How many hours to be X% sure you're up

[Homer]

Introduction

I like to make pointless posts about the volatility of poker from time to time, and today will be no different. Here is a simple way to determine how many hours you have to play to have an X% chance of being up overall. I won't bore you with any derivations.

Method

Step 1: Look up SD and EV on PokerTracker. Compute (SD/EV)^2.

Step 2: Use the chart below to find the percentage of time you want to be up. Multiply the associated factor by the result of Step 1 to get the hours (n) you need to play to be ahead that percentage of the time.

<font class="small">Code:</font><hr /><pre>% Factor
60 1.6
70 2.3
80 3.4
90 5.2
95 7.0
99 11.1
99.9 16.7</pre><hr />
Example

Let's say you want to know how many table-hours you have to play to have a 95% chance of being ahead overall. Your EV is 2 BB/tbl-hr and your SD is 12 BB/tbl-hr, so (SD/EV)^2 = 36. The multiplication factor for 95% is 7.0, so n = 36*7 = 252 tbl-hr.

If you want to know how long you'll have to play to be up 99.9% of the time, n = 36*16.7 = 601 tbl-hr.

So, if you play 2 tables at a time, 40 hours a week, you'll need to play for ~3 weeks to have a 95% chance of being ahead. You'll need to play for ~2 months to have a 99.9% chance of being ahead.