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.

[SCfuji]

this clarifies some things... thanks homer.

[SomethingClever]

What are you using for EV? Your winrate? How do you know it's accurate?

[Homer]

[ QUOTE ]
What are you using for EV? Your winrate? How do you know it's accurate?

[/ QUOTE ]

Yeah, sorry about that, I tend to use those terms interchangeably, which I guess is wrong. You have to to be sure that your winrate is relatively accurate before these calcs have any meaning. Once you're sure of your winrate, though, you can use this as a sort of reality check...

"Holy [censored], I can't believe I only broke even playing full-time for the last three weeks. The odds of that must be, like, totally infinitesimal. I bet the site's rigged. Oh wait, there's a 1/20 chance of that happening, nevermind."

[Tapin]

Wow, using this formula I need to play 900 hours to be 70% sure I'm up, and my entire PT DB has 971 hours in it.

I've never felt more like a donkeyfish than this moment.

[SomethingClever]

[ QUOTE ]
[ QUOTE ]
What are you using for EV? Your winrate? How do you know it's accurate?

[/ QUOTE ]

Yeah, sorry about that, I tend to use those terms interchangeably, which I guess is wrong. You have to to be sure that your winrate is relatively accurate before these calcs have any meaning. Once you're sure of your winrate, though, you can use this as a sort of reality check...

"Holy [censored], I can't believe I only broke even playing full-time for the last three weeks. The odds of that must be, like, totally infinitesimal. I bet the site's rigged. Oh wait, there's a 1/20 chance of that happening, nevermind."

[/ QUOTE ]

Haha, ok.

I just ask because I have been breaking even for 23,000 hands, or approximately 71 table hours.

Edit: Wait... I think I'm confused as to what table hours are. Would this # be 71 or 285? I'm 4-tabling.

I have no friggin clue what my winrate is or if I'm even a winning player at this level.

[captZEEbo1]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
What are you using for EV? Your winrate? How do you know it's accurate?

[/ QUOTE ]

Yeah, sorry about that, I tend to use those terms interchangeably, which I guess is wrong. You have to to be sure that your winrate is relatively accurate before these calcs have any meaning. Once you're sure of your winrate, though, you can use this as a sort of reality check...

"Holy [censored], I can't believe I only broke even playing full-time for the last three weeks. The odds of that must be, like, totally infinitesimal. I bet the site's rigged. Oh wait, there's a 1/20 chance of that happening, nevermind."

[/ QUOTE ]

Haha, ok.

I just ask because I have been breaking even for 23,000 hands, or approximately 71 table hours.

Edit: Wait... I think I'm confused as to what table hours are. Would this # be 71 or 285? I'm 4-tabling.

I have no friggin clue what my winrate is or if I'm even a winning player at this level.

[/ QUOTE ]

285

[OrangeKing]

Ah, read the statistic wrong - looks like I need to play for 260 hours to be 99.9% sure I'll actually make a profit. [img]/images/graemlins/smile.gif[/img]

[GrannyMae]

[ QUOTE ]
Wow, using this formula I need to play 900 hours to be 70% sure I'm up, and my entire PT DB has 971 hours in it.

I've never felt more like a donkeyfish than this moment.

[/ QUOTE ]

but your self-deprecating humor is excellent!

top scores!

[LondonBroil]

My example:

Hands played: 18784
Hours played: 320.57
BB/hr: 2.50
Standard Deviation: 33.8161 (Is this high? I play mostly 400-600 NL)


So (SD/EV)^2 would be (33.8161/2.50)^2 = 182.964

Taking my hours played of 320.57, I'll go backwards and say 320.57/182.964 = 1.75 factor (putting me at around 62%)

Does this mean that over the next 18,784 hands I only have a 62% chance of winning? That's scary as that's 2 whole months!