Explanation

Instructions

First select one of the two radio buttons. If you want to chart your winrate and a confidence interval gven your win rate, standard deviation, desired confidence interval, and number of periods played, select the "Win Rate" radio button. Otherwise, select the "Total Winnings" radio button to chart your total winnings and a confidence interval.

*Important: the period may be number of hands, hours, or other convenient unit. However, the winrate and standard deviation must be in units that are consistent with the units of the period.

Example 1: if you have a winrate of 1.5 BB/100 hands, a standard deviation of 16 BB/100, and have played 15,000 hands, then enter the period in hundreds of hands, i.e. 150.

Example 2: if you have a winrate of 1 BB/hour, a standard deviation of 10 BB/hour, and have played 993 hours, then simply enter the number of hours, i.e. 993, in the period textbox.

Enter your information and click the "Chart It" button. You can click the "Chart It" button multiple times to see a series of simulated results. Note that all four textboxes must contain valid data. Follow these guidelines for your entries:

• Win Rate: may be a positive or negative number.
• Std. Dev.: must be a number greater than 0.
• Confidence: must be greater than 0 and less than 100. Example: if want to graph a 50% confidence interval, enter the number 50 in this textbox. Note that the default is 95% confidence.
• The number of periods played must be a number greater than 0.

Math

Note that no units are expressed in the program. So long as you use consistent units, the answers will be correct in the same set of units.

The upper bound of the confidence interval is calculated as W-Φ^-1(p)σ√P

and the lower bound is

W+Φ^-1(p)σ√P.

Win rate is simulated by

W_n={W_n-1+ΔP[ W+Φ^-1(p)σ/√ΔP ]}/P

while total winnings are

T_n=T_n-1+ΔP[ W+Φ^-1(p)σ/√ΔP ].

P is total number of periods, T is current total winnings, W is win rate, σ is the standard deviation of the win rate, ΔP is some fraction of P (ΔP=P/200 is used for convenience in graphing), Φ^-1() is the inverse standard normal cumulative distribution, and p is the probability of achieving a particular win rate. The value of p ranges between 0 and 1 and is generated randomly.

Other Stuff

This program uses the JFreeChart chart library, which is licensed under the GNU LPGL.

Disclaimer: I am not a mathematician or a professional programmer. I believe this program works correctly but I offer no warrantee of any kind. You are free to use this program as you wish, but you must do so at your own discretion.

If you have suggestions or notice an error, please let me know. You can find contact information at the bottom of the page linked below.