After having had runs of both ridiculously good and bad luck lately, as well as SCTrojans numerous comments about a lifetime not being a big enough sample size, I got to thinking about how much variance really does impact profit in MTT poker.

So I looked through some stats and figured that your average good player makes it ITM about 15% of the time. Then I made the following crude assumptions:

*A good player is twice as likely to final table as an average player.
*A good player is twice as likely to finish in places 1-3 as they are 7-9

Then I ran it assuming 100 of these "good players" each played the FTP 50-50 (including rake) -

100 times:
Worst Profit/tourn = -$48 Best = $248

500 times:
Worst Profit/tourn = -$14 Best = $124

1000 times:
Worst Profit/tourn = -$21 Best = $115

5000 times:
Worst Profit/tourn = $21 Best = $64

100000 times:
Worst Profit/tourn = $36 Best = $46

1000000 times:
Worst Profit/tourn = $39 Best = $43

10000000 times:
Worst Profit/tourn = $40 Best = $41

Basically...variance between two players of the exact same "skill level" is huge even over 5000 tournaments. Also, this shows that a player who is roughly 80% ROI over infinite MTTs can actually run at -42% ROI over 1000 tourns. This is definitely worth thinking about before you call someone out over their stats when you have a sample size of two or three hundred tourns.

Also, along the way with this simulation, the worst streak of not cashing was at 79. This is also worth thinking about next time you think you're having an impossibly bad run, and it also fits in with most theories about conservative big-field MTT bankroll management.

Nice post, variance is a bitch.

Post more. This should be in the 99 thread too...

can you explain this to me? i dont get it

Post more.

Nice post.

It constantly amazes me how alot of people don't see how much variance there really is in tournaments.

In an extreme case there could be a player who is one of the best in the world that will never get his break because he simply loses most of his key flips/etc late. Variance is THAT powerful in tourneys.

And I agree that a lifetime is not near a large enough sample size to balance out all the variance in tourney poker. Here's a thought....that no matter how good you are, its mathematically possible that you may never win another big field tournament in your lifetime simply due to variance.

really really cool post

yep, i actually blogged about this yesterday. almost every successful player at any level has a friend who they consider to be very talented who just can't seem to break through in tournaments for whatever reason. some people play great and also run way above expectation and are considered amazing players, which they are. while maybe another player plays even better, but can't overcome their own shitty luck. or others who play stupid, and run great for a short time.

many players end up quitting poker because of their lack of success in mtts. they just assume they stink because they've never had a big score. sure, some players actually do stink, but some do not, and just run bad enough for a long enough time that they theyre not good enough.

some intelligent players really cant even fathom the true meaning of variance pertaining to tourneys and luck, situational luck, etc. etc. and some dont believe in luck and think it all evens out for everyone lol (generally because they are a product of positive variance and delusional about their own game, obv different degrees for some opposed to others (vietcong being on the extreme end of one spectrum))

ok, better stop before the valium rambles more

this sounds exactly like my last year or so...

the last 6 months especially have made me realize just how fucking brutal variance is...

have to admit at this time last year there is no fkn way I would have thought I could lose for this long...

sounds like a lot of people i know

^^^^^^^^^^^^^^^

Agreed.

I tried to replicate what you did (I'm bored) and once I got started I realized you probably made about another 10 assumptions or decicsions in order to do the analysis. As posted there is no way to validate your result (which might be dead on 100%, but it might not.) The crux of any good analysis like this is in the assumptions anway so please fill in the details!

not to be a dick because it sucks for you right now... but you have had the good side of variance in how well you ran last year... and whether you ran exceptionally well or not, you were able to get huge scores from good play and running decent, which net net pays you a lot more than someone who runs average over the same period. Emotionally though, it sucks to get paid it all up front and then go through a downswing.

Not sure about online tournies since you can play way many, but I had a friend who ran real bad in cash games online at some point, and over the sample he had, he was 30/70 in equity (whenever he was allin, he ran 20% worst then he should have) and he told me his sample was big enough to compare to a lifetime of tournies, so basically you could play a big event almost every week of your life and not play enough hands to eventually come even close to breaking even luck wise. Kind of scary.

Well naturally you can go even deeper with this topic and base your play style around it.

If you make the assumption that variance being the beast that it is you could play insanely loose aggressive and unorthodox in order to try and make most of your pots winable w/o showdown. Doing this however becomes problematic as playing this way in an attempt to reduce variance may actually increase your variance depending on the players your playing against.

Bottom line is that the only sure way to win a pot is to win w/o showing your cards at the end.

I really like this topic though as its something I've went over in my head countless times. I've been at several final tables where first place is getting a handsome 50K-100K and never ran well enough to take it down.

my average tourney size is a lot smaller than this, as are a lot of people, would be very keen to see some results for 500 and 200 people average field sizes.

maybe a table would work well?

great post, btw

i once went 0/65 on full tilt mtt cashes...... i kept reviewing hand histories etc.... seeing what was off on my game, but i felt confident that i was playing solid. I guess it just shows how brutal variance can be at times.

Eventually the cold streak snapped and began cashing normal again, but def brings home the point of proper br management. I generally play way under my bankroll in most situations, which has allowed me to overcome some nasty downswings in mtt's.

Very interesting post. I would be interested to see what the results would be look for an average and bad player too.....lets face, unless we are that delusional, we are not ALL top players :)

SNGs FTW!

ok. I've reworked the "profile" of the sample player. My assumptions are now that the player cashes 20% of the time, but is half as likely as the "good" player from before to final table, and then once at the final table, is twice as likely to bust out 7-9 rather than 1-3.

This player profile creates a player that runs at about -8% ROI after rake over infinite tournaments.

Over a sample of 100 players playing 1000 tourns:

Worst: -$23/tourn Best: $30/tourn

Over this sample of 1000 tournaments - the "luckiest" player actually won the tournament 3 times. It's pretty clear that it is this possibility that keeps losing players in the game. So next time you see someone luckbox their way to a big win, keep in mind that this luck factor is probably what keeps the poker economy alive.

Over a sample of 10,000 tourns:

Worst: -$13/tourn Best: $6.6/tourn

So basically, over 10,000 tourns, it's statistically possible for a long-term losing player to run at a 13% ROI, and probably have a decent P5s PLB score and a great OPR ranking.

Over 50,000 tourns:

Worst: -$7/tourn Best: -$0.20 a tourn.

While there's still a big gap between the unluckiest and the luckiest players after 50,000 tourns, this is seems to be the point where even the luckiest -8% ROI player will almost certainly lose money.

This is only for a sample of 100 players though, correct? If you expand that to 1000 or 10000 players you would no doubt see someone win money over 50k tournaments who was a losing player.

If I run it for 1000 players I get 1 player with an avg profit per tourn of $1.16.

10000 players I get a player running at $1.65.

So yeah, once you factor in how many players are playing online poker...there are bound to be some serious statistical outliers in real life tournaments.

my only point, and using Waco's results as an example, is that MTT results variance is associated wth a fairly normal distibution (and this has nothing to do with the very good skills of players with results).

"Variance" as commonly referred to here = negative variance.

"Running like God" = positive variance.

Someone who experiences a lot of positive variance, whether it is running like God or even just running decently at key times - combined with a period of large negative variance - will make a lot more money than someone who runs average (average ups and downs over the same period). Obviously, high volumes of MTTs will smooth that, and how many it takes is the point of the OP.

I'm not tryng to all diminish the results or skills of Waco or any winning player, but rather to point out that statistical variance encompasses the positive results as well as the negative.

This is really interesting. Is there some user friendly program to do these variance calculations? free download?

Not that I know of. I just wrote up a quick program without a real user interface to see how the numbers worked out and to satisfy my own curiosity.

RVG's ROI simulator

^^This is technically for sngs I think but can be used for mtts just the same.