I intended to write a nice introduction but I got too tilted from losing the last one to write it again. Bankroll management isn’t exactly a breathtaking concept, but it def is an important part of the game. Bad BRM can turn a winning player into a losing player, or even worse, a potential high stakes player into a mid stakes regular. imo many people on 2p2 use ******edly conservative BRM that won't get them anywhere, and they certainly have potential to play higher stakes than they are currently playing.

also I'll be using SNG buyins et al to keep it simple, but all of this is applicable to cash as well

Kelly strategy

Forget about all the „magic“ 20 buyins, adding 5 BI per level, muad'dib & all other inferior stuff;
Kelly betting strategy is mathematically proven to badly beat any other strategy in the long-term. I don't wanna write the unnecessary theory part about expected growth again. If you want to know more about it, google „ganchrow sbr“. Here is the formula

B = ROI / variance

B is the target size of the buyin. Variance for 2mans is ~1, while variance for 4mans is ~4. While you should generally not want to exceed B, crossing the limit is not bad as most ppl imply. However you still don't want to play much different levels. E.g. if Kelly says you should play $30s, you shouldn't put the majority of your volume in $50s or $20s.

Since Kelly is a very aggressive strategy and will make you move up the limits very fast, but downswings can last even two limits, most ppl opt for the less aggressive ½ Kelly strategy. It is the same as the original one, except you only wager B/2. Some ppl use fancy crap like ¼ Kelly or 1/8 Kelly. This is imo ******ed and just a big setback that has no rational reason except fear of busting ur roll

Hourly rate

Now, we know which buyin levels to play, but what games? Most ppl say turbos are more profitable as you can play more of them in the same amt of time and the ROI difference between turbos and regspeeds isn't big enough to cover that. E.g. let's say you have a $1k roll and can choose between playing FTP turbos and deepstax. You can play 7 turbos per hour at 10% ROI, so you win 0.7 BI per hour playing turbos. OTOH you can only play 3 deepstax per hour at 20% ROI, so your EV is 0.6 BI per hour.

So the turbos are the right choice? Nope. The trick is, you can play twice as high stakes in deepstax compared to turbos, coz ur ROI is twice as high. Since u have $1k roll and play by ½ Kelly, you'll be playing $57.5 turbos (for ~$40/hr) or $105 deepstax (for ~$63/hr). The general idea is that, if ur ROI is N times higher in game A compared to game B, you'll have to get in N^2 times more games per hr in B compared to A to make B's hourly rate bigger.

Some other general guidelines: If u can't play long sessions coz of RL scheduling problems, give more value to the game w a shorter avg duration, as it'll give u more time to fill at the end of ur session. E.g. if u can play in a 2 hr window, u won't be able to start a game after 1 hr in if u play deepstax, but you'll be comfortably opening lobbies even 90 minutes in if u play turbos. Also, if u have a close call between 2mans and 4mans, take the 2mans coz the variance increases as your ITM rate approaches 50%.

(to be continued)

Can you tell me if I'm doing this right? Say I have winrate 4ptbb/100 and sd 75ptbb/100. Then my variance is (75ptbb/100)^2=5625/10000=56ptbb/100, so that my B=4/56=about 7% of my br?

Nice explanation; this part never really sunk in with me. After reading it, it seems so obvious now that I cant believe I did not realized this fully.

Waiting for 2nd part.

awesome... I should think about this more, thx J

+1

Could you elaborate on: "Bad BRM can turn a winning player into a losing player"? I don't get that part.

OK part 2. There may be more if I think of sth

Playing professionally

The B = ROI / variance formula works great when building ur roll and moving up, but once u start withdrawing and spending money IRL, you won't be able to count on it any more. However it's possible and ez to adjust for losing money to withdrawals. The way to do it is to calculate the total wagering ur gonna do for the period you'll be using ur withdrawn money IRL, and assume the withdrawal is additional rake. E.g. if ur a $100 turbo reg playing 500 tourneys per month and plan to withdraw $2k this month, you'll be wagering a total of 500 * $500 = $50k. $2k is 4% of this, so when ur gonna play a turbo, take off 4% from your real ROI to determine your buyin using B=ROI/variance. If ur real ROI is 10%, your pro ROI is only 6%, so you'll need almost twice the roll.

If ur playing a different game, you might have a different total wager and thus a different amount to subtract. E.g. if ur simultaneously playing $35 superturbos and can play 3k STs withing the same timeframe, the total wager will be $105k, so you'll only need to subtract ~2% from your ST ROI.

Obv this means ur gonna need a really big roll if ur gonna withdraw a large part of ur earnings. Also if u withdraw your exact EV from ur games at the end of the month, you're 100% guaranteed to go bust. OTOH if ur withdrawing little, u can play w an aggro BRM.

Miscellaneous

Rakeback: Many ppl choose sites w RB over sites w/o RB, but tbh RB doesn't make a big difference in games w a big edge (stars-type regspeeds, deepstax, NBIs, 4mans, any type of HUMTT etc). E.g. even if u don't have RB on FTP, u should still be willing to take their deepstax over Stars regs coz of the hourly rate. Obv in some close calls RB can make a big difference, but it isn't as major as most ppl think.

Omaha: I've read some ppl say u need 50+ BI for HUPLO SNGs. This is pure nonsense. While in-game variance in PLO is def huge and much bigger than in NLHE, it does nothing to impact outside variance, so u should still use the same formula outlined up there.

Cash: Everything written here is valid for cash as well, except you should take the winrate in ptbb/100 as ROI and (SD/100)^2 as variance. However, B is not the variable you will be after. A better formula is R = variance / ROI * 2, (that's R = variance / ROI * 4 for ½ Kelly), where R is the size of your roll in big blinds.

Buying action: The general rule of thumb is, if a player w a much bigger roll is selling ½ his action vs a fish, you should not take the offer. You should buy action according to the (½-)Kelly formula (yes you should def buy it as it gives u much better hourly rate than actually playing ).

Satellites and taking shots: Sattying into a tourney to play it is very rarely max EV. If ur not rolled for the tourney, u can save time and cut the middle man by selling ur action and getting the tourney inside your roll constraints. If ur rolled 4 the tourney, ur usually better off just buying straight into the tourney and saving ur hourly rate. If the satty is so juicy that playing it is still better than playing ur regular games, then wtf r u doing grinding HU

I think he's referring to playing too high and busting one's roll.

JSpazz, I don't get the "B = ROI / variance". Isn't there something missing to relate to the size of your BR?

Anyway, nice post, thanks!

I forgot to tell this in part 1. B in cash games means 1ptbb divided by ur total roll and it's a clumsy number. Using my formula in part 2, R = variance / winrate * 4 = 5625 / 4 * 4 = 5625bb ~ 56 buyins. The ptbb/100 part is kinda confusing as the "100" doesn't get squared

Check out MindOnMind and his well. I'm sure he's a great player who can beat the games but we know how it all ended.

@Almito: I guess I missed the part where I say that B is the percentage of roll u want to invest . E.g. if you have $1k and B=0.05, you want to invest close to $50

Ok got it!
You wrote "B is the target size of the buyin", when I read it I thought about the absolute size, not a percentage of the BR. Makes sense now!

Good stuff Jspazz I had never heard of or seen the kelly strategy but it certainly caught my attention.

ohhhhhhhhhhhhhhh

edit: nvm you explained, I'll just keep this anyway since it also works


buyin = bankroll * roi

choose the highest buyin that is less than (bankroll * roi).

Once you have calculated this, make sure you are giving a realistic assessment of your roi for that specific buyin level. If you overestimate it, you are making a -EV decision. Since most people overestimate their roi you may want to go with half kelly.

so i should be playing 500s with my 5k roll? doesn't make sense to me :P

Yes if you think you have 10% roi at the 500s

hmmm

if u have 10% ROI, you'll be in for a bumpy ride 1/2 Kelly is prob the best compromise between fast bankroll growth and risk of ruin, and it won't drive u insane like full Kelly. Obv all this is assuming you never withdraw. If you live from poker, you have to adjust your ROI downward as I said in part 2

if your current roi is 10% after a big sample of $20 games and your bankroll is $500 you go straight to 50s or move up to 30s to find out your roi there?

If he can beat the games he's a winner in my opinion, he just experienced negative varience. Bad BRM can make you go bust more or reduce your profit but it won't turn you into a losing player. At least that's how I see this.

@naymlis As I said, go w 1/2 Kelly, which is ROI / variance / 2. If u have 10% ROI at $20s, you prob have the same at $30s, so you'd need ~$600 to play $30s and ~$1k to play $50s. Obv if u used full Kelly, you could play 50s w $500

If you bet your whole roll on every game, you're guaranteed to eventually go bust, as your expected growth is negative. When you play a lot of games w too aggressive BRM, you'll sometimes have huge winning streaks, but too often you'll end up busto. I don't know how is mindonmind doing these days (he prob rebuilt his roll), but playing $1100s w 5 buyins as he wrote in his well is too much risk for a too small reward

ok thanks

Point taken, thnx for elaborating.

what is (SD/100)^2?

Since I grind for extra income I thought it might be helpful to try to figure this out for myself. Say I intend to play 1000 husngs in a month, and would like to withdraw 1k at the end of the month: I should drop $1 off my roi per game (5% at 20s, 2% at 50s, 1% at 100s).

If I have a 10% roi at the 20s and would like a monthly income of $1,000, I need a BR of:

BR% = (10%-5%) / 1 = 5%, so I need 20BIs, or $400 on full Kelly, $800 on half Kelly.


If I have a 7% roi at 55 turbos, I need a BR of:

BR% = (7% - 2%) / 1 = 5%, so I need 20BIs, or $1,100 on full Kelly, $2,200 on half Kelly.

Does that sound right?

Nice post Jspaz. Thx for putting this together.