Am I calculating variance correctly?

[hutennis]

Using Granchrow formula for calculating variance

variance = (bet_size)^2 * (decimal_odds - 1)

I did calculation for my results and got a bit confused.

For each and every bet variance equals either exactly my risk amount for bets on favorit
or my expected profit for bets on underdog.

AO Units at risk DO Variance
(103) 1.03 1.97 1.03
(161) 1.61 1.62 1.61
(106) 1.06 1.94 1.06
(112) 1.12 1.89 1.12
189 1 2.89 1.89
100 1 2 1
118 1 2.18 1.18
180 1 2.8 1.8
109 1 2.09 1.09 Etc.

Have i done it correctly and if yes what is the reason?

TY for help

[Ganchrow]

Using Granchrow formula for calculating variance

variance = (bet_size)² * (decimal_odds - 1)

I did calculation for my results and got a bit confused.

For each and every bet variance equals either exactly my risk amount for bets on favorit
or my expected profit for bets on underdog.

etc ...
Have i done it correctly and if yes what is the reason?

TY for help

Yes, your observation is entirely accurate.

Recall that the win size on a wager of BetSize at decimal odds of DecOdds is simply:

WinSize = BetSize * (DecOdds - 1)

So the standard binary outcome variance formula could be rephrased as:

σ² = WinQuant * BetSize

So if you chose to wager to win 1 unit for USOdds ≤ -100, then your binary outcome variance could be calculated via:

BetSize(USOdds≤-100; WinSize=1) = -USOdds 100 units

σ²(USOdds≤-100; WinSize=1 unit) =
= 1 * BetSize
= -USOdds 100 units²

And similarly, if you chose to risk 1 unit whenever USOdds ≥ +100, then your binary outcome variance could be calculated via:

WinSize(USOdds≥+100; BetSize=1 unit) = USOdds 100 units

σ²(USOdds≥ +100; BetSize=1 unit) =
= WinSize * 1
= USOdds 100 units²

[hutennis]

TY for your comment, Ganchrow.

I have another question though.

How should i adjust to increasing size of my units as far as continues calculation of variance, SD, and Z score?

Do i simply plug in my new unit as a multiple of my original one? Or is there something else to consider?

TY

[Ganchrow]

How should i adjust to increasing size of my units as far as continues calculation of variance, SD, and Z score?

Do i simply plug in my new unit as a multiple of my original one?

Yep, that's all there is to it.

I will remind you that using Z-scores to calculate p-values is just an approximation via the central limit theorem and as new bet sizes increasingly differ from old your conclusions will become less accurate, biased towards later results at larger bet size.

[hutennis]

Would tracking different bet sizes separately get rid of bias showing me more or less fair picture of how my ideas are performing?

EDIT.

How about another idea?

What if I bring unit at risk and profit down to an universal size by dividing those numbers by coefficient I use to establish the bet size?
Will it eliminate the bias?

[mroster]

I'm new to poker and want to ask why are you calculating the variance anyway? Does it affect you play or your results in the long run. I read a lot about poker and gambling recently and I thought variance evens out in the long run anyway? Am I completely wrong?

[bztips]

Would tracking different bet sizes separately get rid of bias showing me more or less fair picture of how my ideas are performing?

EDIT.

How about another idea?

What if I bring unit at risk and profit down to an universal size by dividing those numbers by coefficient I use to establish the bet size?
Will it eliminate the bias?

What I do is calculate the variance using (bet as a % of bankroll) as my measure of the bet size. That way you don't get overweighting toward your more recent bets (assuming your bankroll is growing!). Is that what you're proposing?

[grasya11]

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