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#11
11-09-2007, 08:46 AM
 GrumpyB Member Join Date: Jul 2007 Location: Down and Out in Paris and London Posts: 94
Re: bankroll

Pzhon,

Your posts are just pure class - thank you, thank you, thank you.

But can I just check that I've got this right, please:

[ QUOTE ]
[img]/images/graemlins/diamond.gif[/img] Suppose you decide you want to use comfort level 3 as a starting point, and you believe your win rate is about 15 big blinds/100 and your standard deviation is 90 big blinds/100. Bankroll = 3 * 90^2/15 = 1620 big blinds, or about 16 full buy-ins.

[/ QUOTE ]

Well I thought I'd use your forumula in reverse, just to work out my current comfort level. So I used my current figures:

Win rate: 41 bb/100
[@ NL10 over past 3,000 hands. Yes, not a big enough sample, I know, and not even typical as someone just gave me 3BI in less than 50 hands with three mega-stoopid all-ins, but lets just pretend].

Std dev: 72/100 [over 20,000 hands @ NL10, NL25 and NL50]

Bank Roll: 39 BI [@NL10]

and the formula

Comfort = [BR.WR]/V

where BR = Bank Roll, WR = Win Rate, V = Variance [SD squared]

But when I plugged in the figures [39 x 41]/[72 x 72] I got a comfort value = 0.3084

Confusion - that looks real uncomfortable - and then I see that while the SD and WR in you formula are expressed in x/100 your BR was expressed in bb. So should I really have worked this out as:

comfort = [3879 x 41]/[72 x 72] = 30.7

That would look much nicer.

[And I'm real sorry this is such a really dumb question, but I'd really like to make sure I get this.]
#12
11-09-2007, 10:34 AM
 pzhon Senior Member Join Date: Mar 2004 Posts: 4,515
Re: bankroll

Yes, you can compute your current comfort level by

comfort = bankroll * true win rate / (standard deviation^2).

As you note, everything on the right hand side should be expressed in the same units. You can convert everything to \$, or to big blinds, or to buy-ins.

The comfort level of 31 looks like you are being quite conservative, so you might be looking at the possibility of moving up when you get more data on your win rate. However, it's natural to go above your target comfort level since the stake levels are discrete (there is no NL \$17 to try en route to NL \$25) and the games get tougher as you move up.

If your win rate at NL \$25 expressed in \$/100 is lower than your win rate at NL \$10, then in the short run, it is better to play NL \$10 regardless of your bankroll. You might still take shots at NL \$25 with the hope that your win rate will improve, or that you will more rapidly gain the skills to beat higher levels while playing NL \$25 than NL \$10.

To determine when moving up is justified in the short run, you can compute the comfort level of the difference between the two levels,

differential comfort = bankroll * difference in win rates / (difference in variances)

For example, suppose you win \$10/100 with a standard deviation of \$80/100 at NL \$100, and \$15/100 with a standard deviation of \$180/100 at NL \$200, and suppose your bankroll is \$5000. The difference in win rates is (\$15-\$10)/100 = \$5/100, and the difference in variances is \$180^2 - \$80^2 = 26000 square dollars per 100 hands. Your differential comfort level is 5 * 5000 / 26000 ~ 0.96. Generally, you should move up if the differential comfort level is more than half of your target comfort level, so if your target level is 2 or greater, this says you should stick to NL \$100 at the moment. This may be the case even though your comfort level at NL \$200 would be 5000 * 15 / 180^2 ~ 2.3 which might be slightly greater than your target comfort level, and you would much rather play NL \$200 than nothing.
#13
11-09-2007, 11:47 AM
 GrumpyB Member Join Date: Jul 2007 Location: Down and Out in Paris and London Posts: 94
Re: bankroll

Wow, that's great. I really appreciate you taking the time to explain this.

Thank you.
#14
11-09-2007, 12:31 PM
 Nightlight87 Senior Member Join Date: Aug 2007 Posts: 171
Re: bankroll

Pzhon your posts are fantastic. Lots of great information thats well explained, much better than a set 20BI rule. Thanks.
#15
11-09-2007, 12:33 PM
 PBiddy412 Junior Member Join Date: Nov 2007 Posts: 1
Re: bankroll

Okay, I'm a little confused by this equation. Where does that standard deviation come from? Say I wanted to go with 4, being conservative,with a 2% roi (according to sharkscope), what would the standard deviation be?
#16
12-01-2007, 05:57 PM
 HoldenFoldem Senior Member Join Date: Nov 2005 Location: BC, Canada Posts: 1,075
Re: bankroll

Nice post. very clear and concise. the examples i found particularly helpful . ty

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