How do you define variance? We clearly are not talking about the same thing.

Variance is observed results that are not equal to expected results. Every AI hand (unless one of you was drawing completely dead) has variance, as you never received 68% (or whatever) of the pot. You always get 100% or nothing. Since a good SS strat has a ton of AIs early in the hand when Vs and Hero will have a lot of outs, there will naturally be a ton of variance.

Since you are risking less each hand, you may have smaller overall swings, but even that is not necessarily true, as SSers have many more hands go to showdown than deep TAGs, or even LAGs.

It's just frustrating to see every time a post comes up where hero doesn't have 100 bb, we have to have 3-4 ppl say top up pre. At least half of the ****ty regs/ newer players that buyin for 100bb would be better off buying in for less.
It really doesn't help discussion about the hand in question at all. It's autopilot advice

I measure variance in dollars. I don't understand the argument to measure variance any other way as a poker player.

It's not just all-in hands that have variance. Almost every single action you take except for folding has variance, including betting the nuts on the river. If you are deep-stacked and make a 100BB river bet, that's usually going to be much higher variance than a 20BB short stack GII pre-flop.

If you measure variance in buy-in units, then sure, a short-stack has higher variance, but that doesn't make any sense as a unit of measure when we are poker players who care about money won/lost, not buy-ins won/lost.

It is possible that very short stacks will just GII pre with hands that deeper stacks would cold-call, which contributes to more pre-flop variance for a short stack, but a deep stack can play a wider range pre-flop including more 3-bet/4-bet bluffs (remember every hand we don't fold adds variance). A deep stack can also play later streets where bigger money goes in when a short stack can't.

snap call and don't even think twice. this is one of the best hands you will show up here with.

browni, you are only looking at it as lower variance because both the win-rate and loss-rate are capped, so the overall dollar swings are also capped. Variance is not "how big a downswing is possible" though. Variance is "how much do observed results vary from the EV of plays made." Sure, SS strat = smaller overall swings, but it also means way more of them.

Exactly, so the amount that observed results can deviate from expectation is limited by one's stack size.

We are talking about variance as the same thing, but for some reason we are drawing different conclusions.

I'm not exactly sure where the disconnect is. I can give empirical evidence as well.

From my PT4 database for hands played as the dealer:

"PF Stack Size","My C Won","Hands","StdDev(BB/100)"
"Stack less than 2 big blinds","$0.63","7","13.29"
"2 bbs < Stack <= 5 bbs","$0.91","6","13.57"
"5 bbs < Stack <= 10 bbs","$5.06","35","40.86"
"10 bbs < Stack <= 15 bbs","-$11.75","60","57.36"
"15 bbs < Stack <= 20 bbs","-$7.04","90","67.55"
"20 bbs < Stack <= 30 bbs","-$29.50","381","68.03"
"30 bbs < Stack <= 40 bbs","-$13.24","606","71.40"
"40 bbs < Stack <= 50 bbs","$30.25","1,208","77.18"
"50 bbs < Stack <= 75 bbs","-$14.51","2,678","93.47"
"75 bbs < Stack <= 100 bbs","$138.50","4,546","96.80"
"100 bbs < Stack <= 125 bbs","-$58.71","4,222","101.32"
"125 bbs < Stack <= 150 bbs","-$93.27","2,015","97.31"
"150 bbs < Stack <= 200 bbs","-$41.35","2,317","109.31"
"200bbs < Stack <= 250 bbs","-$24.77","1,047","100.14"
"250 bbs < Stack <= 300 bbs","-$63.62","497","75.84"
"Stack >= 300 bbs","-$67.68","808","126.97"

The standard deviation (and with it variance) is increasing until stack size of (125, 150], after which it's pretty erratic.

I wouldn't consider the bigger stack sizes reliable datapoints as that is only the starting stack of a player, not the effective stack. At higher stack sizes the effective stack is likely lower than the player's own stack size.

Sigh. Tired of the derail. It's a factor of how often we see showdown and especially how often we end up AI with cards yet to come, as I mentioned above. Think of it as red line vs. green line. If that doesn't make sense to you, let's just agree to disagree and stop derailing the thread about it.

I don't understand your point about the red line vs. green line, sorry.

Apologies for derailing the thread. I could start a new one in a more appropriate place, but I don't know what else I can say anyway. I have provided mathematical and empirical evidence, and I'm not sure how else to explain it logically.

I don't know if I have enough credibility with you for you to trust me here, but you are misunderstanding something and you should think more on the subject before continuing to perpetuate this idea that short-stack play is higher variance that full/deep-stack play.

I won't post on this topic in this thread again. If you wish for me to continue replying you can move the discussion somewhere else. My motivation to continue this discussion is to help others better understand the concept of variance, so if others don't want to continue I don't have a desire to.

OK, last try, because I don't know how to split this out into a new thread. If this doesn't close the discussion, I'll ask another mod to give me a hand.

SDEV is not the same thing as variance. You are right that the overall swings will be bigger when you play bigger pots. Variance though is how much you are at the mercy of the cards and the way the cards fall determine your outcome more than your skill. When you play short-stack, you are at the mercy of the cards, and more of them, more often than when you have enough chips behind to deny odds to draws, etc.

Does that make sense?