer other benefits like the fact that they adapt to your schedule. (I quit MTTs in college because I was sick of having to tell people “There’s an x% chance I’ll be free later.”) SnGs might feel a bit monotonous, but once you have your first losing year, you’ll no longer think large-field MTTs are so fun anyway. So, if you play large-field MTTs at stakes where 180s are an alternative (say up to ~$55s) and you like money, play 180s instead.
(Small-field MTTs also have another benefit: Their distribution is pretty damn close to normal for samples of over 1,000 tournaments. This means that you don’t need to do the fancy stuff that I’m doing to get results like this. You simply need to play around with the normal distribution. If you don’t know how to do this, ask your local nerd.)
Of course, for high-stakes MTT players 180s aren’t an option (yet). Many of the people who talked to me after my previous post said that they try to balance out the extreme variance of the large-field MTTs with small-field MTTs. So, I’ll look at how that works out. I’ll give my HS player 20% ROI (not bad for HSMTTs) in tourneys with 180+ players and 15% ROI in smaller fields. I’ll assume a maximum buy-in that’s 4x the minimum buy-in. Here’s how that works out:
20% ROI in Large Fields, 15% in Small Fields, 4x Buy-In Spread
| % Small Field | Tourneys Played | EV (in min buy-ins) | Chance of Loss | Chance <0.5x EV | Chance > 1.5x EV | Chance >2x EV |
| 10% | 100 | 34 | 62.6% | 65.6% | 28.8% | 26.5% |
| 10% | 500 | 172 | 46.0% | 54.1% | 33.3% | 28.2% |
| 10% | 1000 | 330 | 38.4% | 48.4% | 34.4% | 28.0% |
| 10% | 2000 | 675 | 28.5% | 42.0% | 33.1% | 23.6% |
| 10% | 5000 | 1677 | 16.1% | 33.2% | 28.7% | 16.0% |
| 30% | 100 | 32 | 60.3% | 64.1% | 29.3% | 26.4% |
| 30% | 500 | 157 | 45.0% | 52.8% | 33.6% | 27.6% |
| 30% | 1000 | 320 | 36.7% | 47.5% | 33.2% | 25.9% |
| 30% | 2000 | 641 | 27.1% | 41.9% | 32.0% | 22.4% |
| 30% | 5000 | 1621 | 14.4% | 32.3% | 27.7% | 14.5% |
| 50% | 100 | 30 | 58.1% | 62.8% | 30.5% | 27.5% |
| 50% | 500 | 149 | 42.8% | 52.2% | 32.4% | 26.7% |
| 50% | 1000 | 290 | 35.1% | 46.4% | 33.1% | 25.4% |
| 50% | 2000 | 602 | 26.0% | 40.9% | 31.4% | 21.5% |
| 50% | 5000 | 1496 | 12.7% | 31.5% | 27.1% | 14.0% |
| 70% | 100 | 28 | 53.1% | 57.9% | 33.1% | 29.8% |
| 70% | 500 | 139 | 39.2% | 49.7% | 33.3% | 26.9% |
| 70% | 1000 | 278 | 31.3% | 44.5% | 32.7% | 23.8% |
| 70% | 2000 | 576 | 22.3% | 38.8% | 30.1% | 19.3% |
| 70% | 5000 | 1399 | 9.8% | 28.9% | 25.2% | 11.8% |
| 90% | 100 | 26 | 49.5% | 54.4% | 36.8% | 33.1% |
| 90% | 500 | 131 | 34.9% | 45.2% | 35.1% | 27.0% |
| 90% | 1000 | 266 | 26.4% | 40.5% | 32.8% | 22.2% |
| 90% | 2000 | 528 | 16.9% | 33.4% | 28.9% | 16.0% |
| 90% | 5000 | 1319 | 6.0% | 23.6% | 21.8% | 7.8% |
| 100% | 100 | 25 | 47.4% | 52.4% | 38.5% | 34.3% |
| 100% | 500 | 131 | 31.3% | 41.9% | 37.0% | 27.8% |
| 100% | 1000 | 256 | 23.4% | 36.8% | 33.7% | 22.1% |
| 100% | 2000 | 513 | 14.0% | 30.0% | 28.5% | 14.2% |
| 100% | 5000 | 1285 | 4.0% | 19.9% | 19.5% | 5.0% |
The picture’s really not that great. Even if you play 70% small-field tourneys, you still have an almost 10% chance of losing over 5,000 MTTs and 31.3% over 1,000 tournaments. That’s obviously much better than the respective 20% and 42% that I found in my previous post for a similar player who plays only large-field MTTs, but it’s still much higher than the 4% and 23.4% that comes from small-field MTTs alone. (You’re technically giving up equity here by playing smaller field tournaments, as the table shows. But, they take less time, so you could replace tables as those tourneys end if something else that you want to play is available or just spend that extra time doing something more fun than playing poker. You can also get away with playing higher buy-in small-field MTTs if they’re available. So, whether that’s actually a negative depends on your specific situation.)
So, if you play small/mid-stakes MTTs, I highly suggest that you move to 180s. If you play mid/high-stakes, you can either suffer the slings and arrows of outrageous MTT variance or do something else. If you do choose to tough it out, the above data should hopefully convince you to expect lots of variance, play in smaller fields when possible (even at the expense of ROI… I often hear people give the opposite advice), and to try to play MTTs with fairly consistent buy-ins. Good luck, though. You’ll need it…
Where the Data Came from (You Probably Don’t Care)
I’ve got my hands on some much better data. A lot of different people from 2p2 were nice enough to let me use their results instead of Shaun’s, and some of these guys have played more tourneys than Jesus. I was pretty psyched to use that data already, but then a backing group that backs a ton of people was generous enough to share its data with me. That’s really awesome because it means that I can eliminate selection bias by looking at players’ results after they were backed. To do this, I asked for data on the first twenty people that this group started backing in tourneys since its formation in August, including players that later left or were dropped. I will only be considering results after they were backed (except when I say otherwise), including results from players after leaving the group. So, the results here were not chosen because someone was proud of them or because I noticed them–They were chosen because their performance before these results impressed a backing group.
I filtered out bounties, rebuys, shootouts, games other than NLHE, tourneys with less than 46 entrants (as these have hugely different payout structures), and tourneys with less than a $4.40 buy-in. This left me with 18 players (One blocked himself on Sharkscope and was only backed for one day, and one only played tournaments that I’m not counting) who played 16,176 relevant tournaments with an average buy-in of $22.24 (ranging from $4.40 to $530), an ROI of 42%, and an ITM of 14%. So, yeah, this backing group has some good players, and I’ve got me a pretty sweet data set.
I generated the results in these tables in the obvious way: I ran simulations in which a “tournament” was a random selection of a result from my data set. I used the same trick that I used in my previous post to get the distributions of players with different ROIs. Namely, I multiplied the prizes in the data by a constant factor of ( 1+ newROI)/(1+oldROI) without modifying buy-ins. In theory this should lower the variance of lower ROI players, but I actually looked into this and it’s not the case: I checked the derived distributions against real players with various different ROIs, and they agreed remarkably well for 500+ tourneys. For smaller samples, the actual distributions are different, but the statistics I give in these posts are still almost identical.
It would be interesting to compute CE for the different options.
http://forumserver.twoplustwo.com/17/small-stakes-limit/5k-milestone-post-rake-traps-variance-traps-948355/
2 thumbs up
Really like the reading of these articles, nice job! I’m thinking of translating them in french, for publishing them on my website; would u allow me to proceed ? Could be very useful to spread the word !! 😉
ezekiel,
Sounds cool. I’m fine with it as long as you properly credit me and link to the original.
yep, of course, it would be done accordingly to these conditions.
Thanks a lot for being positive to my request. I’ll comme back here to inform you when done.
Excellent Read. Thank You.
Ty for your work. lol´d @ Jesus(aka Spacegravy) graph.
Well done!
greetz
awesome work.
Could you do the same with 45mans and 18mans?
Would be really interesting how much less variance they are.
if you decide to do stats on 1 table SNGs, Id recommend using pandurrrr as an example. From what I can tell this user has played tons of tourneys almost all at the $33 buy in on Full Tilt and pretty much generates a steady 8% ROI while playing something like 15 tables a time. I know that is selection bias but is a good example. unfor this user has opted out of most tracking sites…
really great stuff Noah, more of these if you can
Great posts Noah. Have you ever tried approaching the problem of tournament variance by blind level? What I mean is from cash games you know a player needs n hands at particular stakes to determine m bb/100 with whatever confidence level. From there it wouldn’t be too hard to calculate how many tournaments it takes to get that kind of sample (gigantic, I personally don’t have it for anything but the very early levels).
Hi aaron,
I’m not 100% sure what you mean. Do you mean trying to approximate tournament ROI from the structure and bb/100 at different blind levels? If so, that sounds like a really really hard problem….
i’ve been looking for something like this for ages,brilliant work!
now i know why i suffer from depression… great contribution… i certainly helps put those horrible runs in perspective…
of course the issue is, are those runs indicative of my long-run average expectation and the months where i show decent profit aberrations… or vice versa…
and how exactly does one learn and improve in a world where short term results can be so different than long run expectations…
i guess that is why community is so important – because the collective wisdome of 1,000,000 buy ins is (messily)aggregated…
fine work sir!
Noah,
This is great work. I’m working on a project now modeling the impact on backers of the DOJ related shift from online (high volume / low ABI) to live (low volume / high ABI). My theory is that for the overwhelming majority of even the most profitable players, this move will be impossible without a creative backing deal. I would appreciate the opportunity to discuss your data and methods. You can reach me at ChicagoAlPoker gmail com.
Thanks,
Al
so knowing all of this….can someone PLEASE explain how there are so many merge MTT regs with perfect upticking graphs….over thousands of games NO variance playing the highest stakes??
@Kavilla — the reason why so many regs have the uptick at Merge is because the small fields. The Merge MTTs are like 180 mans.
Nice articles. I’m personally against MTTs for a living, due to variance and the life-limiting time requirements.
I’m wondering, do your numbers take into account the very real fact that pros do a LOT better than nonpros at the final stages, for several reasons (SNG experience and much stronger nerves)? They pick up a sick amount of equity here.
Gnug,
I used real-world data. So, yes, I did account for that.
I guess it would be much too much to ask for you to do something like this using the Merge MTTs. Since the fields are so much smaller I’m sure it really changes the numbers significantly and it would be really good to see it worked out.
Noah buddy if you put in the time to improve your game that you put in to this post you yourself could have a 80% roi like Deeb….Assuming a 20% roi is assuming a very mediocre player….If you wish to be a mediocre player then this is a good post….I haven’t had a 20% roi or less since my first year of playing….take all of your stats and times them by 3 or 4 and see what you come up with….In short you are a mediocre player trying to give advise to bad or other mediocre players….Good luck with that.