Bankroll size depends primarily on your tolerance to risk, win rate, and standard deviation.

If you're not concerned about going broke, can replenish the funds, and have an outside source of income (yeesh, sounds like I'm counting cards again), bankroll management isn't so important. Gamble with whatever you like.

That's one extreme.

The other is where you have x amount of money, it is your last money, and there is no way of replenishing it.

That's the other extreme.

So, how many buy ins do you need?

It's a very simple 2 step process.

Step #1. Take your standard deviation (found in Session Notes -> More Detail) per 100 hands. Multiply it by itself.

Mine: 24.2 PTBB/100 hands thus

24.2 x 24.2 = 585.64

Step #2. Now divide this number by your win rate:

Mine: 6.40 PTBB (currently)

585.64/6.4 = 91.5 PTBBs (183 bbs)

That number is the number of PTBBs that I need to have for a 13% risk of ruin. So in this case, 9 buy ins of 20bbs. Be forwarned, however, that 13% ROR is much higher than it sounds. There is, for instance, a 50% chance that you will lose half your money at some point.

I think this is a good buy in for case #1. He wants to move up quickly, might ride a few waves of success and never look back, and if he busts out ... no big deal. It was only a few dollars.

A more conservative player will likely want to reduce his risk of ruin. He doesn't want to see his bankroll fluctuating 50% in any given session. For this, we simply double the bankroll requirements to 18 buy ins. 13%x13% now gives us a 1.69% risk of ruin. This is nice compromise, virtually eliminating ruin ... while still offering a good player a chance to move up in levels in a reasonable time frame.

That last case, where this money is your last in the world, might wish to triple the bankroll requirements to 27 buy ins. .13x.13x.13 = .2% ROR. You'll never lose all your money, but progress might be slow.

Keep in mind, these bankroll requirements are based on MY stats. I've geared my strategy to minimized fluctuations, first, while still maintaining a solid win rate. As I move up, I recalculate my bankroll requirements based on my stats for each level. I've seen SDs as high as 42 with some players, with that same win rate, you will need almost 28 buy ins for a 13% risk of ruin. 56 for a moderate approach, and 84 for a super conservative player.

This is why it isn't always about expectation, lowering variance can be crucial to success. If you have only half of you're required bankroll for the Full Kelly approach (13% ROR), you will go broke. 100% certainty. I will go broke if I stay at my same level, and only have 5 buy ins. And someone with the same win rate, but a 42 SD will go broke with 14 buys ins.

Keep in mind, also, that if you don't mind moving down a level (or three)... even a Full-Kelly (13% risk of ruin, 9 buy in approach) is not as bad as it might appear. Little known fact, if you have the bankroll, and the character, to accept moving down 3 levels if your bankroll tanks ... risk of ruin is virtually eliminated.

Anyway, I'm no mathmatician (shucks, I can't even spell it) but I hope this is of some value for those wondering what sort of bankroll they need.

All the best,
Z.

Oh, this just occurred to me ...

I haven't actually seen this sort of analysis done regarding buy ins, stack sizes, win rates, sds, rors, etc ... before. I know Sklansky did something similiar with limit, but I'm not sure if the buy-in structure of NL (and the potential to lose it!) adds a different wrinkle to the calculations.

I believe the numbers are the numbers. And as I follow a very consistent strategy (always buy in for 20, always cash out at 40), I believe the formula is good to go.

But I am not a theoritician. I could be completely wrong.

I believe Geo is quite bright in this area. If he could confirm this methodology, it would be appreciated.

Best,
Z.

I just realized that I had $1.04 left in my Doyle's Room account doing nothing after I had cashed out. So I decided why the heck not? Lowest NL game is .02/.04. I s**t you not, very 1st hand in the BB I pick up KK. 3 limpers, Button raises to .12 cents, SB calls, I push for $1.04 total and only button calls w/ AQo. Flop is all low cards Ten high, turn is a Ten, River is a King. Starting just like Fergusen w/ $1.

If you could eke out $2/hr per NL100 table long term though, rakeback would make this ownage. Avg $0.02 rakeback per hand, 5K hands per day (avg 8 hours per session per site, playing several sites, ten tables total), for 150Khands per month=$3000 + $600(earnings). Not too shabbeh when you don't actually have to do anything. That is, I would never consider doing this except with a custom bot. Playing above NL100 with this seems certain death due to good players clueing, NL50 may actually be more profitable, though less rakeback.
The infrastructure required for that is currently beyond my means, but who knows? ;]

MT, every time you play a hand in microlimit, God kills a kitten.

Wow, even worse than I thought. You're training yourself to play reflexively and to not pay attention. Unwise. We are creatures of habit, fwiw.