Question on Bankroll and Stakes

    • nitaidean
      nitaidean
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      Joined: 15.05.2010 Posts: 60
      Hi all, a question if I may:

      I recently decided to start playing SNG's on my FTP account (up till now been doing mainly cash games on stars) to keep poker interesting. I started the account with $500, and got it up to $570 in about 100 $2.25 tourneys (i multitable the 9, 18, 27, and 90 player games).

      My question is: what roll would I need to move up to multitabling the $6.50 tourneys? And besides having the right roll, since 100 is no sample size, what minimum amount of games do I want to have on a certain level before moving up? I mean obviously anything less than 1000 is no real sample size, but I'm not gonna stay on this level until I get to 1000 if I pass like the $750 BR right? It just feels silly to be playing with 300BI. Then again, I want to make sure I'm beating this limit before I go up (though ATM im on 25% ROI).

      Thanks!
  • 9 replies
    • Bigniux
      Bigniux
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      Joined: 09.01.2009 Posts: 2,098
      Hello, i'm playing 45mans on stars. For turbo's i use 90 BI for 18mans, 130 BI for 45mans and 200 BI for 180mans. For 90mans should be something like 150-160 BI. If you play non turbos, you can even be a bit more agrro with your BR. About moving, i found stakes being kinda similar(spreaking about field), so i just play the limit that my BR allows me to ;)
    • pzhon
      pzhon
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      Joined: 17.06.2010 Posts: 1,151
      The bankroll you need depends on your ROI, which games you are playing, and your personal risk tolerance. A simple, consistent formula is

      Bankroll = (comfort x SD^2)/(win rate)

      comfort is something which depends on your risk tolerance and your ability to move down in stakes if you hit a bad streak. A comfort level of 2 is generally considered aggressive. A comfort level of 4 is conservative. You can use the same comfort level across many forms of advantage gambling. One other meaning of the comfort level is that your instantaneous risk of ruin, your chance to go broke if you stay in your current game, is about 1/7^comfort.

      SD = standard deviation measures how spread out the results are of each tournament. For single table tournaments, this does not depend much on your playing style. In a 50-30-20 structure, your standard deviation is going to be about 145%-155% of a buy-in. In larger tournaments, the standard deviation is larger, and it becomes more sensitive to your playing style and how much you win. In a 45-player tournament, the standard deviation may be 280%-330% of a buy-in. In a 180 player tournament, the standard deviation may be 500%-800% of a buy-in.

      Your win rate should be expressed in the same units as the standard deviation, say in buy-ins. You can include rakeback and bonuses. If you regularly take money out of your bankroll, then you should reduce your win rate by these withdrawals.

      For example, if you use a target comfort level of 3, and you have an ROI of 5% in STTs, then you should have a bankroll of 3 x 1.55^2 / 0.05 = 144 buy-ins. With the same level of risk tolerance and in the same games, if your ROI is 10%, then you only need 72 buy-ins. If you have an ROI of 40% in 180 player tournaments with a standard deviation of 6 buy-ins, then you should have 3 x 6^2 / 0.40 = 270 buy-ins. MTT buy-ins are much easier to lose than STT buy-ins.

      If your bankroll falls to below the target bankroll, that is ok, you don't have to move down immediately. However, if your bankroll falls to less than half of the target amount, then you should move down. Playing with less than half of the target bankroll means that playing should be viewed as an expense.

      It is normal not to know exactly what your ROI is. You can make tentative calculations, and update them as you get more information. A rough 95% confidence interval for your ROI after n tournaments is your observed ROI +- 2 SD / Sqrt(n). You might want to play enough that this confidence interval does not include 0 before moving up. Be prepared to drop down again if you do not have good results at the higher level.
    • taavi1337
      taavi1337
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      Joined: 29.05.2009 Posts: 2,920

      This post has been edited 1287 times(s), it was last edited by pzhon: Today, 01:04.
      The result is nice :f_thumbsup:
    • Bigniux
      Bigniux
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      Joined: 09.01.2009 Posts: 2,098
      nice post, pzhon. How did you came up with these formulas? I'm also interested in confidence intervals. How do i get that constant number for other confidence levels(90%, 99%)?
    • pzhon
      pzhon
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      Joined: 17.06.2010 Posts: 1,151
      The main formula is based on a fractional Kelly system, with Kelly fraction 1/comfort. You might look up the Kelly Criterion and fractional Kelly systems.

      The Central Limit Theorem says that if the results of your tournaments are independent (no tilt or power failures), then the total and ROI are roughly normally distributed. Percentiles of a normal distribution can be described by the number of standard deviations above or below the mean. So, if you compute the standard deviation, you can look up the 95th or 99.5th percentile in a table of values for the normal distribution, and translate that to a 90% or 99% confidence interval. For example, 5% to 95% is from 1.645 standard deviations below the mean to 1.645 standard deviations above the mean, so a 90% confidence interval is the observed result +- 1.645 standard deviations.

      Again, the standard deviation you use is not the value per tournament. You scale by the square root of the number of tournaments, multiplying by sqrt(n) for the standard deviation of the total, and dividing by sqrt(n) for the standard deviation of the average result or ROI.
    • Bigniux
      Bigniux
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      Joined: 09.01.2009 Posts: 2,098
      Ok, thanks a lot for explaining. To make it totally clear, confidence interval shows the possibility of getting results from that interval? I mean, if we have [5, 15] 95% confidence interval for our ROI on some sample, this means that 5% of the time our ROI is in interval: (- infinity, 5) and (15, infinity), right?


      I'm looking forward to taking a deeper look at Kelly system. Could you recommend some more books/stuff to take a look, related with maths, statistics, probabilities. Stuff, which is not really neccesarry, but could be helpful knowing it :)
    • pzhon
      pzhon
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      Joined: 17.06.2010 Posts: 1,151
      Originally posted by Bigniux
      Ok, thanks a lot for explaining. To make it totally clear, confidence interval shows the possibility of getting results from that interval? I mean, if we have [5, 15] 95% confidence interval for our ROI on some sample, this means that 5% of the time our ROI is in interval: (- infinity, 5) and (15, infinity), right?
      Correct.

      I'm looking forward to taking a deeper look at Kelly system. Could you recommend some more books/stuff to take a look, related with maths, statistics, probabilities. Stuff, which is not really neccesarry, but could be helpful knowing it :)
      I haven't read it myself, but one popular book is Fortune's Formula which is about the Kelly criterion. You might also want to look at the references on the Wikipedia page for the Kelly criterion.
    • Bigniux
      Bigniux
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      Joined: 09.01.2009 Posts: 2,098
      Thanks for references.

      I was also wondering if Gambling Theory has something to do with poker. Since it's quite more mathematical stuff. But i remeber that D. Sklansky in "Theory of Poker" wrote something about it. I might have the possibility to take one half year course on it, so i would have easier decision knowing the answer to this question :)
    • pzhon
      pzhon
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      Joined: 17.06.2010 Posts: 1,151
      I am not sure what a course on gambling theory would cover. It is possible that it would be useful, but possible that it would cover other material.

      Bankroll management is not just for poker, and ideas for bankroll management might be discussed in mathematical finance courses.

      Game theory courses should cover material which is applicable to poker. Some of the earliest work on game theory studied bluffing in model poker games. (Combinatorial game theory is different, and does not apply to poker, but rather to games like nim or go endgames.)

      Many of the issues online poker players need to understand should be addressed in a basic course on statistics. For example, suppose you have seen someone 3-bet 3 times out of 10 opportunities. How is that different from someone who has 3-bet 30 times out of 100 opportunities?