Any discussion is welcome, but I am more interested in NLH specifically what factors. I am specifically wondering what factors are the reason for live poker being higher variance than online poker.

The pots are larger.

More multiway spots

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How did you arrive at live poker being higher variance than online?

https://forumserver.twoplustwo.com/2...ation-1187138/
this forum and other articles - using some of their hourly std dev and converting it to bb/100. And comparing that number to the avg std devs it gives you on prime dope.

Playing wider and more aggressively increases variance.

Playing tighter and more passively decreases variance.

This applies to the entire table dynamic, not just your strategy.

Consider a simplified game: no dead money. Your opponent bets some amount and you call. You have some probability of winning, p and let x be the bet amount. Your possible outcomes are x or -x. The EV is px - x(1-p) which simplifies to x(2p-1).

To calculate variance, for each outcome subtract the outcome from the EV, square that result and multiply it by the probability for that outcome. The sum of these values is the variance. I won’t go through all the algebra but for this case the variance works out to be 4x^2(p-p^2). For those familiar with calculus, take the derivative with respect to p and set it to zero and find a maximum. For those unfamiliar p=1/2 gives the maximum.

What does that mean? First of all it means that marginal situations have the highest variance. 22 all in PF vs AK would be a high variance play. Second it shows that low variance should not be your main goal — after all drawing dead is zero variance. Maximizing EV is the goal. Variance can be frustrating, but we shouldn’t be passing up +EV spots to minimize variance.

speed of play (25 hands per hour live vs. 10x+ online) affecting hourly winrate.

What does that have to do with variance?

First two replies are pretty much 100% of the reasons. Pots are bigger live because people fold pre less often and open sizes tend to be huge. Those are some of the same reasons win-rates are higher.

Your skill level vs your opponents should play a role too. For example, let’s say some player’s skill level is equal to all of their online opponents but held a significant edge over their live opponents. Overall, this should end up causing live to be lower variance than online. Of course some short-term factors such as the number of hands per hour would impact this as well. However, I’d say it’s more likely for the typical poker player to hold a larger edge vs their live opponents compared to online, which should help drive down the long-term variance for live play. Similar to flipping a fair coin vs a rigged coin.

Stack depth and maximum buy in will play a role too.

This is something I am not sure about. On the one hand, it seems that bigger stack sizes would increase the amount available to bet, which would increase variance on average. On the other hand, stack depth increases the available skill edge to good players and, as we know, higher win rates produce less variance.

So, do these factors cancel out? Which one might be more significant?

Of course, but why does wider and more aggressive tendencies cause greater variance? Is it simply the fact that bigger bets are used and more often?

This is interesting. Lately I have been toying with the idea of deliberately playing a low-variance strategy. My main logic being that playing in a low-variance fashion would be better to deal with mentally, which perhaps would allow me to play better. I assumed that one could play a low-variance style that did not lose much if any EV compared to an optimal strategy. I wonder just how much the low-variance strategy might lose compared to the potential EV gained from the ostensibly improved mental game thereafter.

Every reason boils down to the same thing - people putting more money into the pot. Larger pots = bigger swings = higher variance.

• Continuing wide - puts more money into the pot
• Maniacs - put more money into the pot
• Lots of multiway spots - people put more money into the pot
• Deeper stacks - more potential money to go into the pot
• Huge bet sizes - more money going into the pot

So, does this mean that the highest EV strategy will naturally have the highest variance of all +EV strategies? Since, the highest EV strategy will use the biggest bets it can to maximize EV.

If this is true, how is it that skill edges produce lower variance? Shouldn't they produce more variance?

I’m having trouble looking at these scenarios without considering the skill level difference between the players. We know that the deeper stack depth will favor the stronger player, however, bigger stack sizes alone may not matter. Would two equally skilled players observe different variances at 30bbs vs 500bbs?

Out of curiosity, how are you guys defining “variance”?

I’m far from well informed on this topic, but I always took it as std dev in bb/100

My guess is that two equally skilled players would have higher variance at 500bbs. However, if we assume one player is much more skilled than the other, I wonder if the better player would actually experience less variance if both of the players are 500bbs as opposed to 30bbs

Well if u play 4 tables of 100NL online and play 1K hands in a night vs playing 1 table of 500NL live and playing 100 hands in a night I think it’s kinda obvious.

It’s not us defining it. Variance is a well-defined standard term in statistics. For each hand, subtract the result of the hand from the EV for that hand and square that value. Take the sum of these values for each hand and divide by the number of hands.

Standard deviation is simply the square root of variance, and often is used interchangeably in poker discussions. It has the advantage of having the same units as EV (either BB or $) and can therefore be used to determine likely win rates.

Variance is standard deviation squared, but in the context of this conversation they are mostly interchangeable.

Win-rate has very little to do with variance. If you are crushing and 90% of your sessions are between $0 and+$1000, your variance would be exactly the same as someone with 90% of their sessions between -$500 and $500. The first player with a much higher win-rate will rarely have downswings while the second player will be all over the place around $0, which is what I think most people mean when they say the first player experiences less variance, but they are using the term incorrectly.

Deeper stacked play very obviously increases variance due to larger pots being possible, up to a point where large stacks just stop being in play I guess.

Sure - now how would you go about that? It’s not as if each hand has some standard EV value. Essentially, I’m curious what exactly is being measured in this context when variance is referred to.

Variance as a sample statistic is the average of the squared deviations of the sample values from the sample mean.

For poker, a deviation for a particular hand would be the profit/loss in the hand minus your average profit/loss over the sample of hands played. Note that the mean will generally vary over time as you improve (hopefully), change stakes, change venue, change game. Therefore, one’s variance is probably not a static measure.