Thread: bankroll
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Old 11-09-2007, 07:46 AM   #10
Join Date: Mar 2004
Posts: 5,363
Re: bankroll

Bankroll management is for winning players who do not want to deposit more. If you aren't sure that you are a winning player, you may need to set a budget rather than practice bankroll management.

A good way to set your bankroll requirements for many forms of advantage gambles is to use

bankroll = comfort * standard deviation^2 / win rate.

The comfort levels you accept depend on your personal risk tolerance and ability/willingness to move down when you hit a bad streak. Most people are happy with a comfort level between 2 (aggressive) and 4 (conservative). You may need to set a much higher comfort level if you are planning to withdraw almost all of your winnings. Your risk of ruin if you stay in your current game without withdrawing or learning is about e^(-2*comfort) ~ 1/7^comfort.

When you are taking a shot at a level, you can use a much lower comfort level than normal because you should be planning to move down quickly if you hit a bad streak. Set a stop loss, and move down if you lose it. Usually you should avoid playing with a comfort level lower than half of your target comfort level.

Your win rate depends on you, and the levels at which you play. No one can tell you what your win rate is. It can take a lot of hands to get an accurate estimate of your win rate from your results alone. If you don't have a long track record, then you might view the calculation as conditional, not set in stone, and revisit it as your estimates of your win rate improve. Your win rate includes any bonuses or rakeback you get on a regular basis. Regular withdrawals lower your win rate.

Your standard deviation should be measured over the same period and in the same units you used to express your win rate, whether that is big blinds/100 hands or $/hour. Standard deviation is estimated by PokerTracker (Session Notes->More Details). If you play single table SNGs, it is about 1.7 buy-ins per tournament. For multitable tournaments, the standard deviation rises with the number of players, and with your win rate. A marginal winner playing 200 player tournaments may have a standard deviation of 5 buy-ins, while solid winner may have a standard deviation in the same tournaments of 6-7 buy-ins. If you play LHE, your standard deviation is about 15 BB/100 for full ring, and 17 BB/100 for 6-max. In NLHE, standard deviation is more sensitive to your playing style, particularly in shorthanded games, but typical values are 85 big blinds/100 for full ring and 95 big blinds/100 shorthanded.

Examples:<ul type="square">
Suppose you decide you want to use comfort level 3 as a starting point, and you believe your win rate is about 15 big blinds/100 and your standard deviation is 90 big blinds/100. Bankroll = 3 * 90^2/15 = 1620 big blinds, or about 16 full buy-ins.

If you want to use comfort=3, and your win rate is 2 BB/100 and your standard deviation is 16 BB/100, then your bankroll should be 3 * 16^2/2 = 384 big blinds. (Although many people repeat "300 big blinds" and many people repeat "20 buy-ins," the latter is typically much more conservative for online low stakes games.)

If you play SNGs, and want to use the same comfort=3, and have a ROI of 15%=0.15 buy-ins and a standard deviation of 1.7 buy-ins, then your bankroll should be 3 * 1.7^2 / 0.15 ~ 58 buy-ins.

If you play MTTs, and use comfort=3, with a ROI of 50% and a standard deviation of 6 buy-ins, then your bankroll should be 3 * 6^2 / 0.5 = 216 buy-ins.[/list]The bankroll you need for a particular level of safety is sensitive to your win rate, which typically drops as you play in tougher levels, and rises if you play in softer games. Do not assume that a fixed number of buy-ins or BB is appropriate at all levels. If you are playing for pennies, 10 buy-ins may be conservative, while an expert may need 50 or 100 buy-ins to be safe in high stakes games. That high stakes professionals talk about 40 buy-in drops does not mean you need anything close to be safe in soft microstakes games. That you haven't seen a 10 buy-in downswing in low stakes games doesn't mean you are safe with 20 buy-ins in mid stakes games.

These guidelines do not depend on the number of tables you play. Multitabling does not inherently increase your risk of ruin for a given bankroll level. If your win rate drops or your standard deviation changes or for psychological reasons you require a different comfort level, then you should factor those changes into the formula.

Your bankroll represents all of the money you can afford to lose playing poker. Particularly for low stakes players, your bankroll is often not your balance. If your calculations say you should have 400 BB, you don't need 400 BB on each site you might play, and it is ok if some of the money hasn't been deposited yet.
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