How many SNGs...
...do you think I need to play before I can start making forecasts along the lines of "each SNG adds $x to my bankroll (no matter how I finish)?" I've been doing quite well lately (in the money 70% of the time over my past 20 SNGs), and I want to know at what point I can comfortably quit my job (just kidding:))
Thanks!
Thanks!
Comments
An answer I'm more confident with: Many more than most people would initially think.
ScottyZ
Anyway, an ITM rate of 70% sounds too high to be sustainable in the 'long run'
Obviously, you can calculate a $/tourney average with any sample size, but only as that sample increases will your confidence go up
This is calculated as follows
First, calculate your standard deviation per tourney
SD = SQRT((Prob 1st)(net $ 1st)+(Prob 2nd)(net $ 2nd)+(Prob 3rd)(net $ 3rd))
your standard deviation after n tourneys will equal (SD)(SQRT(n))
to figure a degree of confidence to +/- X dollars per tourney
X/(SD/SQRT(n)) = Z
Take this Z value and convert on a table of the normal standard distribution
These tables will come up on any google search
This converted value (a) will give you your % confidence as in the following formula
% confidence = 100(2a-1)
I have an excel spreadsheet which will calculate confidence values on this address
http://www.aleomagus.freeservers.com/Spreadsheet
It is the 'universal' file
This spreadsheet calculates confidence on the 'stats' page in three different catagories
Your WINNING confidence (confidence to +/- your avg profit/tourney)
+/- $2 per tourney
+/- $1 per tourney
If you just fiddle around with input values, you will find that indeed, the sentiments in this thread are correct
It will take about 250 tourneys for an player getting what I consider a 'typical' standard deviation with modest win rates (25% ROI) to be only 65% confident that their results are accurate to within 10% of the initial buy-in.
This is to say that after 250 tourneys, a 10+1 sng player like I describe could be 65% confident that their win rate (of about $3 profit/tourney) is accurate to within +/- $1
Not insipring, I know, but such is life
In truth, a sample of 500-1000 tourneys is where you really start to become confident with any degree of accuracy
On the bright side, a sample as small as 100 can actually give you a pretty high (over 90%) degreee of WINNING confidence. So you may not know right away how much you can expect to profit, but you can be pretty certain that you will not go broke.
Regards
Brad S
That's like saying someday you are going to finish in the top 3 of each and every sng tourney you play in. I'd say never. No reflection on you. Just the law of averages. No one wins all the time. No one. Probably not the way you meant it though huh?
I've also had hot streaks like that too, but then along come the cold streaks. lol
I like Scotty's answer. 500 seems like a long enough time to do a calculation of long term averages.
Your ITM (In The Money) Rate is not very important when forecasting future expectation.
ITM will have an immediate effect on your variance, but nothing more
Your ROI (Return on investment) or your $/tourney average is what you should really be looking at. Actually, your $/hr is perhaps even more important
Many great SNG players like to gamble early with big coinflip hands and take a significant knock to their ITM% by doing so. This has the effect however of shortening average time per tourney, so they can actually improve their hourly rate if they are capapble of weilding abig stack well when they do win early gambles and can post more wins.
On the other hand, it is entirely possible to be a 50%ITM player and be losing money.
As far as what is actually sustainable:
Excellent players have between a 38% and 50% ITM in one table (10 player) sngs. Higher than this is very difficult and would hurt your return on investment as you would likely be gambling less for the win and sneaking into 3rd more often. Beyond 55% is impossible over a large sample.
Excellent players have between a 20% and 50% ROI. At the $10-30 levels, 40% is VERY good. At higher levels, less and less should be expected. The best $215 player I know makes about 25%ROI.
Hope this helps
Regards
Brad S
My apologies to anyone who has been trying to figure SD and confidence with this info...
I have made one tiny error but a significant one nonetheless
Quote:
SD = SQRT((Prob 1st)(net $ 1st)+(Prob 2nd)(net $ 2nd)+(Prob 3rd)(net $ 3rd))
should read:
SD = SQRT((Prob 1st)(net $ 1st^2)+(Prob 2nd)(net $ 2nd^2)+(Prob 3rd)(net $ 3rd^2))
The spreadsheet has always done this correctly. I simply forgot to square the net $ amounts for each prize finish
Regards
Brad S
I believe the correct formula for the per tournament standard deviation of a bankroll change should be:
SD = SQRT((Prob 1st)(net $ 1st^2)+(Prob 2nd)(net $ 2nd^2)+(Prob 3rd)(net $ 3rd^2)+(Prob Out_of_Money)($ lost^2) - (Average bankroll change)^2)
[using the convention that a $ loss is a negative number]
Note that "$ lost" is simply the tournament buy-in (+ fee), and it is correct to use *net* $ wins. The "Average bankroll change" the same thing as the (per tournament) win/loss rate.
This comes from the formula
Var(X) = E[X^2] - mu^2
where X is the (per tournament) change in bankroll, and mu = E[X].
ScottyZ
I noticed those errors after the first one I noticed, and my spreadsheet does not do this correctly either.
I have constructed a confidence calculator with this correct formula for standard deviation
It is here:
http://www.aleomagus.freeservers.com/Spreadsheet
Take a look and let me know if you see any other errors.
Regards
Brad S