SnG Bankroll Calculations (Warning: Math Ahead)

[chillin411]

Since there always seem to be a lot of questions about SnG bankrolls, and why is 30 buyins always the magic number, I thought I'd write out the math to explain where that number comes from, and what adjustments you need to make for your own personal bankroll.

This is the bankroll formula in all of its glory (this works for all disciplines of poker, by the way):

Bankroll = -(s²/ 2*ER) * ln(RoR)

Where...
:: s represents the sample standard deviation
:: ER represents the assumed earn rate
:: RoR represents the assumed risk of ruin

Now, the sample standard deviation for full table SnGs is in the neighborhood of 1.5 to 2 buyins. If you play at a site like Stars with 9 player tables, your SD will be closer to 1.5; if you play at a site like Party with 10 player tables, your SD will be closer to 2. Both will be fairly close to the center of this range, however.

So, let's do a problem. Suppose you have a 15% ROI, and you're playing as a hobby, so we'll set the risk of ruin at 5% (0.05). If you were playing for a living, I would set this number very low, typically at 1% RoR.

At this point, it's just plugging it into the equation:

Your win rate in SnGs is your ROI, which in this case is 0.15 buyins.
Your SD is in buyins as well, we'll use 1.75.
Your RoR should be in decimal format, so we'll use 0.05.

Bankroll = -(1.75² / (2*0.15)) * ln(0.05)

After running that through the calculator, you end up with 30.58 buyins.

Of course, there's no need to actually sit there and pull out your TI-83 in order to do this, you can always plug in the numbers into the ITH Bankroll Calculator. With the bankroll calculator, the only change is that it takes RoR as a percent instead of a decimal, so for a 5% RoR, you would type in 5 instead of 0.05 like we did above.

And voila! You now have the reasoning behind the 30 buyin SnG bankroll function. I would suggest experimenting with the ITH Bankroll Calculator with your own ROI and risk tolerance, and see what kind of numbers you come up with.

[mojay]

Thanks chillin411 you're a star!!!

[nsidestrate]

I have always wondered at the math behind this requirement. This is an outstanding post. Thanks, Chris!