PokerStrategy Articles – Bankroll

//PokerStrategy Articles – Bankroll
PokerStrategy Articles – Bankroll 2018-05-18T17:36:54+00:00

Bankroll Forecasting

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.