Bankroll Management & Shot Taking (essay/long)

[TStoneMBD]

Many people seem confused about bankroll management. I am not an expert on bankroll management but I do think I have some insight to help those that feel lost on the subject. Maybe this thread will help rid of some of the bankroll questions in the future.

I think the key to bankroll management is that you want to make sure your risk of ruin remains low at all times.

Let's say for instance that your main game is 15/30 holdem and you play for a living. You don't feel comfort having less than $30,000 in cash playing in this game for a living, so you dont want to go below 1000BBs. Some people are more comfortable than others about having less money, so 500BBs might be enough for you. Realize however that if you play with a smaller bankroll there may come a time in which you are forced to move down and rebuild. Moving down will likely mean a lower hourly rate so you want to keep this from happening at all costs.

So you have your original $30,000 (1000BBs) for 15/30, but you're doing well and your bankroll has grown. You now have $40,000 after a $10,000 month. You take a look at some of the bigger games online and you think that if you had a bankroll to play in those games, you would be making more money per hour then you are now. This is the time to take a shot.

You have $10,000 in spare money that you can afford to lose. If you lose that $10,000 you still have enough bankroll to maintain playing at 15/30 and your risk of ruin is still very low. With your $10,000 you could take a shot in a bigger game. However, I really only recommend taking shots in bigger games where you feel your hourly rate will be higher then your current game. $10,000 in this situation is more than enough to take a 50BB shot playing as high as 100/200. That's right, with a $40,000 bankroll I am advocating playing in the "big game".

Making the decision to take a shot at 100/200 is pretty simple if you conclude that the 100/200 game will yield the highest hourly income that any game could bring for you. However, there is a better question to be answered. Would taking a shot in a lower game with a lower hourly rate be better than taking a shot at 100/200?

With $40,000 you now have enough money to take a $10,000 shot playing 30/60. You think that you would make less in the 30/60 then the 100/200 but your risk of losing the $10,000 is substantially less because you are playing with a 160BB bankroll in comparison to a 50BB bankroll.

This is where advanced math comes in, but I really couldn't do it on my own and I would have to ask someone to contribute the math to this thread. The math also probably won't help many people in situations like this because it's complicated and somewhat overkill. What's important is that you understand the concept of money management well enough to make relatively accurate decisions on bankroll management.

So let me throw some numbers out there for you.

-You are currently making $100/hr playing 15/30.
-If you move up to 30/60 you approximate that you will be making $150/hr.
-If you move up to 100/200, you feel that you will be making $200/hr.

Now if you asked a novice money manager what the best way to increase your hourly rate would be in this situation, he would immediately say to play in the 100/200 game. Well that is actually not necessarily true. Here is why;

With a 50BB bankroll for 100/200 you will often go broke. This will send you back to 15/30 where you are making $100/hr again. With a 160BB bankroll for 30/60 you will seldomly go broke and you can continue making $150/hr for a long time.

If you go broke in the 100/200 game with a 50BB bankroll 60% of the time, your hourly rate would be $100/hr 60% of the time and $200/hr 40% of the time. 100(.60) + 200(.40) = 140. This means that your hourly rate is $140/hr based on risk of ruin.

If you go broke in the 30/60 game with a 160BB bankroll 10% of the time, your hourly rate would be $100/hr 10% of the time and $150/hr 90% of the time. 100(.10) + 150(.90) = 145. Your hourly rate for moving up to the 30/60 game would be $145/hr.

Therefore according to these (arbitrary) numbers, based on hourly expectation alone, it would be correct to stay in the 30/60 game until you have a lower risk of ruin (more than 50BBs) in the 100/200 game. However, some of you may prefer to sacrifice the $5/hr edge you have in the 30/60 game by moving up to the 100/200 game where you will develop as a player faster. That is a very good arguement. Some of you are more conservative then others and don't want to risk $10,000 on a high risk endeavor.

Some of you may be wondering how it's possible to have a 60% risk of ruin with a 50BB bankroll if you are the favorite in the game. Well, if you were an average player in the game with 50BBs, half of the time you would turn the 50BBs into 100BBs, the other half of the time you would go broke. Then, with your 100BBs, half of the time you would turn it into 200BBs and the other half of the time you would go broke. To continue, half of the time you would turn your 400BB bankroll into 800BBs, and the other half of the time you would go broke. A risk of ruin for an average player with 50BBs is way, way over 50%. For a winning player it goes down substantially of course, but it is dependant on winrate and standard deviation, something I definitely do not feel like discussing today as things get really complicated and arbitrary.

I certainly haven't covered everything in bankroll management or shot taking for that matter. For instance, because your risk of ruin is much smaller in the 30/60 game then the 100/200 game, you could argue that the 30/60 game actually has a larger winrate than the $145 expressed above. Why? Because you will be able to build a bigger bankroll faster at 30/60 then at 100/200 (with the $5/hr difference) which allows you to decrease your risk of ruin at 100/200 exponentially faster since your bankroll grows faster by playing at 30/60. Confusing, I know.

Lastly, alot of bankroll management and shot taking has to do with your ability to recover your losses in quick order. Many people say that you need to have a 50 buyin bankroll to play in multi-table tournaments, which is a fair assessment. However, if you were making $30,000 a month playing poker and only had $100,000 to your name, it is perfectly reasonable to buyin to a World Poker Tour $10,000 tournament every couple of months or even every month! Your risk of ruin is virtually 0% with this form of shot taking because your income far exceeds your risk.

To conclude, I hope I've helped some of those who are confused on bankroll management. I might have just ended up creating more confusion. I certainly hope that wasn't the case. The intent of this essay was to show that shot-taking is an excellent approach to increasing your hourly rate while maintaining a very low risk of ruin. I recommend that you guys take shots on a regular basis, but my personal (yet controversial) opinion is that you only take shots in games where your hourly earn increases.