Variance Tool for the Mathematically Challenged

[Robb]

I posted the details how to calculate "typical" downswing scenarios in this thread, but folks complained about the very simplified math involved.

http://www.flopturnriver.com/phpBB2/...ls-t67185.html

So I decided to do y'all a favor. I made the following Excel Spreadsheet and posted it on my website at school (I'm a math professor at NGCSU in Dahlonega, GA, for those who don't know). I teach stats every day, an intro course and a calculus-based course for math majors. Here's the link.

http://radar.ngcsu.edu/~rsinn/links/varcalc.xls

What does it do? You enter your win rate and standard deviation (easily found in PT), and it calculates the decile ranges for your expected short term win rate (or loss rate, as the case may be). It's set to analyze 10k hand periods, but you can adjust it as needed. It also gives some "downswing" stats, letting you know worst case scenarios for ice-cold coolers and what they can do to your bank roll.

Finally, you can use it to personalize your bankroll requirements for moving up a level. Directions are included.

I would be happy to answer any questions you have about the calculations or estimates or how to use them. Caution: the provider makes no claims as to accuracy or usefulness of content, especially not the Bank Roll requirements for moving up!! LoL. Use 40 BI when moving up or proceed at your own risk!! The spreadsheet just provides hard numbers (personalized based on your stats) that experts are using when they come up with their recommendations.

[Muzzard]

Sweet dude!

[Robb]

Here's a segment of the discussion on Spoon's Bankroll Management for People with Balls thread (linked above). I checked the math, and it seems accurate enough. The math below is NOT hard, but if it's intimidating, grab the XLS file from my website and play around a bit. I did. And it's interesting how, despite my 5+ ptBB/100 win rate lately, I can still expect to lose $$ in about 1/3 of my sessions.

When we think of bankroll management, we want to lower our risk of ruin to some certain standard, and for everyone this is different. Demiparadigm, before dsaxton staked him for meth, did a really great post explaining these statistical truths behind bankroll management as well.

You check out your SD and win-rate, decide what risk of ruin you want, plug it all into a formula, and out comes how many buy-ins you should play with at a certain level. That's tailor-made bankroll management, which I thought was discussed in the bankroll management 101 thread, but maybe I was mistaken.

Edit: I found the post Demi made,
http://www.flopturnriver.com/phpBB2/...ly-t22364.html

A Simple Way to Calculate Your Personal "Downswing" Stats

I teach stats, both the intro general ed course and calculus-bases prob-stat course for math majors. While Demi's post is certainly mathematically correct, I fear some FTR folks will see all the equations and just puke, rather than opening PT and doing the work with a calculator.

Do this simple exercise: open PT, filter to all hands in the database at your main level, and note your ptBB / 100 win rate. Go to sessions tab and click "more detail" in top right. Write down your Standard Deviation / 100 hands.

Example: me, NL10, 65k hands
win rate: 4.6 ptBB/100
standard deviation: 46 BB/100

Let's use 100 "typical" sessions of 100 hands (since PT uses BB/100 units). We can estimate our earnings by gathering them into the middle 95% (what generally happens) and then outliers: 10k heaters and 10k coolers.

Here's how it works using a simplified formula that's very accurate (the details are below, for the curious):

M = SD / 5

Example: M = 46 / 5 = 9.2

Now get the two endpoints of your interval by taking your winrate and first adding and then subtracting M from it:

Example:
Lower Bound = 4.6 - 9.2 = -4.6
Upper Bound = 4.6 + 9.2 =13.8

This means that over any 10k hands, I can expect my win rate to be between -4.6 ptBB/100 and 13.8 prBB/100 95% of the time. Now here's the kicker: 2.5% of the time I can expect it to be WORSE than -4.6 ptBB/100, and 2.5% of the time I can expect it to be BETTER than 13.8 ptBB/100.

For me, at NL10, a -4.6 ptBB/100 over 10k hands would mean I dropped 460 ptBB's, or $92. And 2.5% of the time I can EXPECT EVEN WORSE!!!

On the bright side, or positive variance, I can expect to be up >13.8 ptBB/100 over 10k hands 2.5% of the time, as well.

Notice two things. First, it's easy to calculate. Second, this illustrates Spoon's point: This is a decent win rate. Imagine for the moment you've moved up and are eking out on 1.5 ptBB/100, with the same variance. Then, the Lower Bound is -7.7 ptBB/100, and over 10k hands you can expect to lose AT LEAST 770 ptBB AT LEAST 2.5% of the times you play 100 sessions of 100 hands (10k for the math challenged).

That's 15.4 buy-ins. And it happens 1/40th of the time to a WINNING player who's on a 10k cooler - playing well, and just experiencing negative variance.

Just run those quick calculations on your own stats, and see what you come up with. And then ask yourself "how much bankroll do I need if I'm taking a 1 in 40 shot at losing 17 buy-ins," or whatever your Lower Bound number (the estimate of your personal 10k cooler damage) turns out to be.

If you think this kind of negative variance doesn't happen, just ask guys like Miffed and Spoon and any other of the folks who've logged 400k hands. Miffed, as I recall, was down nearly 50 buy-ins on a frigid cooler last Fall. Spoon was down 26 buy-ins (or 13, if it was NL200) in January. Those are just the ones I remember off the top of my head.

Just to get the math right,the actual calculation is as follows:

Lower Bound = WR - 1.96 * SD / sqrt(n) , where
WR = win rate in ptBB/100
SD = standard deviation in ptBB/100, and
n = number of 100 hand sessions under consideration.

The Upper Bound = WR + 1.96 * SD / sqrt(n)

I used "2", so that 2 / sqrt(100) = 2/10 = 5. This is pretty accurate since I rounded my standard deviation down (it's actually 46.85, not 46).

The summary chart of your personal expectation in poker is this:

Over 40 typical periods of 10k hands, you should expect:

1 cooler at least as bad as your Lower Bound
38 periods between the Lower and Upper Bound
1 heater at least as good as your Upper Bound

The math is simple. If you have 40k hands in your database, or more, you can calculate these statistics easily and accurately, tailored to your game on your site against the villains you face.

One final note. When you move up, remember that your win rate typically goes down. If you have a 4 ptBB/100 at your current level, can you really expect much more than 1.5 ptBB/100 for the first 10k hands at the level above? That lower bound for most players is going to be in the 12 - 18 buy-in range. In 10k hands. Playing winning poker.

Does 40+ buy-ins for moving up seem so "nitty" now? If it does, then actually sit down and do the calculations, dammit!! Playing poker well for the long term is all about managing variance.

Final caveat: it's late, I'm a morning person, and i'm exhausted. I will have to recheck all the math I did in the morning before I'm willing to claim it's 100% accurate. But i'll let y'all know with an edit when I've rechecked everything.

[will641]

this is interesting and ill have to try it out later. if this is accurate you could make some money with this, imo.

[Robb]

this is interesting and ill have to try it out later. if this is accurate you could make some money with this, imo.

It's statistically accurate. It can probably help someone with tons of experience make sense of their experience. I wouldn't consider trying to make money off it. Seems too basic for that.

[paulwright]

Awesome Robb - very interesting and insightful...

[Unibomber14]

i will never understand this s***. Maybe I shoulda gone to college.

[Robb]

i will never understand this s***. Maybe I shoulda gone to college.

What's to understand? Just plug in your numbers and glance down at the decile distributions. Each range should occur 10% of the time. I did this so people would not HAVE to go (back) to college