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  #21  
Old 10-27-2005, 01:56 PM
burningyen burningyen is offline
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Default Re: Turbos vs. regular SNGs (variance)

[ QUOTE ]
Turbos will have less variance only because there are 9 players instead of 10. In SNGs, your variance will always be near the same, regardless of your ROI because it depends on your place percentages and 13%/13%/13%/61% yeilds a variance similar to the one that 10%/10%/10%/70% gives.

Somebody around here learn some math for christsakes.

The square root of the sigma-squared is your standard deviation. That's why your standard deviation only increases as the square root of the number of games you play, while your profit increases linearly (ideally).

[/ QUOTE ]
Worst post ever.
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  #22  
Old 10-27-2005, 01:59 PM
AleoMagus AleoMagus is offline
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Default Re: Turbos vs. regular SNGs (variance)

[ QUOTE ]
Game. Set. Match.

[/ QUOTE ]

Hardly

Why is it that if any poster asks a question about something like whether he can expect a 20% ROI in the 33s, everyone comes out of the woodwork to flame him and tell him to read the faq, or do a search. They do this very pompously too, I might add. I mean pompous in ways that makes this thread look like child's play

BUT... when someone says the same thing about mathematics that have been covered in this forum a million times before, everyone gets offended?

Regards
Brad S
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  #23  
Old 10-27-2005, 02:01 PM
AleoMagus AleoMagus is offline
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Default Re: Turbos vs. regular SNGs (variance)

[ QUOTE ]
So if we assume that an above average player will enjoy a better ROI in a standard SNG because of elongated play time, then his variance should be lower there.


[/ QUOTE ]

well...no. not variance

but yes, he will feel smaller swings relative to his bankroll growth

Regards
Brad S
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  #24  
Old 10-27-2005, 02:14 PM
pooh74 pooh74 is offline
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Default Re: Turbos vs. regular SNGs (variance)

[ QUOTE ]
[ QUOTE ]
So if we assume that an above average player will enjoy a better ROI in a standard SNG because of elongated play time, then his variance should be lower there.


[/ QUOTE ]

well...no. not variance

but yes, he will feel smaller swings relative to his bankroll growth

Regards
Brad S

[/ QUOTE ]

And I believe that was what OP was asking. A few people tried to respond and the thread unraveled. I have close to zero formal training in mathematics, but I do know when someone with low self-esteem is looking for a flame war. (Not you obviously).
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  #25  
Old 10-27-2005, 02:39 PM
AleoMagus AleoMagus is offline
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Default Re: Turbos vs. regular SNGs (variance)

[ QUOTE ]
And I believe that was what OP was asking.

[/ QUOTE ]

Fair enough. I mean, I know that's what the OP was asking. That's what everyone is asking when they ask about variance. Trouble is they keep calling it variance, and that's only a part of it.

...then the math inclined get frustrated when nobody gets why variance is pretty constant.

Believe it or not, I am not actually that formally trained in math myself, so I don't know it the metric I describe has a technical name. If it doesn't I nominate 'fluctuation metric' or maybe 'swing metric'. Even 'relative variance' seems ok, as that is what we are really talking about - variance relative to average profit.

I am pretty sure it must already have a name

Regards
Brad S
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  #26  
Old 10-27-2005, 02:55 PM
pooh74 pooh74 is offline
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Default Re: Turbos vs. regular SNGs (variance)

[ QUOTE ]
[ QUOTE ]
And I believe that was what OP was asking.

[/ QUOTE ]

Fair enough. I mean, I know that's what the OP was asking. That's what everyone is asking when they ask about variance. Trouble is they keep calling it variance, and that's only a part of it.

...then the math inclined get frustrated when nobody gets why variance is pretty constant.

Believe it or not, I am not actually that formally trained in math myself, so I don't know it the metric I describe has a technical name. If it doesn't I nominate 'fluctuation metric' or maybe 'swing metric'. Even 'relative variance' seems ok, as that is what we are really talking about - variance relative to average profit.

I am pretty sure it must already have a name

Regards
Brad S

[/ QUOTE ]

Fair enough...

Though variance being a constant in reality then frees up the term for our purposes to mean what OP meant it to be. [img]/images/graemlins/wink.gif[/img] FWIW, I am not that interested in these things and only play to get better, have fun, and make money. However, in my first response to this thread I addressed the OP's question quite well for HIS purposes. I also felt like Nick M's response was right on as well...

Again, if we want to start calling it "swing", thats fine by me...
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  #27  
Old 10-27-2005, 03:11 PM
schwza schwza is offline
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Posts: 113
Default Re: Turbos vs. regular SNGs (variance)

[ QUOTE ]
Definitely more variance compared to their normal SNGs, and lower ROI, but higher $/hr .

[/ QUOTE ]

care to back that up?
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  #28  
Old 10-27-2005, 03:44 PM
swiftrhett swiftrhett is offline
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Default Re: Turbos vs. regular SNGs (variance)

Maybe the swing metric you brought up is something like (profit / #ofgames) - (standard deviation / #of games). So, if a player has an ROI of 20% and a standard deviation / tourney of 1 buyin, then the tourney buyin scales as the square root of the number of games he plays. So, for instance, if this player does 100 games / week, that's a "swing metric" of 20% * 100 / 1 * sqrt(100) = 20 - 10 = 10. Basically, this means, even one standard deviation from your average, you expect to be up at least 10. You could divide them if you're looking for relative swings I guess. The problem with quantifying this is that players who play wildly different amounts of tournuments see this very differently, and in general your standard deviation goes down relative to other things if you play more.

[ QUOTE ]
[ QUOTE ]
And I believe that was what OP was asking.

[/ QUOTE ]

Fair enough. I mean, I know that's what the OP was asking. That's what everyone is asking when they ask about variance. Trouble is they keep calling it variance, and that's only a part of it.

...then the math inclined get frustrated when nobody gets why variance is pretty constant.

Believe it or not, I am not actually that formally trained in math myself, so I don't know it the metric I describe has a technical name. If it doesn't I nominate 'fluctuation metric' or maybe 'swing metric'. Even 'relative variance' seems ok, as that is what we are really talking about - variance relative to average profit.

I am pretty sure it must already have a name

Regards
Brad S

[/ QUOTE ]
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  #29  
Old 10-27-2005, 04:30 PM
AleoMagus AleoMagus is offline
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Location: Victoria BC
Posts: 252
Default Re: Turbos vs. regular SNGs (variance)

[ QUOTE ]
in general your standard deviation goes down relative to other things if you play more.


[/ QUOTE ]

I'm not sure this is really that much of a problem

Consider two players A and B who both play $11 SNGs
A has a 30% ROI and a SD of ~$18.50/t
B has a 3% ROI and a SD of ~$18.50/t

per SNG, if we define this metric as SD/profit:

A would have a value of 6.16
B would have a value of 61.6

this means that compared to one another B would perceive ten times the swings.

After 100 SNGs,

A would have a SD/100t of $185 and a profit/100 of $330
B would have a SD/100t of $185 and a profit/100 of $33

per 100 SNGs then, continuing to define this metric as SD/profit

A would have a value of $185/330 or 0.56
B would have a value of $185/33 or 5.6

So, compared to each other, B still experiences swings ten times as big relative to his bankroll growth. Over 100 SNGs however, they both experience much smaller swings relative to expected growth than they do over a single SNG. This all makes sense to me.

After all, if player A runs badly, he will recover much more quickly, and may even continue to show a profit. If player B runs badly, he will take much longer to recover and will almost certainly show a loss. The reason why the values for 'swings' are much lower in the 100 SNG case is that we are treating a 100 SNG sample as a single unit, and obviously when dealing with these units, swings will be much smaller. When dealing with 100 SNG samples, this metric is lower for the very reasons that you earlier mentioned. SD does not increase linearly, whereas profit does.

As far as wildly different 'swing' values based on differing amounts of games, the solution is just to use the single unit value, much as we do with SD. After all, SD is wildly different as well when we consider differing samples, and we know how to deal with that.

I haven't yet compared this to your suggested metric for takling about swings, so I guess I'll take a closer look at it now, and post again when I can see if there is an advantage to using it. If I am missing something, let me know.

Regards
Brad S

PS - for anyone wondering what these 'swing' values mean, it is just the multiple of your expected profit that you may be up or down from your expectation over the sample.

ie - with a swing value of 61, if you run 1 SD bad, it will on average take you 61 tourneys to recover (return to that expectation). similarly for larger samples
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  #30  
Old 10-27-2005, 04:44 PM
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Default Re: Turbos vs. regular SNGs (variance)

[ QUOTE ]
Turbos will have less variance only because there are 9 players instead of 10. In SNGs, your variance will always be near the same, regardless of your ROI because it depends on your place percentages and 13%/13%/13%/61% yeilds a variance similar to the one that 10%/10%/10%/70% gives.

Somebody around here learn some math for christsakes.

The square root of the sigma-squared is your standard deviation. That's why your standard deviation only increases as the square root of the number of games you play, while your profit increases linearly (ideally).

[/ QUOTE ]


Your standard deviation (per game) doesn't 'decrease' at all--in fact, it converges quite rapidly mostly (if not purely) as a property of the tourney structure.

I think what you mean is that as you play more and more games, your ideal aggregate profit increases linearly whereas the difference between your actual and ideal aggregate profit (for any given confidence) increases logarithmically.

I guess your wording is technically true if we're viewing blocks of SNGs as 'supergames'--your standard deviation per supergame does increase logarithmically as you increase the number of games per supergame.

Anyway, I think your OP is rude.
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