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PokerStrategy Articles - Bankroll

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.

 

 

 

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