Re: A Question About Variance and ITM
 

Well, strictly speaking, 50% ITM would be the highest SD possible provided that your results were all 1st and OOTM. Higher or lower ITM% could easily yeild more variance practically speaking.

Actually, now that I think about it, in order to really get a 50% ITM, I'd bet you'd have a relatively low SD in comparison to some. The reason for this is that I think in order to get 50% ITM you would be sneaking into 3rd a lot with a shortstack instead of taking some risks to go after 1st. So 50% ITM would yeild a lot of 3rd place finishes (I suspect) that might otherwise be 1sts or 4ths. 3rd and OOTM is smaller in terms of variance from the mean so your SD might go down.

I should also make it clear however that this is NOT what you want. You want a 40%ish ITM with lots of variance and a nice healthy ROI. Higher ROI figures will usually give you more variance because that means more 1st place finishes and 1st place finishes deviate from the mean quite a bit.

Regards
Brad S

Edit. One other important thing.
Almost all SD results that you will find in a realistic sample of SNGs will be close. Closer than you might expect. A completely average player with absolutely uniform finish results for example will have an SD of about $16+ in $11 SNGs. The best players who finish ITM 45% and get ROI 40% will be getting about $19. I have said in the past that almost any SNG winner who wants to immediately estimate his SNG SD can just take the net profits for a second place finish in their particular SNG level and use that. IT will be close every time (usually a bit too big but not by much).

This is to say that SNGs played in any realistic fashion will yeild very similar amouts of variance. So why doesn't it feel that way? Because some are big winners and some are big losers but some are playing a break even kind of game. Foe those whose results are not netting them a big profit or loss either way, that fluctuation can feel huge because it can make a player go from moderate winner to moderate loser over even large samples. Players who are getting 30%+ ROI tend not to worry so much about variance because even the big negative swings will usually still net them a slight profit or at worst only a small loss. (unless of course they are living off their profits. Then it can feel pretty bad too to make $50 in a month)

Re: A Question About Variance and ITM
 

This is an interesting topic, here is my thoughts, flame and discussions welcome.

First, generally people are negative about standard deviation since it creates random fluctuations in you bank roll. Is this really that bad? Let’s think about two imaginary scenarios:

Scenario 1. Let’s say your ITM is 39% and equally divided into 1st 2nd and 3rd. For 10+1 the average ROI=2 and STD=18.12.
Scenario 2. Now if you increase the 1st finishes, let’s say all your ITM is first. Now ROI=8.5 and std=24.5. Now your STD increases, but you sure love the second Scenario better. So the std alone is not a good indicator of how you do.

Thought 1.
It does not make sense to think standard deviation alone without ROI. In fact if you want to use std, ROI/std is better measure since the two cases gives 11% and 34.6%. This is pretty much like Sharp Ratio in statistical arbitrage.

Now go back to real life. I category two types of players in SNG games. Most of the people follow the strategy from Rock-Maniac transition, but I constantly see people even in 10+1 games play very loose and aggressive early on try to build a big stack lead by out playing weak opponent. Let’s use Scenario 1 to describe the first type player and for second type, let using
Scenario 3. ITM 30%, 1st 22% 2nd 4% 3rd 4%. ROI=2 and STD=20.91.
We see that reduce the ITM from 39% to 30% hurt the result a lot, you need to have 22 of 30 1st finishes in order to get the same ROI while the ROI/STD is 9.5% less than the first scenario. That’s probably why there are more people play tight early on.

But as long as your play falls into one of those two catogories, STD does not have much meaning (as least not negatively). As we see in scenario 2, higher STD is welcome while fixing you ITM. To see another scenario, assuming your ITM=39%, you have only 1st and 3rd finishes, to match the same STD, you need to have a break down of 1st/3rd 15/24 std=18 and ROI is only 1.3!! [img]/images/graemlins/shocked.gif[/img]

I think one of the main reason people care about ROI/STD is trying to see the leverage effect. For a good strategy, if you have same ROI but much less STD, your back roll allows a much bigger leverage effect. Of course, everybody like to see a linear increase of bank roll, but the discreteness of the payout (you have only 4 payout choices 39/29/9/-11, you cannot be paid exactly 4$ every time you play although that will be ideal!) couples with the fact the more or less correct strategy has very similar STDs make STD a very weak indication. I would be surprised to see two guys with similar ROI have drastically different STD.

So overall, if you play rock-maniac strategy, I don’t think STD is very revealing nor is ROI/STD.

I am sure there are errors in my post, let me know what you think.
[img]/images/graemlins/smile.gif[/img]

Re: Some thoughts (a bit long)
 

[ QUOTE ]
So all in all, I think a strong SNG player, with strong mentallity and no serious ego-problems, can know pretty little about variance and SD, and still kill the games. I don't see how knowing more about his SD could "improve" his game, excepy only in some extremely minor way (taking a decision that gives him same _exact_ ROI as other decision, but with lower variance. Is this really "improvement"? Can you even think of such an example in an SNG?)

[/ QUOTE ]

You are right, of course

... but some of us are big nerds and like to talk about these things anyways. [img]/images/graemlins/grin.gif[/img]

And the same goes for the bizzare, absolutely irrelevant preflop whole table AA examples! And all the other weird never-will-apply-to-any-game-ever theoretical conversations!

One of these days the probability forum is going to get jealous.

Regards
Brad S

Re: Some thoughts (a bit long)
 

[ QUOTE ]
... but some of us are big nerds and like to talk about these things anyways

[/ QUOTE ]

Don't get me wrong, I enjoy thinking about "non-practical" matters quite a lot. And your particular thoughts about SD and SNGs are very interesting, IMO. But I feel there are people who might think that some of this could have a significant impact on their decisions, regarding the play in a specific game, and their BR management, if they could understand SD and ROR "fully". And I thought I could help by pointing out it's more of a theoretical, speculative debate.

[img]/images/graemlins/laugh.gif[/img]