Ok after getting my brain into math mode, Its been awhile lol. looking at angels formula, something seems missing.

Variance = (1/number of sessions)x - ((hourly earn)^2/number of sessions)(T) =
(1/10)(52,666) - ((20)^2/10)(100) =
5,267 - (400/10)(100) =
5,267 - 40 = 5,227

T= The number of hours played, but seems to have no affect on the formula tho, what am I missing? The 100 at the end of formula line is # of hours.

also I found a couple of formulas for once you get your standard deviation to save a couple of steps.

BR requirement: http://www.reviewpokerrooms.com/poker-g ... ments.html
Risk of ruin: http://www.poker-tools-online.com/riskofruin.html

_________________
http://twitter.com/ron200sx

according to the formula it should be multiplied by 100(number of hours) so the answer should be 1267 not 5227. Making standard deviation 35.59.
What the hell is going on. Im going nuts. Please someone tell me if angel made the mistake or me. lol

_________________
http://twitter.com/ron200sx

Ok, I plugged my numbers up to Feb 19, 2010 into Angel's formula and compared it to axb001's formula, and they came out to be pretty close.

Stake ............ axb001's formula ........ angel's formula
1/2NL .............. $165.19 ................ $164.85
2/5NL .............. $399.99 ................ $383.97

And now for the fun part, BR requirements for moi, using different risk of ruins, rounded up to the nearest dollar:

Risk of ruins -------- BR req (1/2NL) --------- BR req (2/5NL)

5% .................... $2000 ...................... $5015
1% .................... $3074 ...................... $7709
0.1% ................. $4611 ...................... $11564

Seems very reasonable numbers to me.

How about some sensitivity analysis using some arbitary win rate? Let's keep the ROR at 5% with same SD, and let's vary the win rate and see what happens for 1/2NL.

Win Rate ..... BR req (1/2NL) where ROR = 5%

$20.35 .............. $2000
$10 ................. $4325
$5 ................... $8771
$2 ................... $22013

So according to this formula, if I can tolerate a 1% chance of going busto, I only need 15 buyins ($200 each) for the 1/2NL game. Number seems low compared to conventional rule of thumb (30 buyins), but in line with my data when I looks at my accumulative win/loss plot.

Looks like he make an error in applying his formula. I plugged in the numbers into my spreadsheet using both axb001's formula and Angel's:


SD = $37.52 (axb001)
SD = $35.59 (Angel)

The std. deviation is very low, but looking at this arbitary example, all his sessions are winning ones, and they are fairly consistent. I think the formula is ok, but he did make a mistake in applying it.

Now I am tempted to move my data since Feb 19th into this spreadsheet. Argh, this is the biggest problem with my spreadsheet approach.

ok cool so you do multiply by the total hours at the end. I am not crazy.

_________________
http://twitter.com/ron200sx

when you plugged in your numbers, you did use your hourly rate just for the time frame only right? and not your overall winrate for longer period of time.

_________________
http://twitter.com/ron200sx

I used the win rate for the data period. Otherwise it doesn't make sense.

FWIW, I just finished populating my spreadsheet with the data up to yesterday. The good news is, my standard deviation went down a bit for both 1/2 and 2/5, and my win rate for 1/2 went up a bit. The bad news is, my 2/5 win rate went down a little.

Have to work on that!

You guys are giving me a headache.

_________________
Vegas is my Graceland.


http://twitter.com/chadwilliams71

Sorry, it must be because of the poor formatting. the spaces between the columns seem to disappear when I submit the post. I fixed it now with dots in between.

Just a quick explanation as to why my numbers are different from angel's. Although the formulation looks different, we are using the same calculation with the exception of step 5 of my calculation where I ask you to divide by one less than your number of sessions. If you instead divided by just the number of sessions, then you would get angel's formulation. This is why the numbers are close but not identical (and in fact will get closer the more sessions you play)

So which one is correct? The answer, rather surprisingly, is that they both are, its just that they are calculations for ever-so-subtly different measures. It is akin to the difference between the STDEV and STDEVP functions in EXCEL.

Angel is giving the formula for calculating the standard deviation for a specific set of sessions to date. However, it is a quirk of statistics that the standard deviation of a sample tends to slightly underestimate the "true" long-term standard deviation you would see if you were to carry on playing for many many more sessions. My formula makes this correction. For the puposes of calculating a risk of ruin, it is this corrected value that should be used, as you are extrapolating for the long-term statistical properties of your income profile.

The bigger your sample (i.e. the more sessions you have) the less this correction matters, as you will naturally get closer and closer to the long-term value.

For completeness, here is my formulation again:

1. First you need calculate your overall average win rate (R). This is pretty straightforward – its just the sum of the outcomes of all your sessions divided by the sum of the total number of hours you've played. This figure will be in $/hour.

2. Create a new column of data which contains the 'expected' return for each session. You calculate this by multiplying R by the number of hours in that session.

3. Next create another new column containing your actual return for that session minus your 'expected' return for that session. Call this 'D'.

4. Now create a third new column containing D squared then divided by the number of hours in the session.

5. Take the sum of this third column, and divide it by one less than the total number of sessions you have played.

6. Finally square-root this number. This should be the best estimate of your hourly standard deviation.