13 January 2010
Since ev++ launched, the most
popular feature has been
our Poker Variance Simulator. I have got a couple of emails asking
for some more information on the simulator and what the results mean so I thought I'd
dedicate the first couple of blog posts to that subject.
Terms and Definitions
Before we can understand what is going on in the figures generated by
the variance simulator we need to get a couple of terms and
definitions straight and that (as boring as it is) will be the focus of this post.
BB’s vs. bb’s
There has been a lot of confusion in the past (particularly in the No
Limit crowd where the term BB isn't particularly relevant) regarding
the difference between the term BB’s and bb’s. BB is the
short form for Big Bet which is defined to be twice the amount of the
big blind or bb for short. In a $10/$20 Limit Hold'em game, the small
blind (sb) would usually be $5, the big blind (bb) would bet $10 and a
big bet (BB) would be $20. Big bets (BB's) are only really relevant
in Fixed Limit games where the size of the bet doubles on 4th and 5th
streets.
In online poker circles a BB is often referred to as a PTBB (Poker
Tracker Big Bet) to make the distinction between BB and bb crystal clear.
To sum up 1 BB = 1 PTBB = 2 bb's.
Winrate
Winrate, simply enough, is the amount of money (measured in $'s bb's
or BB's) you won in a certain standarized unit (usually 100's of hands
or hours). A poker player who primarily plays live will often refer
to their winrate in dollars per hour ($/hr). An online no limit or
fixed limit poker player (who are smart enough to be collecting
rakeback of course) will usually refer to their
winrate in big blinds per hundred hands (bb/100) or big bets per
hundred hands (BB/100), respectively.
Typical winrates for good online fixed limit players may be as high as
3BB/100 in very soft games but a winrate of just 1BB/100 is considered
to be quite good in todays tougher online climate. Expert online No
Limit Hold'em and Pot Limit Omaha 6 max players can win up to 10bb/100
(5BB/100) with 4-6 bb/100 being a more reasonable estimate.
Standard Deviation
Imagine a poker game where you play 100 hands and no matter what
happens, at the end of those 100 hands somebody just hands you 10 big
blinds (kinda
like Party Poker circa
2005!). Sounds pretty nice! However as every gambler or poker player
knows it doesn't work that way; tilt, bad beats, suckouts, heaters,
coolers, upswings and downswings all cause fluctuations in the amount
of money you win over a given sample. This fluctuation is what is
commonly referred to as variance by poker players.
Variance can be calculated mathematically using the following formula
where the σ2 is your variance,
the x is your
expected win rate, xi is your results for a given
100 hand sample and N is the number of 100 hand samples. This is
perhaps best illustrated with an example: imagine a player who plays five 100 hand sessions. Looking at the results the player discovers they won the following amount in each 100 hand sample:
| Sample # | Win/Loss (bb) |
|---|
| 1 | +150 |
| 2 | -50 |
| 3 | +25 |
| 4 | -85 |
| 5 | +10 |
| Totals | +50 |
Giving them a winrate for this sample of 10bb/100 (50bb/5). The players variance over that sample then would be
σ2 = 1/5*[(150-10)2 + (-50-10)2 + (25-10)2 + (-85-10)2 + (10-10)2] = 6490
Standard deviation, σ is just defined as the square root of variance so the standard deviation for the example above is σ = sqrt(6490) = 81.
You can find out your standard deviation by tracking large samples of your online hands (or session results for
live players) using a program like Hold'em Manager
or Poker
Tracker 3. To get your standard deviation in Holdem Manager look on the far left of the Reports tab and click on the + sign. Now add the standard deviation stat and save. To find out your standard deviation from Poker Tracker 3, please follow the instructions found on the 2+2 forums: Find your standard deviation in Poker Tracker 3.
The value of your standard deviation will depend on a number of factors including your and your opponents playing styles. In limit hold'em you might have a standard deviation of 18-20 BB/100 while in games like no limit holdem and pot limit omaha your standard deviation will likely be in the neighborhood of 80-120 bb/100. The higher your standard deviation is the more variance (upswings and downswings) you will experience.
Ok, that is enough of the boring math stuff out of the way and in my next post I'll make some pretty pictures like this:
and discuss how we can interpret them.
