variance_cashgame_graph

EV, confidence intervals and samples in bb, best/worst over 1000 trials

To help us better understand poker variance effects, let’s take a look at the graph at the top of the page.┬áIt’s a calculation for a player with a decent 2.5 bb/100 winrate, over 100,000 hands, which is around the number of hands a grinder would do in a couple of weeks, but might take a year for a low volume part-time player. It indicates the following.

  • The player expects to win 2500 bbs on average (winrate 2.5 bb/100 over 100K hands)
  • The player will actually lose 21% of the time over 100K hands
  • We can be 70% sure the player will be somewhere between -662 bbs and winning 5662 bbs
  • We can be 95% sure the player will be somewhere between -3825 bbs and winning 8825 bbs
  • The player needs to start with a bankroll of 5991 bbs, or nearly 60 buy-ins to have a less than 5% risk of ruin(
  • There’s a 76% chance the player goes on at least a 10 buy-in downswing at some point
This tells us that a player with a winrate of 2.5 bb/100 is still exposed to a fairly high level of variance, so it’s best to err on the side of caution. It also reveals that it can take an extended period before data more accurately reflects a players true expected winrate. This can be quite an eye-opener to some players who aren’t familiar with the influence variance can have on results.

Here we can see an MTT example using the 2 months 40K challange. If Acesup was to use the $2K roll and play tournaments with an average buy-in of $5.5 (50 cent fee), he could afford to play 400 tournaments. If he never climbed up in stake and did in fact play 400 MTTs, with an ROI of 55% (likely much higher at <$5.50 games), he could expect the following.

2M40challenge_variance_graph

After 400 x $5.50 tournaments with a significant skill edge, not surprisingly this graph mostly show profit (right blue side).

  • An average profit of $1,196
  • A 5% chance of losing (finishing <$2K after 2 months)
  • 70% sure a result will be between losing $190 and winning $2,933
  • We can be 95% sure of results between -686 and winning $4,040

Adjusting the ROI and the buy-in level are going to have a significant impact on these results. To demonstrate this, let’s say a good poker player played 5 tournaments a night in their spare time after work. They played an average buy-in level of $11, but these tournaments were turbos, which means shorter stacks and faster end times, or put another way, less skill and more luck. With the skill edge they have, they still feel confident of having an ROI of 22.5%.

turbo_variance_graph

Even with a solid 22.5% MTT ROI, we can see a 39% chance of loss (blue under the 0 line)

This player can expect the following results after a month of play.

  • An average profit of $348
  • A 39% chance of being down at the end of the month
  • 70% sure they’ll be somewhere in between down $533, and winning $1,258
Even a player with a significant edge playing 5 tournaments a day for a month will having losing results 39% of the time! So they decide to switch to regular games the next month, rather than turbos, where they have an estimated ROI of 45% (double that of the turbos, which isn’t unusual at all).

mtt_6month_graph

Beating the variance – A high skill edge put to work over a prolonged period.

They could now expect the following numbers after 6 months of play.

  • An average profit of $4,591
  • A 1% chance of being down at the end of the 6 months
  • 70% sure they’ll be somewhere in between winning $2,035, and winning $7,120
It’s clear that gauging results over a longer time frame, and when holding a more significant edge over the field, the chance of losing being attributed to variance is small. In fact in this situation a player will only be losing around 1% of the time and can be 70% sure they’ll be profiting at least a couple of thousand dollars.

So be sure to allow ample time for results to portray meaningful data, and get the greatest skill edge you can by joining sites like Run It Once for cash games or PokerNerve for MTTs.

Note: All of the above calculation were made using a variance calculator.