Hiya, as a guy who has pretty much NO experience with non-NLH games, the current Mercier run made me wonder how does variance in these games compare to NLH.

I am aware of how unbelievably general question this is, but for someone lacking just about any understanding of the other games, I will be satisfied even with a super-simplified answer to get the very general idea.

So, let's say we give a random NLH tourney with a certain blind structure, player field skill level etc. etc. a variance value of 100. What variance value would we assign an MTT with a comparable blind structure and same player field skill level, if the tourney would be held in:

Pot Limit Holdem
Limit Holdem
PLO
PLO8
Stud
Stud 8
Razz
Badugi/Baducey/Badacey ?

Are there any "rules of thumb" that seem to emerge (like, the more the betting amounts are restricted, the less/more variance there is involved) ?

Thanks a lot for any answers.
Oh and in before "three fiddy"

The variance of your tournament results is the same for any type, it doesn't depend on what type of game played.

There will be differences in how high a return you can get, perhaps for some games you could get 40% roi and some only 20%. I suspect this may be what you are actually asking but alas I also don't know much about different game types - I'll give you a bit more on variance though Also, remember that Merciers recent run will also be very dependent upon the field sizes of the tournaments played.

As far as variance goes the better your roi the higher your variance will be. (Well if you could somehow always win or come in at exactly the same place the variance will then be zero same as for always losing but for typical finish distributions as you win/place more often both your roi and your variance will increase).

Variance is a measure of how your results 'bounce' above or below the mean result often poker players use the term in place of bad luck, bad runs, or downswings and this use can confuse things and is wrong really.

The variance is tied very closely to the payout structure, quite large differences in roi's don't actually change the variance much at all.

For typical payout structures (buyin: 0.94, 0.06 rake) with an roi of about 0.0% the variance per game is:
HU: 0.9
6 seat: 2.08
9 seat: 2.23
18 seat: 4.12
27 seat: 5.55
45 seat: 7.37
180 seat: 24.8

As you can see the variance as the field size increases does start to bite hard.

(As an example if you play 45's at 20% roi rather than the 0.0% roi given above the variance per game changes from 7.37 to 8.64 not really that large compared to the difference you see when comparing 45's to 180's. The variance is mostly locked in by the payout structure)

Yeah, you are right there, I definitely misused the word variance.

You know, I was thinking about this Mercier run, obviously he had to run pretty well to get such results. What I was kind of trying to figure out s whether such results would be more/less likely if these were NLH tournaments instead of limit mixed games. Can we give him more/less props for these results reflecting his skill level than if it were NLH events.

That is why I wanted to compare the same tournament fields in terms of both size and skill level.

Can you explain this, please? I do not think I have ever heard anything like this before. In fact, I have heard some bits suggesting the otherwise. Does it have something to do with the fact that the less my ROI is, the more often will I finish in an unpaid postion, which is far closer to my $$$ expectation than, lets say, a final table finish?

You can't really say definitively whether your variance increases or decreases based on your ROI. If you're a mediocre LAG, you can increase your ROI by folding a bit more in marginally bad spots which will decrease your variance, or if you're a mediocre nit you can increase your ROI by finding a few more good bluffing/calling spots which will increase your variance. It depends on your playing style. For tourneys, a 'slide into the money' approach will have less than variance than a 'go for bracelet' approach even if the ROIs are the same.

Typically though, improving your ROI as a winning player in tourneys probably does increase your variance more often than not. Your cashes will be more disproportional since the higher paid spots have different values, and as you get better your have better chances of hitting higher paid spots.

Anyway, the question still stands as to the degree to whether Mercier is a luckbox since he's not winning at NLHE tourneys is or it even that much more impressive? As pointed out earlier, field size is way more important factor than game type, but we can still imagine which would tougher to win; a 10k WSOP NLHE with 100 people or a 10k WSOP razz event with 100 people. The bigger bet games have both more variance and more skill. The more skill is usually the bigger factor giving the better players better ROIs and higher place finishes in comparison to limit. Still, NLHE has been beaten to death by world class players but the same cannot be said of razz. I'm sure several of the razz players haven't played 50k hands of razz in their life. So it actually is possible Mercier (who is routinely plays high stakes razz as part of mixed game) does actually have a higher ROI at razz. Of course that still doesn't really answer the question of how "impressive" that is since he's just beating up on rich players who don't really care about the game.

The standard deviation of a SNG can be calculated knowing your ROI and placing distribution.The following table shows the results for a 9 player 10 buy-im, 1 fee with placing weighted 1,2,3 (finishing 3rd is three times as likely as finishing first if ITM). Clearly variance increases with ROI but at some point it starts to decrease, which makes sense as you start to win more consistently. In the table below, this happens somewhere between 30% and 40%.


SnG- Std. Dev. vs. ROI
ROI SD
-30% $12.84
-25% $13.12
-20% $13.37
-15% $13.60
-10% $13.79
-5% $13.97
0% $14.12
5% $14.24
10% $14.35
15% $14.43
20% $14.50
25% $14.54
30% $14.56
40% $14.53

I would think that game structures that allow for more (big) decisions to be made, such that a skill edge can be pushed, would result in higher ROIs for the elite players.
e.g. Mercier would have no appreciable edge in a 1bb deep flippament, where the only decision is push or fold, and results are almost entirely luck-based, but he might have a considerable skill edge in one of the games with deep stacks and three or more streets of post-flop action.

I have no idea how many hands are played in a Razz - or even a fixed-limit holdem - tourney, and how they compare to NLH MTTs, but the blinds/antes structure would have a dramatic effect on how many opportunities a player has to utilize his skill edge.
In the no limit games, even the best players are "forced" all in against inferior players earlier than they'd prefer. (Apart from Hellmuth, of course. He can fold QQ when he has 8bb.)

None of us, even one of the Phils, is so good that they can sustain 50% roi's in 9 seaters so a very good player will be more like 10%. As statmanhal has shown the variance is increasing if the player moves from 10% toward 30% roi. If somehow this player could move from 30% to 50% in 9 seaters then their variance would drop but I haven't ever seen someone do this for 1000's of games.

The reason the variance is increasing through this period is as you suggested finishing out of the money is closer to the mean so adding an itm finish, especially a high one will increase the measured variance. (This high result itself and also the mean will then rise a little, making the variance part of all the non itms a little higher).

For very small tournies ie, HU it is possible to reduce variance as you increase your roi, I think for HU this will be the usual case as you get past about the break even point, ~50% win rate). For large MTTs though you quite rarely get ITM even as a good player and so a placed finish adds a good chunk to the value when calculating variance. For 180's the point where variance will start to drop is likely to be where you get near to 1000% roi or more but who can do that. (It is always theoretically possible to hit exactly the same position payout for every game you play and then the variance becomes 0.0 but this is not really practical - well except it is easy to do this by always losing!)

Another perhaps interesting point is that I wouldn't advise trying to reduce your variance by playing a certain way as it is quite difficult to know if the act you try will actually reduce it and if so if you actually want this result - higher variance is usually higher roi. Trying to nurse/fold a short stack into the money at times may be very, very wise for icm reasons (max $ev rather than chipev) and also for bankroll reasons so think in terms of icm/br and maximum long term $ results rather than worrying about the roi variance, it is what it is. To control roi variance it is best to choose a suitable field size to play for your comfort level.
Thanks for the calculation statmanhal. A few years ago I did also calc this for 9's but I think I used a flatter finish distribution, eg, 12.5%, 12.5%, 12.5% etc and I seem to remember the max variance then showed up at about the 50% roi mark. I think this seems reasonable as the 3rd placed positions are closer to the mean and in your calc we get a good few more of these. Even so no one has a sustainable 30% roi in them without moving up abi so I would like to wish all us 2+2'ers a nice high variance roi result in MTTs for the future!