Standard Deviation on Pokertracker

[all_in_lam]

Hi, i know standard deviance is a meausre of variance, i.e.
Standard deviation is the square root of variance.

1) meaning variance = stdv^2, but does either of these numbers have a relatable meaning in terms of poker, i.e. if my stdv = 50bb, what does this mean? other than obviously a player with 50 has higher variance than a player with 20

2) and oh yea, where do u find it in PT

[bobbyi]

[ QUOTE ]
i.e. if my stdv = 50bb, what does this mean?

[/ QUOTE ]
That wouldn't really be meangingful because the units are wrong. Your standard deviation is going to be expressed as some amount (dollars or BB) per some amount of time (an hour or 100 hands). So, a standard deviation for LHE could be something like 15 BB/100 (just picking a number to use as an example).

Here's what it means: Standard deviation measures how close to your expectation your results tend to be. Specifically, about 2/3 of the time you end up within 1 SD of the mean. 95% of the time you end within two SDs. 99% of the time you end up within three SDs.

Suppose your SD is 15 BB/100 and your winrate is 2 BB/100. Now suppose you play 100 hands. There is roughly a 2/3 chance that you will end up somewhere between down 13 BBs and up 17 BBs (within 15 of the 2 BBs that you win on average). There is roughly a 95% chance you will end up between down 28 BBs and up 32 BBs (within 30 of the average).

[-zero-]

[ QUOTE ]

2) and oh yea, where do u find it in PT

[/ QUOTE ]

Session Notes -> More Detail

[Sandra Bullett]

Std Dev is seriously important to +EV gamblers (but ignored by many). But, happily, not so much in poker (as the std dev is quite small), unless your bankroll is small.

Gambling isn't so much about maximizing EV, as it is about maximizing EV/risk (risk=std dev). Ie. just like investing in the stock market, and other financial activities, "risk and return" are the two major issues.

If you bet too much (chasing a big win), you risk losing your bankroll, forfeiting the chance of future gambling/winning.

Imagine games where you bet $x and roll a single die. All the following assume that if you lose your bankroll, then you are out of business forever (ie. your bankroll is all you have). All have the same positive EV%. Three scenarios:

1) Never lose

1,2,3: "push", your bet is returned to you.
4,5,6: "win", you get your bet back, plus 10%.

How much SHOULD you bet on this game? The answer is your entire bankroll. You can't lose. Risk of ruin = 0. Bet your bankroll, and regardless of the outcome, keep betting it (it increases after a win, of course). This is mathematically the correct decision.

2) Lose $x is possible.

1,2,3: lose your $x bet
4,5,6: win $x+10%.

How much SHOULD you bet on this game? It depends on what risk of ruin you are comfortable with. Let's say 20% of your bankroll (whatever that is, at the time of each bet)

3) Lose more than $x is possible.

1: lose $x * 100
2: lose $x * 10
3: lose $x * 1
4: win $x *1.1
5: win $x * 11
6: win $x *110

How much SHOULD you bet on this game? A HELL of a lot less than the previous example! If you bet more than 1% of your bankroll there's a 1-in-6 (16.6%) chance of going busto. A 16.6% risk-of-ruin is far too high for any serious +EV gambler. With a non-replaceable bankroll even 5% is too scary. Betting 1% of bankroll is too much, maybe 0.1% would be OK.


So, 3 games all with the same EV%, but with highly variable 'correct' bets (from 100% of bankroll, down to just 0.1%).

In blackjack, where the game mathematics are indentical on every denomination of table, such calculations are critical (and most players don't do them, play on too-high a table [greed!], and go busto).

In poker, most players are restrained from moving up to higher denominations not by their lack of bankroll, but by their lack of skill.

Nonetheless, if you do not have a large bankroll, it can be much better, for example, to 10-table $3/$6 games, rather than single table $30/$60, even if the EV is 1BB/table-hour in both cases (ie. identical EV's of +$60/man-hour). 10-tabling $3/$6 produces a much smaller standard deviation (per man-hour) than single-tabling $30/$60), thus your limited bankroll is safer.

You might be therefore be able to 10-table $5/$10 with the identical risk of single table of $30/$60, ie. risk remains the same, EV is increased, thereby maximizing the EV/Risk ratio.

[jba]

nice post sandra

[daveT]

Your posts are always great, Sandra Bullet. You explain yourself so friggin' well. What great comprehension.

[Sandra Bullett]

[ QUOTE ]
You explain yourself so friggin' well

[/ QUOTE ]

You too (and, thanks)

[ShakeZula06]

[ QUOTE ]
nice post sandra

[/ QUOTE ]