Min. bankroll without knowning variance.

[1800GAMBLER]

With a 2BB/hour win rate in a loose-aggressive i.e. largest swings (possible to assume a variance from that) anyone with any quick figures of an idea of the min bankroll?

Don't put yourself through the math, it's not hugely important, just quote if you have done similar figures for yourself in my type games.

Thanks.

[BruceZ]

Hi Jay,

It depends on the risk of going broke that you want and heavily on the exact standard deviation. Say your standard deviation is 24 bb in 1 hr, that would be 12 times your hourly rate, and say you want a 1% risk of ruin. Then you would need a bankroll of -[ 24^2/(2*2) ]*ln(.01) = 663 big bets. The actual bankroll formulas are in this thread:

bankroll formulas

-Bruce

[1800GAMBLER]

Hi.

Someone meantion Sklansky's article on taking a shot. I'm wondering if i reduce my win rate what factor should that reduce my variance?

Thanks.

[BruceZ]

Someone meantion Sklansky's article on taking a shot. I'm wondering if i reduce my win rate what factor should that reduce my variance?

This is a good question. You may be referring to the essays "Never Go Broke" in Poker Gaming and Life or "Playing According to Your Bankroll" in Sklansky on Poker. The idea here is that you move up to a bigger game, but play sub-optimally, so that your win-rate is not as high as it could be, and so that your variance is low enough that you can afford to play. By doing this, it may be possible to win more than you would by playing optimally in a smaller game. When you play in the bigger game, you play super tight, and you play in such a way as to try and win as many of the pots that you enter as possible, rather than playing to win the most money possible.

A rule of thumb is that your standard deviation should be about 10 times your hourly rate, and lower is better. In your example, if you were to reduce your win rate to 1 bb/hr by playing tight, but at the same time decrease your standard deviation from 24 bb to 12 bb, then you would only need half the bankroll to play with the same risk of ruin. That is, you would only need 332 bb instead of 663 bb. The reason for this is that your bankroll requirement depends on the variance, which is standard deviation squared, so if you reduce your hourly rate and your standard deviation by the same factor, your bankroll requirement is reduced by that factor.

Once again, for reference:

bankroll = -[ (sigma^2/(2*EV) ]*ln(r)

where r is your risk of ruin.

If you were to play in a game with twice the stakes against the same players, and if you were to play optimally, then your bankroll requirement in dollars would double, because your hourly rate and standard deviation both double, but your variance goes up by a factor of 4, so the ratio of variance to hourly rate goes up by a factor of 2. Your bankroll in terms of big bets will be the same since the bet size also doubles. Normally when you move up to twice the stakes, you will not play against the same players, but you will play against tougher competition, so your win rate may go down while your standard deviation still doubles. This will cause your bankroll requirement in dollars to go up by even more than double, and that is why you need a larger bankroll in terms of big bets for high stakes games than you need for low stakes games. For example, if 300 big bets is a good rule of thumb for 10-20 and lower, 300 big bets may not be enough for 100-200. If your bankroll is limited, it may be correct to play tighter than normal, as described above, in order to bring your ratio of variance to hourly rate low enough so you can afford the game, and it may turn out that your hourly rate is still higher than it would be playing in the lower stakes game. If this is not the case, then you would be better off staying at lower stakes.

Note that this is not the same as "taking a shot" which refers to moving to a higher level before your bankroll is large enough to support your desired risk of ruin, and playing optimally at this level until either you have increased your bankroll enough to regain your desired risk of ruin, or until you lose however much you set aside for this shot. This exposes you to a greater risk, while the method described in the above paragraph does not. You can calculate the risk of the shot failing from the risk of ruin formulas given in the link above. Simply substitute for bankroll the amount that you are willing to risk taking the shot, and the computed "risk of ruin" will correspond to the probability of the shot being unsuccessful. If you then return to the lower stakes game, you will have a smaller bankroll than you had previously, and your risk of ruin will be higher. If you multiply this new risk of ruin by the probability of the shot being unsuccessful, this will be your overall risk of ruin for taking the shot.

[1800GAMBLER]

Once again thanks for all the effort.

I don't think i'd have the self-control to play even tighter and change my style of play for this. My reason for asking was that i was going to try a few sessions at the 15/30 before i would be able to transfer money from other sites to this one, but i think it will have to wait and i'll have to hope the game stays soft because everytime i hear 'risk of ruin' i get scared, so i will have to wait.

Thanks again.

Lastly, i always thought the 300BB mark was the point were if you lost that you were sure it aren't a winning player. But in these loose-aggressive games if you have a 1% risk of ruin then 1 in a 100 2BB/hour players will go broke? Or am i over emphasising the variance in these games?

[BruceZ]

But in these loose-aggressive games if you have a 1% risk of ruin then 1 in a 100 2BB/hour players will go broke?

That's correct, if their standard deviation is 24 bb and their starting bankroll is 663 bb. On the other hand, if they lowered their win rate to 1 bb/hr, and cut their standard deviation in half, then only 1 in 10,000 would go broke with that bankroll. Same thing if they doubled their bankroll.