Question of the Day - 09 August 2024

It's real simple. A given game has a given variance, which should properly be expressed in betting units. Thus, the denomination played doesn't matter, as long as the paytable is the same.

A multi-line game has less variance than the same game with the same paytable in a single-line version would have. If someone says "multi-play" game, that's what they're referring to--a multi-line game.

If a player wishes to minimize variance, he can a) play inherently less volatile games, b) play multi-line games (for the same total bet per hand), or both.

What the hell was that? 

Huh…hows that again?

After giving a lengthy explanation to a question asked of him, would say"now, are you sorry you asked?" 

Here's a tangible example of why playing multiple hands/lines has less variance/volatility than playing a single line. If you get dealt 4 of a flush, your chances of getting a 5th card of the same suit are 9/47, or close to 1 out of 5. So, on average, you will fill the flush about 1/5 of the time, but you can easily go 10 times without filling it, and might go 15 or 20. But on a 5-play game, when you get dealt 4 of a flush, the chances are high that you will fill a flush on 1 or more of the hands, so you will have a more even-keel time, and very likely won't experience ZIP, ZIP, ZIP, etc., on a succession of deals that give you 4 of a flush. The variance is lower, and the volatility is lower. I have no idea what Hannum and Cabot are referring to when they say that these will be higher. NOTE: I do not think denomination (size of bet) should be considered when discussing variance/volatility. These terms are about proportionality, i.e., results seen in relation to your size of bet.

The denomination of the wager shouldn't affect the variance (as Kevin opines) but is it possible the questioner wondered if the results were 𝘸𝘦𝘪𝘨𝘩𝘵𝘦𝘥 differently at higher denominations (assuming this was even possible)?

It really depends on your interpretation of variance.
If you play a $25c game win or lose you have a $25c variance 
If you play a $1.00 game you could consider your variance to be 4x larger.
It follows the adage bet more/win more (or lose more).
However from a %% win or lose both are the same.


In a multi hand game if they each are dealt from a fully randomized deck then the only thing that changes is speed of play. If they are all dealt from the single deck of cards then we would be back to the blackboard. 

I stopped to think of today's date.  LOL.

How great to have the brain for math as Mr. Ethier does.

Candy

I play the best possible available video poker pay schedules.  I do not worry about any of the mind-boggling math issues.  I use Bob Dancer's pocket cards all the time when I get a difficult hand dealt to me.  Of course one does not need a guide when one is dealt 4 to a Royal or some such hand.  The complex answer to the questions posed just shows why the average player does not need to "understand" higher math.  When I was a freshman in college, the first class I attended in my calculus course was taught by a guy who began speaking in the same confusing way this answer was given - no basic explanations, just jargon.

A simple example why I don't stress over it.

Say I'm playing 3 Play VP JOB or most any game. I'm dealt Q-Q-Q-10-4. I (and most) would hold the 3 Qs, discard the 10 and 4, hope the fourth Q fills in on one or more of the three hands.  Is there any other way to look at it?  But one never knows, and will never know, what might be/would have been lurking under those Qs on the other two hands.  Maybe something that would make up a better hand on the draw, such as the 'other' Q suited with the rest of a Royal Flush.  Not likely, but good thing we'll never know.  JMHO.

Candy

Isn't there a limit in everything where the analytical component goes 301x too far over the rainbow to the land of, what's the point? I think this is an illustration of that point. Want to make money? Increase your odds of it? Don't gamble. Get a job, invest.  

Sunny has it right.  Want to win more often, don't bet on something that you do not already have the answer to.  How about this question.  Where do you have a better chance of winning or coming out ahead?  VP or the stock market.  Talk about variance in the last 2 weeks!

I can clear up a loose end left by the original answer.  In 9/6 JoB with a max-coin bet and with n plays, the variance is given by the formula

Var = (1/n)19.514676427086+(1-1/n)1.966388673536.

For 1-play, 3-play, 10-play, and 100-play, respectively, we get 19.5147, 7.81582, 3.72122, and 2.14187 for the variances.  Take square roots to get the standard deviations.

Apologies for making the original answer more complicated than necessary.

Here is a more complete answer to the multi-play video poker question:  https://arxiv.org/abs/2409.03607.  Go there and click on PDF.

In particular, the original answer was misleading to suggest that the Hannum-Cabot claim was simply an alternative interpretation; in fact, it was wrong.