[Rainclouds]

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Playing LAG = more variance than playing TAG, by mathematical definition.

It doesn't matter how you win the pots. The mathematical definition of variance is the sum of the squares of the results of your hands. It's not difficult to see that playing more pots = higher sum.

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yes we've all taken stats, variance = std deviation squared. yah yah yah.

the point is that by being in more pots in effect things are more gradual, ie. your std deviation from your winrate is lower, therefore lower variance (smaller wins and smaller losses)

by claiming the fact you play more hands mean you swing more is not the case. consider this:

a person at a 10 person table pays 15bb in blinds every 100 hands. they play 1 hand ever ~200 hands, and win a stack 80% of the time doing so. (This would be the equivalent of getting AA and getting action in on it pf every time it's dealt, clearly this is a hypothetical) So, for 200 hands, they've paid 30bb in blinds, (pots lost w/o showdown) gotten 1 big pot (fewer big pots then our lag counterpart in the next example) and on avg win the +100 bb (.8) and lose -100 (.2), for net +60bb. The dif here (60bb - 30bb) is 30 bb per 200, for a winrate of 7.5ptbb/100. We're using this as our consistant winrate, because it's clear (And I repeat this) your actual winrate is the most important factor to how much you swing, since by defition someone who barely beats the game WILL swing up and down far more consistantly. Any event:


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The variance of this player = 20 x -1^2 + 20 x -0.5^2 + 0.8 x 100^2 + 0.2 x -100^2 = 10025 -> 50.125 per hand, std dev = 7.08/hand

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The next player plays somewhat laggier, to the extent that in this full ring table over 200 hands they play 30 hands. (wow, 15% vpip!) They still are paying 30bb in blinds over this time, and say they win 18 of the 30 hands w/o showdown for 10bb pots each time (net 180bb), bc thats basically psr gets called pf and a cbet takes it down/or a 2nd barrel; lose 10 of those hands w/o showdown (cbet was called or raised) for a loss of 10 bb each time (-10bb net) and play 2 "big pots"; atm you have +180, -100, -30 for net +50, so to reach the magic number of +30bb you need to have net equity of -20 of these 3 all ins. (OUR WON AT SHOWDOWN WILL BE UNDER 50% YET WE'RE THE MORE STREADY WINNER) So, we play a hand for stacks with 55% equity (like a big draw) for net +10bb and we play an all in with 35% equity (like a bare flush draw). Our won at showdown should be roughly 45%, and our losses at showdown will be sum neg, yet:


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The variance of this player = 20 x -1^2 + 20 x -0.5^2 + 18 x 10^2 + 10 x -10^2 + 0.55 x 10^2 + 0.45 x -10^2 + 0.35 x 100^2 + 0.65 x -100^2 = 12925 -> 64.625 per hand, standard deviation = 8.04

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Over the span of a sesh, (say, 1400 hands) where the first guy plays 7 big pots and the second guy plays 14 big pots, it's far more likely the first guy ends with a larger -sesh then the second. however, it's far more likely the first guy has a bigger win too.


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standard deviation of player 1 over 1400 hands is sqrt(1400)x7.08 = 265bb
standard deviation of player 2 over 1400 hands is sqrt(1400)x8.04 = 301bb

They both expect to win 210bb which is 0.8 std devs for player 1 and 0.7 std devs for player 2. Player 2 will have more losing sessions by definition. To compensate for this with the same winrate as player 1, he will have larger winning sessions.

I just proved it mathematically.

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both have the same win rate, and yes, this example is somewhat hard to follow, but the gist is: a. you can play more big pots b. you can play with a smaller edge on the big pots you play c. you can have a poor won at showdown d. but this does not directly correlate with your variation.

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See above.