How Winrate Affects Downswings/Breakeven Stretches

[sthief09]

Same applies as for the last post. Barron, if you don't think this belongs (and I feel that this belongs less than the previous post) please shift it over to MHHUSH.

I don't know 100% if this is right but it seemed right to me. You have a winrate x bb/100. Your standard deviation per 100 hands is 18. You've played n hands. Your standard error is 18/sqrt(n/100). For the whole sample it is 18*sqrt(n/100). Your BB won is x*(n/100). For 99% confidence you are +/- 3 SD. So your BB won will be x*n/100 - 3*18*sqrt(n/100). Take the derivitive, set to 0, and that is your low point, in terms of hand #, given different x's. Plug in your n to the original formula to find your biggest downswing. I always thought this would require a Markov chain, but the method I just described makes sense to me.

I plugged this into Excel, and came up with the following numbers and graph. The graph represents a plot of what a player's Poker Grapher graph would look like if he ran worse than 99% of players. Pretty interesting I think:

<font class="small">Code:</font><hr /><pre>
Winrate 0.25 0.5 0.75 1 1.25 1.5 2 2.5 3 3.5 4
Biggest Downswing -2,206 -1,458 -972 -729 -583 -486 -364 -292 -243 -208 -182
Biggest Breakeven Stretch 4,665,600 1,166,400 518,400 291,600 186,624 129,600 72,900 46,656 32,400 23,804 18,225
</pre><hr />

[1800GAMBLER]

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

[sthief09]

[ QUOTE ]


[/ QUOTE ]


guess theres a lot to be said for playing a game you can crush vs playing a game with a slightly higher earn, especially if you need to pay the bills or are barely rolled for the bigger game.

[jph0424]

It is amazing that someone with a winrate of better than 1BB/100 could be losing after playing 200,000 hands. Scary. I guess my "little" 52k breakeven streak a couple months back doesn't mean I necessarily suck.

[krishanleong]

This all makes sense to me.

I think we haven't seen the absolute earth shaking variance because most people can't play through a huge downswing or are not properly rolled. There have been a few examples of player having this extreme variance (NLSoldier and sbx). I think we'll see more of it in the future as more prepared players play through super tough swings.

Krishan

[sthief09]

[ QUOTE ]
This all makes sense to me.

I think we haven't seen the absolute earth shaking variance because most people can't play through a huge downswing or are not properly rolled. There have been a few examples of player having this extreme variance (NLSoldier and sbx). I think we'll see more of it in the future as more prepared players play through super tough swings.

Krishan

[/ QUOTE ]


and this graph ignores tilt

[Glenn]

You did this incorrectly. First of all 3SD's is 99.7% confidence, so the chance of a -3SD event is only .15%. Secondly, (and more importantly) finding the number of hands where a 3SD downswing gives you the biggest negative result is not the correct way to approach the problem of "how much can I lose in a row". This is similar to the bankroll method Mason uses in GTaOT and it is flawed. The problem is much more complex because there are many sets within the set of data, but there is also correlation between them. Search brucez's posts for an actual detailed explanation. The easiest way to analyze this problem is through simulation which can be done with relative ease in excel.

[climber]

Glenn,
Would you have a couple minutes to show us how to simply do this is excel "the right way?"

[PokerPrince]

I like soda.

[phish]

Yeah, this is incorrect. for example for someone with a winrate of 1.5/100 and std dev 18/100, the max downswing is under 500 and max breakeven stretch is about 130K hands.

To do this in excel set up the following columns:

1. # of hands (by increments of 100)
2. expectation (multiply column 1 by winrate (1.5 or 2 or whatever)
3. variance (multiply column 1 by 324) The variance is the square of the std dev, so if std dev is 18, variance is
18*18=324. You could substitute some other std dev assumption.
4. std dev = square root of column 3
5. 3 std dev downswing = column 2-(3 x column 4). This is your expectation minus a 3 std dev downswing.

Then simply copy the formula straight down the column and you'll see that column 5 grows (more negative) but after a certain point becomes positive. The largest negative number is your max downswing and the number of hands it takes to be positive tells your max breakeven period.