So I was reading that article today and decided I wanted to see what kind of bankroll is needed for my NL fun. I play on .50/1.00 NL on Gaming Club.

This is the equation as listed in the article:
Bankroll needed = -(SD^2/2*hourly win rate)ln(risk of ruin).

So i got out my TI-83 Plus calculator to tackle this monster. PT gives me my standard deviation at $45 an hour under the more detail button in the "sessions" section.

Here is how the equation looks when I set it up with my SD($45) and Hourly win rate($32):

Bankroll needed = -(45^2/2*32)ln(.01).

If I plug this in the calculator I get an insane number like 10 million or $145. So I decide I'll make it easier on the calculator and myself. If I just do -(45^2/64)LN(.01) it comes out to $145.71. Ok, so the $145.71 number must be correct.

Well, I dunno about you but I'd like to have more then $145 dollars for a NL game of .50/1.00, wouldn't you?

Am I doing something wrong? can anyone help me here??

Good question, kenny, we'll get in touch with Angel and ask him.

I'll get back to you as soon as possible.

OK, I am working on an excel spreadsheet to make this much easier for everyone. But I think I found an error on the page. Before I finish the spreadsheet, let me make sure that I have this correct.

The main page article says (scroll down, under 'Variance')

line A =(1/10)(52,666) - ((20)^2/10)(100)
line B = 5,267 - (400/10) (100)
line C = 5,267 - 40
line D = 5,227

But look at the transition between line B and line C. (400 / 10 * 100) is 4,000, not 40. Isn't it??

So line C should say 5,267 - 4,000
And then line D = 1,267
The square root of 1,267 is $35.59 give or take, not the $72 quoted on the main page.

Do I have that correct?

If I am correct, then this calculation provides a needed bankroll of $145.83 for this player. This seems very low, and in fact is very close to the number that KennyG came up with for his required bankroll.

Another thought.

These numbers may NOT be low at all.

Take Kennyg's numbers.

The $145 is 145 big bets. That seems pretty low, but you are apparently a hugely winning player at these limits -- $32 / hour is 32 BB/hour! So for such a good player, you would expect the required bankroll to be relatively low.

Also, a 1 percent risk of ruin is pretty high. This again would tend to make the required bankroll fairly low.

If you use a 0.1 percent risk of ruin and Kennyg's numbers, the recommended bankroll becomes $218.57, a little over 200 BB which is a pretty normal recommendation.

Anyway, my spreadsheet is done. It should be easy to use and self-explanatory. Tell me where to send it and somebody can test it to make sure it works correctly, and then post it for people to download and use.

Superman (d'oh! I've let the cat out of the bag), you can email it to me at admin@livepokerforum.com and I will send you back a download link.

Looking forward to giving it a try once tetsuo gets it up. Becasue there in noway I was going to figure any of that out.

Thanks K3nt your the man!

OK, I fixed it up and sent it.

Only Superman with his xray vison was going to catch the error. You can be the farm that Kowboy with his numbers cyphering was never, ever, eveeeer going to catch it.

$218 is great for limit...but I guess the equation can't take in the fact of a NL game. I could easily lose $218 in one bad session. Now where is that imaginary mathmtacian when I need him. Maybe there is some way to changethe equation of benfit NL players. K3nt you seem really good at math...any idea?

Off the top of my head, I think that the reason the bankroll suggestions are low for NL is because during an NL session, you can have wild swings within a single session or even within an hour. In a $1/$2 NL game, you could be down two buy-ins early on and then make it all back plus a little bit extra by the end of the session. Writing down "1 session, 3 hours, +$35.00" doesn't do justice to what you just went through, or how likely you are to go broke.

So for no-limit, perhaps, instead of a SD per session or per buy-in, you would need to calculate your SD and win rate every five or ten minutes or so.

Or maybe even per hand!!!

Yes, I like that idea a lot. Every hand is a "session" unto itself in NL, because you have a real chance of losing 100 or more BB in any given hand.

Let's plug some test numbers into the spreadsheet.

An average win rate of $0.25 per hand and a SD of $10.00 per hand (I just pulled those numbers out of my butt) gives a recommended bankroll of $921.03 for a 1% risk of ruin, or $1,381.55 for a 0.1% risk of ruin. Those numbers look a little more realistic, maybe.

Of course, nobody would want to manually input the results of every hand they play, so this would be a job for PokerTracker. I have done very little with PT, so I don't know if it can figure out your SD and win rate per hand. Does anybody know if it's possible?

OK, I ran some more numbers in the spreadsheet. I was mostly trying to see what a realistic SD would be for an overall winning player. (Trying to find out if the $10 I pulled out of my butt made any sense.)

I used 1000 hands. To make it easy on myself, I assumed you folded 95% of your hands -- that's 95 rounds of the table with 80% results of $0.00, 10% results of -$0.50, and 10% results of -$1.00.

The other 50 hands I split like this.

You won $200 3 times.
You won $100 5 times
You won $10 10 times
You won $5 5 times
You lost $5 5 times
You lost $10 10 times
You lost $25 7 times
You lost $100 5 times.

Your overall win rate is $0.28 per hand, or 28 BB/100. Your standard deviation is $15.02. The recommended bankroll is $1,839.33 for a 1% risk of ruin, and $2,758.99 for a 0.1% risk of ruin. That's 18 to 27 buy-ins, not far off the mark of what people often recommend.

Do you lose $100 5 times out of a thousand hands? Or is that way too high, or too low? (I honestly have no clue as I've never played the $100 game.)

Are your overall swings bigger or smaller than these?

Anyway, this type of play results in a SD of $15.02 per hand. Adjust your likely SD up or down based on your sense of your swings vis-a-vis the ones above.

I'm thinking that a standard deviation guess of 10 to 20 bucks per hand may be pretty realistic for $100 NL. But for now that's still just a guess.