Wiz says multi-line vp = more variance

https://wizardofodds.com/games/video-poker/appendix/3/

var of single line JoB = 20
var of 50 line JoB = 5793

i keep hearing in this forum that more lines = less variance.
Wiz says differently.

so for my $15k coin-in at $1 STP 7/5 BP, i should have opted for single line instead of playing triple line.

Besides time constraints, is there any reason to play more lines if you have a choice of single line at the same pay scale on the same machine?

Quote: 100xOdds

Besides time constraints, is there any reason to play more lines if you have a choice of single line at the same pay scale on the same machine?

My understanding is that playing single line is better if you are trying to reduce variance.

Jazbo has some stuff from about 20 years ago about bankroll requirements and variance for N-play machines. http://www.jazbo.com/

You have to do the analysis for a fixed amount of coin in. If you are playing 1 dollar demon single line, you should compare that to the variance of 2 cent denomination 50 play because it represents five dollars of coin in per play of the machine.

Quote: randomperson

You have to do the analysis for a fixed amount of coin in.
If you are playing 1 dollar demon single line, you should compare that to the variance of 2 cent denomination 50 play because it represents five dollars of coin in per play of the machine.
link to original post

ahh.. variance for same amount per spin.

for me, it's different.
single line is $6 per hand, triple line is $18.
so is this why people are saying multi-line is less variance??

Quote: 100xOdds

Quote: randomperson

You have to do the analysis for a fixed amount of coin in.
If you are playing 1 dollar demon single line, you should compare that to the variance of 2 cent denomination 50 play because it represents five dollars of coin in per play of the machine.
link to original post

ahh.. variance for same amount per spin.

for me, it's different.
single line is $6 per hand, triple line is $18.
so is this why people are saying multi-line is less variance??
link to original post

My simple minded way of looking at things... the more hands you play, the faster to you get to long term averages. Therefore less variance.

Quote: 100xOdds

Quote: randomperson

You have to do the analysis for a fixed amount of coin in.
If you are playing 1 dollar demon single line, you should compare that to the variance of 2 cent denomination 50 play because it represents five dollars of coin in per play of the machine.
link to original post

ahh.. variance for same amount per spin.

for me, it's different.
single line is $6 per hand, triple line is $18.
so is this why people are saying multi-line is less variance??
link to original post

STP adds variance too... right? If you wanted lower variance, you could play 5 coins/line.

Quote: Dieter

STP adds variance too... right? If you wanted lower variance, you could play 5 coins/line.
link to original post

yes it does.
But I'm compensated for that with +0.25% ev.

What I want to know is if betting single line or triple line is lower variance for $15k coin-in. ($6/hand vs $18/hand)

Quote: 100xOdds

Quote: Dieter

STP adds variance too... right? If you wanted lower variance, you could play 5 coins/line.
link to original post

yes it does.
But I'm compensated for that with +0.25% ev.

What I want to know is if betting single line or triple line is lower variance for $15k coin-in. ($6/hand vs $18/hand)
link to original post

I don't think the.comparison is apples to apples unless the single line game costs the same as the 3 line game; so $3 x 6 vs $1 x 6 x 3.

The variance is less if the total amount bet, over all plays, is the same.

Quote: Wizard

The variance is less if the total amount bet, over all plays, is the same.
link to original post

I'm trying to grind through some remedial statistics tutorials to better understand this. It has been a long time since that class, and I was honestly more focused on the parties (and disreputable pastimes) than the knowledge at the time.

I'd appreciate any pointers to useful explanations; I think the high level textbooks all moved out with the ex a long time ago.

Quote: Wizard

The variance is less if the total amount bet, over all plays, is the same.
link to original post

less for which case?
single line ($6/hand) or triple line ($18/hand)

Quote: 100xOdds

Quote: Wizard

The variance is less if the total amount bet, over all plays, is the same.
link to original post

less for which case?
single line ($6/hand) or triple line ($18/hand)
link to original post

I think he's saying that if you can bet $x on a single line game, that the variance is less if you can bet $x on a multi-line game. (pay table being the same)

Quote: 100xOdds

Quote: Wizard

The variance is less if the total amount bet, over all plays, is the same.
link to original post

less for which case?
single line ($6/hand) or triple line ($18/hand)
link to original post

Sorry, I should have made that clear. $6/hand triple-play has less variance.

I'm going to take the opposite position. I'll give the intuition and back that up with the math.

We are asking the question of whether three separate $6 single hands for $18 total bet has more or less variance than $18 bet all on one spin of three handed $6 a hand. The total amount bet is the same in either case but in one case the player does three independent six dollar hands. In another case the player does one three handed spin.

The multi-hand version has more variance. This is because the single line version has three independent dealt hands while the multi-line version has three positively correlated dealt hands, and you are fixing the amount of money bet on each hand. Imagine thinking about the variance of the deal for a second. In the three handed case, the deal is the same for all three hands. If you get 4 to a royal or a dealt three of a kind, its the same across all three hands. This increases your variance because the dealt hand is either all good or all bad across all hands. In the single line case, you can get some terrible deals and other good ones. The draw variance is similar between the two because the draws are independent in either case.

Now to do the math behind it.

The variance of three hands of single line JoB at a one dollar denomination:
3*19.51=58.54

These are independent hands so variance scales linearly with the number of hands

The variance of the three handed version is 70.34 which is higher, as given by the table from the website.

The logic is that the three handed version has correlated hands while the single hand version has independent hands.

Quote: Wizard

Quote: 100xOdds

Quote: Wizard

The variance is less if the total amount bet, over all plays, is the same.
link to original post

less for which case?
single line ($6/hand) or triple line ($18/hand)
link to original post

Sorry, I should have made that clear. $6/hand triple-play has less variance.
link to original post

Thx!

How about this scenario of same bet size:
Need to do $15k coin-in to get bonus tier points.

Which has less variance (assume same pay table)?
$1 double play STP ($12/spin)
.25 Eight play Stp ($12/spin)

Quote: 100xOdds

Quote: Wizard

Quote: 100xOdds

Quote: Wizard

The variance is less if the total amount bet, over all plays, is the same.
link to original post

less for which case?
single line ($6/hand) or triple line ($18/hand)
link to original post

Sorry, I should have made that clear. $6/hand triple-play has less variance.
link to original post

Thx!

How about this scenario of same bet size:
Need to do $15k coin-in to get bonus tier points.

Which has less variance (assume same pay table)?
$1 double play STP ($12/spin)
.25 Eight play Stp ($12/spin)
link to original post

For the same game, and same pay table, then ".25 Eight play Stp ($12/spin)" will have less variance than "$1 double play STP ($12/spin)".


See general example below:

Example: Assume "X" is the total you want to bet each spin, and "X" is the same for both games, then the game with less variance will be the one with more "plays" (when playing the same pay table).