Equivalent VP variance

[FWMR]

For the math-savvy:

I would like to get an idea of how much "swing" there is in BJ versus video poker.

In the video poker world, variance is measured in "bets squared": Some common figures are 20 for jacks or better, 25 for "4/4" deuces wild, and about 40 for double double bonus. I am guessing much the same for blackjack, although the standard deviation and per-hand variance is much lower--say (1.4 bets)^2 = 2 bets squared.

The per-hand variance of double double bonus is 40 bets squared. If playing at a denomination of "u," the variance is 40 u^2. Using this as a benchmark (and ignoring return), what unit size in blackjack would give the same amount of swing?

[Dog Hand]

FWMR,

The variance for flat-betting at BJ is about 1.3, with small changes due to the house rules: see https://wizardofodds.com/games/blackjack/variance/

So, if your BJ bet is "b" (note that b is your initial bet: the var. value accounts for splits, DDs and BJs), then the var. is 1.3 b^2. If you want to equate that to the DDB var. of 40 u^2, then we get this:

1.3 b^2 = 40 u^2

Solving for b gives us:

b = (40/1.3)^0.5 u, so b = 5.55 u

Thus, if you're playing $5/spin at DDB (5 coins on a $1 machine), then flat-betting $27.50 at BJ will have nearly the same variance per round: $$1000. One caveat is that the variance PER HOUR will still be much higher for DDB than for BJ, since you'll likely play 5-10 times as many rounds per hour at VP than at BJ.

Note also that if you vary your BJ bets, the variance will be much, Much, MUCH higher than 1.3.

Hope this helps!

Dog Hand

[FWMR]

Note also that if you vary your BJ bets, the variance will be much, Much, MUCH higher than 1.3.

Thank you. One more: I see figures like SD = s and average bet = a for certain bet spreads on sites like WoO. Is the per-hand variance (sa)^2, s^2, or something else? Then, how would you figure an equivalent base bet b?

[Dog Hand]

Thank you. One more: I see figures like SD = s and average bet = a for certain bet spreads on sites like WoO. Is the per-hand variance (sa)^2, s^2, or something else? Then, how would you figure an equivalent base bet b?

FWMR,

One advantage of using SD rather than Variance is that SD has the same units (in the sense of dimensions) as EV. For example, say for a certain game the SD is 5. If your bet is $100, then your SD in terms of dollars will simply be $500, while your variance, which is SD^2, will be $$250,000: note the variance has units of "dollars squared".

Hope this helps!

Dog Hand

[FWMR]

FWMR,

One advantage of using SD rather than Variance is that SD has the same units (in the sense of dimensions) as EV. For example, say for a certain game the SD is 5. If your bet is $100, then your SD in terms of dollars will simply be $500, while your variance, which is SD^2, will be $$250,000: note the variance has units of "dollars squared".

Hope this helps!

Dog Hand

I may be on the right track then. WoO provides SD and variance for certain strategies. For example: SD = 2.5 for a $5:$50 spread with average bet 2.7 units. Is the variance (2.5 x 2.7 x $5)^2, or just (2.5 x $5)^2?

[Dog Hand]

I may be on the right track then. WoO provides SD and variance for certain strategies. For example: SD = 2.5 for a $5:$50 spread with average bet 2.7 units. Is the variance (2.5 x 2.7 x $5)^2, or just (2.5 x $5)^2?

FWMR,

This one: (2.5 x $5)^2. The "2.7" factor is why the SD is larger than the flat-betting value of, typically, 1.15 units.

Dog Hand

[FWMR]

Thank you.

[DSchles]

This one: (2.5 x $5)^2. The "2.7" factor is why the SD is larger than the flat-betting value of, typically, 1.15 units.

Why would you be using just the $5 bet to calculate the overall variance??

Don

[RS]

You sorta (specifically) mentioned to ignore the return, but I think this is something that is still VERY MUCH worth mentioning. I don't know about others, but at least for me, I don't really care what the hourly swings are going to be. I care what it looks like in the long run. I'm looking at N0 (in terms of hours, weeks, or months). Look at the SD-to-EV ratio. If you're playing a game worth $500/hr but the SD is $1,500/hr, it's going to be a cake walk. If you're playing a game worth $100/hr and with an SD of $3,000/hr, well that's a whole 'nother ball game.

Remember, SD is how much you can swing from EV.