It is the start of a new year and after 500000 hands of NL100 as an average risk 5bb/100 winning player with a SD of 100 you have a choice; accept the offer of a full time 9-5 job with 2 weeks holiday at the average UK wage of £24,000 ($38,000) per year or earn the same money playing online poker.
It is not a simple choice and the answer should always be take the job unless you are single, financially secure for at least the next 12 months, properly bankrolled and really understand how to play the game (among many other factors), but let us examine the online poker option.
How much money are you really talking about, before and after tax in 2011 ($1.60 : £1)?
|Gross Salary||Nett Salary||Gross Per Hour||Nett Per Hour|
|£ 10,000||£ 9,163||£ 5.00||£ 4.58|
|£ 20,000||£ 15,963||£ 10.00||£ 7.98|
|£ 24,000||£ 18,683||£ 12.00||£ 9.34|
|£ 30,000||£ 22,763||£ 15.00||£ 11.38|
|£ 40,000||£ 29,563||£ 20.00||£ 14.78|
|$ 38,400||$ 29,892||$ 19.20||$ 14.94|
Therefore you require a win rate (WR) of almost $20 per hour as a full time taxed player or $15 as a casual (non-taxed) player.
If you aim for $20 per hour at NL100, how much bankroll do you need and how many hands do you need to play in the year?
BR = Comfort Level x SD^2 / Win Rate
The Comfort Level you accept depends on personal risk tolerance and ability as well as how willing you are to move down during a bad streak; the higher the figure, the less risk you are willing to take with your bankroll (a level of 3 is average risk).
Standard Deviation is the square root (SQRT) of variance and a guide to the consistency of past results; the lower the figure, the more consistent the performance.
However you need a high degree of confidence in relation to win rate over hands actually played.
There are 3 degrees of confidence (68%, 95% and 99.7%) for the possible range of Win Rates:
- 68% Confidence Limit = 1 x SD / SQRT of (Blocks of 100) Hands Played
- 95% Confidence Limit = 2 x SD / SQRT of (Blocks of 100) Hands Played
- 99.7% Confidence Level = 3 x SD / SQRT of (Blocks of 100) Hands Played
The more hands you play, the more confident you should be of past performance being an accurate measurement to use for future bankroll requirements.
The minimum and maximum Win Rates for a wide range of SD and hands played can be shown for all buyin levels with a 99.7% confidence limit using an average or ‘mean’ WR of $0:
|SD||3SD||Hands (n)||n/100||SQRT (n/100)||3SD/SQRT(n/100)||Range||Min WR||Max WR|
|300||900||10000||100||10||900/10 = 90||180bb||-90bb/100||90bb/100|
|200||600||10000||100||10||600/10 = 60||120bb||-60bb/100||60bb/100|
|100||300||10000||100||10||300/10 = 30||60bb||-30bb/100||30bb/100|
|50||150||10000||100||10||150/10 = 15||30bb||-15bb/100||15bb/100|
|20||60||10000||100||10||60/10 = 6||12bb||-6bb/100||6bb/100|
|10||30||10000||100||10||30/10 = 3||6bb||-3bb/100||3bb/100|
|300||900||50000||500||22.4||900/22.4 = 40.2||80.4bb||-40.2bb/100||40.2bb/100|
|200||600||50000||500||22.4||600/22.4 = 26.7||53.4bb||-26.7bb/100||26.7bb/100|
|100||300||50000||500||22.4||300/22.4 = 13.4||26.8bb||-13.4bb/100||13.4bb/100|
|50||150||50000||500||22.4||150/22.4 = 6.7||13.4bb||-6.7bb/100||6.7bb/100|
|20||60||50000||500||22.4||60/22.4 = 2.7||5.4bb||-2.7bb/100||2.7bb/100|
|10||30||50000||500||22.4||30/22.4 = 1.3||2.6bb||-1.3bb/100||1.3bb/100|
|300||900||100000||1000||31.6||900/31.6 = 28.5||57.0bb||-28.5bb/100||28.5bb/100|
|200||600||100000||1000||31.6||600/31.6 = 19.0||38.0bb||-19.0bb/100||19.0bb/100|
|100||300||100000||1000||31.6||300/31.6 = 9.5||19.0bb||-9.5bb/100||9.5bb/100|
|50||150||100000||1000||31.6||150/31.6 = 4.7||9.4bb||-4.7bb/100||4.7bb/100|
|20||60||100000||1000||31.6||60/31.6 = 1.9||3.8bb||-1.9bb/100||1.9bb/100|
|10||30||100000||1000||31.6||30/31.6 = 0.9||1.8bb||-0.9bb/100||0.9bb/100|
|300||900||250000||2500||50||900/50 = 18||36bb||-18bb/100||18bb/100|
|200||600||250000||2500||50||600/50 = 12||24bb||-12bb/100||12bb/100|
|100||300||250000||2500||50||300/50 = 6||12bb||-6bb/100||6bb/100|
|50||150||250000||2500||50||150/50 = 3||6bb||-3bb/100||3bb/100|
|20||60||250000||2500||50||60/50 = 1.2||2.4bb||-1.2bb/100||1.2bb/100|
|10||30||250000||2500||50||30/50 = 0.6||1.2bb||-0.6bb/100||0.6bb/100|
|300||900||500000||5000||70||900/70.7 = 12.7||25.4bb||-12.7bb/100||12.7bb/100|
|200||600||500000||5000||70||600/70.7 = 8.5||17.0bb||-8.5bb/100||8.5bb/100|
|100||300||500000||5000||70||300/70.7 = 4.2||8.4bb||-4.2bb/100||4.2bb/100|
|50||150||500000||5000||70||150/70.7 = 2.1||4.2bb||-2.1bb/100||2.1bb/100|
|20||60||500000||5000||70||60/70.7 = 0.8||1.6bb||-0.8bb/100||0.8bb/100|
|10||30||500000||5000||70||30/70.7 = 0..4||0.8bb||-0.4bb/100||0.4bb/100|
If you use the SD of 100 and the 500000 hands already played, the range of possible future Win Rates are from 0.8bb/100 to 9.2bb/100 (5bb/100 + or – 4.2bb/100).
The range of Bankroll required for the year reflects the range of possible win rates, from 3260bb (3 x 100*100/9.2) to 37500bb (3 x 100*100/0.8) or $3260 to $37500 at NL100 (33 – 375 buy-ins).
The number of hands required per hour is $20 / WR * 100 or 217 to 2500 (435K to 5M in the year).
Therefore you can be 99.7% confident of being successful with the current win rate if your past consistency of performance continues through the current year, but your bankroll requirements may change considerably due to variance. You should aim to bring the SD figure down by being more consistent in results and also try to improve the win rate.