Posted: Fri Jul 20, 2012 2:22 am Post subject: Re: New article by Alex Rousso - Return on Investment
Pizzicato wrote:
evelyn wrote:
I have not seen an ROI of over 100% over a large sample at any level in the 180s.
I wasn't referring to 180's when I made my comment about 100% ROI's at lower - midstakes tournaments...
Fair enough but I think that might be illusory anyway. From my own research the bigger tournaments are roughly about the same standard as the equivalent 180s. It's impossible to tell with any certainty because of the massive volumes required to find out.
Posted: Fri Jul 20, 2012 3:49 am Post subject: Re: New article by Alex Rousso - Return on Investment
Quote:
Great post it looks like the ROI calculator I use works ! I think all the MTT players would really thank you if you did something similar for 200, 400, 1000 and 5000 runners. I have not seen this information anywhere before and it is very useful.
Thanks, as far as the 200, 400 etc bigger fields go the plot for each would basically look exactly the same but be proportionally wider at each point due to the higher variance, ie, stdev in them. I suppose it wouldn't be too difficult to do a few (only need to calc. the stdev really) and stick them onto the same graph - I'll try it out and post it up at least for the 180's.
I think these results by using the gaussian and 'The Central Limit Theory' are fine, about as accurate as you could possibly want once the number of games is in the 1000's. In practice it's kind of pointless being accurate at these points as you can't play enough games fast enough to have a steady roi although it is useful to see the shape of this ideal case.
There will be ways to get a narrower confidence range with small number of tourney's by different approaches, maybe by a technique called Bootstrapping for instance, but I have never seen this done for poker results. Perhaps people with more knowledge than I could chip in some ideas.
Posted: Fri Jul 20, 2012 5:08 am Post subject: Re: New article by Alex Rousso - Return on Investment
That's beyond my competence but maybe one of the Alexs could take it further. Accuracy is important not because players will get through the number of games required for convergence but so they can look at the variance and calculate their bankroll requirements. Players going broke by playing stakes which are too high for their bankroll is very common in poker.
Posted: Fri Jul 20, 2012 12:08 pm Post subject: Re: New article by Alex Rousso - Return on Investment
For 180s still with a 25% roi, a typical finish distribution will be something like
(0.6, 0.6, 0.6, 0.6, 0.7, 0.7, 0.9, 1.0, 1.1, 1.1, 1.1, 1.1, 1.1, 1.1, 1.1, 1.1, 1.1, 1.1)
There may be a bit more of a peak heading toward the 10th spot but as 10 to 18 all get payout there is no need to worry about this only the average earned at these points. Anyway, the distribution won't have a massive effect (so long as it's not all 2nd or something) as the stdev won't change much for any believable 25% roi.
With this distribution the mean is 0.2508, (25%) the stdev comes out as 5.510977, so variance = 30.370866
At 20000 these have a 90CI range of 18.6% to 31.4% (sompared to 45s 25% of 21.5% and 38.5%)
(alt+p)[/img]
As you can imagine for other sizes you will just get a family of wider plots for larger fields. The stdev will be larger the more players for standard tournies and so the 90% CI will widen. Again, the most likely roi is still the central point, 25% in this case. And these are ideal cases not real life practical.
One thing to notice is that if you thought your roi range would be tight at say 10000 games you might have thought that it would be really, really accurate perhaps twice as good at 20000 but this is not the case. You get a sort of diminishing return for the extra data.
The sqrt(10000) = 100, the sqrt(20000) = 141, so it's only 1/1.41 better at this point. To get it half as wide as 10000 you would need to have 200^2 games = 40000 games.
Perhaps these CI's are useful to some extent for bankroll management but I think downswing probabilies are more useful overall and it is possible to produce graphs for these (easyish upto 180s) - but these are the stuff nightmares are made of.
Posted: Tue Jul 31, 2012 2:38 pm Post subject: Re: New article by Alex Rousso - Return on Investment
MetalBox wrote:
One thing to notice is that if you thought your roi range would be tight at say 10000 games you might have thought that it would be really, really accurate perhaps twice as good at 20000 but this is not the case. You get a sort of diminishing return for the extra data.
Yes. Have you seen the "How many hands is enough?" table from this article (seems like a bazillion years ago now - and yet it's only four!):
This is for cash games rather than MTTs, but the exponential number of hands down the LHS column tells the same story. Kind of depressing really! _________________ Twitter: PicklemanPoker
Pickleman articles: http://www.bluffeurope.com/poker-news.../pickleman-poker/
Posted: Tue Jul 31, 2012 9:06 pm Post subject: Re: New article by Alex Rousso - Return on Investment
pickleman wrote:
MetalBox wrote:
One thing to notice is that if you thought your roi range would be tight at say 10000 games you might have thought that it would be really, really accurate perhaps twice as good at 20000 but this is not the case. You get a sort of diminishing return for the extra data.
Yes. Have you seen the "How many hands is enough?" table from this article (seems like a bazillion years ago now - and yet it's only four!):
This is for cash games rather than MTTs, but the exponential number of hands down the LHS column tells the same story. Kind of depressing really!
Yes, this for cash has the same relationship, you get this dimishing (1/sqrt(no. games) effect for the amount of games. The two rows 100,000 and 500,000 the sqrt of the bigger number is roughly double the other so the hourly winrate range is roughly only half as wide even though you will have played 5 times as many games. To get this range down by half each time you always need 4 times as many results.
Oh, from my previous post I did check what amount of results was needed for a 180 man to produce a good gaussian distribution. An arbitrary rule of thumb in stat. books is that 30 is often good, due to the very spiked nature of these tournie payouts we need a few more but by 100 it gets close(ish), by 250 pretty good and 500 it gets hard to see a difference. I have stuffed some graphs to show this onto a blog post. Once you have 500 results the CI is going to be accurate below this there may be some way to get a better estimate but nature, via the CLT, steps in and in big numbers (500+) the wide range is likely the best estimate you can really do (maybe some trend analysis just may help - I'm not sure). For 1 table tournies the icm'd allin EV, will have a lower stdev and hence be a better predictor.
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