Your poker bankroll, Kelly and you… the path to high stakes

Poker bankroll management is a familiar term for any serious poker player these days, yet there seem to be so many conflicting pieces of advice. Furthermore, with the acknowledged higher variance in PLO, do the guidelines provided for NLHE games still apply?

In order to create this article, I used an adjusted Kelly betting simulation to build optimal poker bankroll criteria for a number of commonly discussed scenarios for Pot limit Omaha games. For those of you unfamiliar with the use of the Kelly principles, the simulation aims to tell us which game to prefer given the parameters of win-rate for each game, standard deviation, and our accepted risk of ruin. When I use the term ‘prefer’ I mean, mathematically, at which stake will our bank-roll grow quickest without jeopardizing our future profits? For the purpose of this article, I used the standard deviation of 144bb/100 from my own database of several hundred thousand hands. I adjusted the win-rate and accepted risk of ruin depending on the simulation. It is worth noting that I do not recommend being a regular at any limit without reaching a win-rate of at least 5bb/100 for that limit. The remainder of this article will discuss the main conclusions which I drew from these bank-roll simulations.¹

1. If you know you can beat the games, you should move up aggressively.

This situation is relevant for a professional player who has had to make a big cash out for personal reasons and finds himself short for his regular limits. If you are confident you can beat a set of limits for a similar win-rate then you should move up as soon as you reach 70 buy-ins for the next level. The caveat is that if your win-rate for a lower limit is higher (by 2bb/100 or so) than the next, your bank-roll will grow more quickly if you stay at that limit for a little longer.

It’s worth noting that these ‘aggressive’ guidelines indicate 60-70 buy-ins to move up to your new limit, which will involve staying at a given limit with as many as 120 buy-ins for that limit. The parameters I used to build this table included a 2% risk of ruin and assumed a win-rate of 5bb/100 for every limit. If your expected win-rate is lower than this for a given limit then play the highest limit which you are rolled for with a 5bb/100 win-rate and concentrate on getting better!

2. If you are a winning recreational player, jump into higher games liberally

When you can replenish your bank-roll at will and have a source of income other than poker, you can tolerate a much higher risk of ruin. This dramatically alters the rate at which you can move up when on a rush (assuming you are a winner at the higher limit). Besides, if you are a recreational player, you want to have fun, right? How are you going to know if you can beat the higher stakes if you don’t play them? If you are winning at a given limit and have the bank-roll described below, jump in!

The table above offers a 25% risk of ruin, so it is NOT for the professional player unless you harbor burger-flipping aspirations. However, the 22 buy-in bank-roll requirements can have you on a rush to the high stakes at a rate a pro could only dream of!

3. If you see a juicy game at a higher limit, you must take shots

Even though your win-rate may be only 5bb/100 in your regular game, your win-rate will vary dramatically from table to table, depending on the make up of each table. Consequently, there will often be times where a higher limit game will offer you a 10bb/100 win-rate. Under these circumstances, your bank-roll requirement to add that juicy table to your games plummets, and it becomes correct from a mathematical perspective to pick that game ahead of another regular limit table. Take care not to use this as a justification to start multi-tabling that limit however, taking shots at juicy games is very different from just gambling above your roll.

As the reader can see, this approach takes a lot of discipline, since it can mean that whilst our regular game is 3/6 PLO, we should be adding a single juicy table of 10/20 PLO when we can. Without an iron-will (and a stop loss) a smart financial speculation could degenerate into a bank-roll implosion.

A word of caution

The final table I shall present is highly relevant for the professional player, namely that if you have a higher win-rate at a lower limit you should be very reluctant to move up without large resources behind you. This advice is tempered by the reduction in rake as you move up limits but for rake-adjusted bb/100, so-called ‘nitty’ bank-roll management is the quickest way to guarantee that your roll grows.

The table above gives the threshold at which we should prefer to be a regular in the 400PLO games ahead of the 200PLO games despite the reduced win-rate. It argues for a tighter bank-roll management strategy the better we are at a given limit, not on the basis of risk of ruin, but because our roll will grow so much more quickly with a high win-rate. I can attest to this personally, since by insisting on generating a high win-rate (10bb/100+) for a given limit before considering moving up my bank-roll has grown this year with relatively few downswings compared to my peers.

If you are a professional player you should move up to a new regular game only once you have 70 buy-ins for the new limit. However, you should take shots at juicy higher limit games aggressively, which will accelerate your progress up the ranks.

If you are a mass multi-tabler your win-rate will be similar from limit to limit and so you may proceed up the ranks as in the first table. If you are a more technical, few-tabler then you should be very cautious before making a new limit your permanent home but will be in a position to take full advantage of the necessary shot-taking.

If you are a winning recreational player you may disregard all the constraints that the professionals have. Once you have 22 buy-ins for the next limit, take a shot and ride that wave!

Thanks for reading and good luck at the tables,

Quad