Video Poker VP Variance

I'm curious about the variance of VP when it comes to single line vs. multi line games. I've researched a bit around the web, and found several articles/posts that state that multi line VP has a higher variance than single line (more volatile for your bankroll).

This seemed counter-intuitive to me, but I realized that most of these comments were comparing equal denominations, for example, playing 5 lines max bet at $5 per credit ($125 coin in) vs. playing single line max bet at $5 per credit ($25 coin in). In this instance, the 5 line game would obviously have a much higher variance, as you are risking 5 times as much money per "spin" as you are in the single line game.

But what if the coin in amount is equal? For example, playing single line max bet at $5 per credit vs. 5 lines max bet at $1 per credit? In both of these cases, the coin in amount would be $25 per spin. Logic tells me that the variance would be lower for the multi line game....am I wrong?

Sorry for being so wordy, just trying to get my point across clearly. Thanks!

 

For the same coin-in per spin the variance is FAR lower with multi-hand VP. I play 10 hands on my WinPoker frequently, and all you need to see is all the times with 50 coins bet I win 10 or 20 or 30, (like when holding 1 high card or a small pair). You can't do that with single-line, you'll just lose 5 or win 5/10 or whatever. It's pretty obvious. Much smaller swings. And on the other side, when you win 2000 on Aces with the kicker, you bet 50 to do so, not 5. Again, lower variance.

 

You're not wrong and neither are they. But they're not comparing apples to apples. Its because they're comparing equal denominations like you stated.

The Wizard of Odds has the breakdown of single-line vs. multi-line volatility here: http://wizardofodds.com/games/video-poker/appendix/3/

In your first example where they are using the same denom for both, the correct comparison to compare a single hand of the multi line game would be to compare it to 5 hands of the single line game, not one like they are doing.

So using the numbers from his chart it would be:

5 hands of a single line JoB game is 4.4175 * sqrt(5) = 9.878
1 hand of 5 line Job game is 5.2326

So the volatility of a multi-line game is considerably lower when you actually compare an equal number of hands.

Of course, if you're betting 5x as much its going to be much more volatile on your bankroll per spin (just multiply those numbers by the total bet amount) but not per hand.

Basically the standard deviation for N lines in multi-line increases by less than sqrt(N), which is the amount it would increase for N hands in single-line.

 

Theory is great, but the reality is - multi line is more volatile. I have played it at 3, 5 and 10 handed since it was introduced to casinos and that is a fact.

Yes, the game you choose (JorB, DD, DDB, Deuces) will also have an effect on this, but the reality is - it is more volatile.

It's fine if you are getting dealt winning hands, but the reality when playing in a casino is you will have streaks. If you are not getting the big dealt hands, you need a larger bankroll through the "down swings" (just like any form of VP). most people don't have the bankroll, or the stomach to continue through the downswings so they end up losers. And others, don't know when to quit when they are ahead and end up giving back the profits.

Also, with multi play - your errors are compounded 3, 5 or 10 times depending on how many hands you are playing. So, if you don't know perfect strategy for 1 line VP, and play multi hand, your incorrect play will cost you more.

 

Thanks for posting. I only recently started playing multi-line (mostly 3 line) and although I have a small sample size to date, I am as comfortable playing 3 Line $1 as 1 Line play ($1 or $2). For players seeking to earn specific day comp awards (Diamond in a day - which I know isn't offered anymore - CET now offers bonus points at certain point levels) or for drawings, comps, etc, 3 or 5 line play is a great way to go and you have a shot a a three hand 4OAK or SF/RSF!

 

No expert here, but what I have seen it is better to play single line vs multi line for the same bet.

for example: Say you have a $25 dollar bet limit.

Single line VP = 5$ denom, max $25. Highest possible win is a Royal($25,000), on the draw, which is approx 1 in 40,000 odds.

5Play, $1 denon= $25 max bet. Highest possible win is a Dealt Royal same $25,000 top prize, but has approx 1 in 650,000.

For me, I will take the better odds to win the same amount.

 

It depends on what you want. Since OP asked about variance, you hit it on the head. There's greater variance in the single line $5 game, because you have a bigger chance of hitting a bigger prize and a bigger chance also of hitting zero.

 

With all things equal, I do not see how there is any variance between single vs multi.

Assume the pay tables are equal and there are not any special side bets, multipliers, etc.

Each of these two scenarios seem the same to me:

A) Play 1 line at $.25 (done 1000 times would be $250 bet)

B) Play 5 lines at $.25 per line (done 200 times would be $250 bet)


Why would these be any different?
Both examples put $250 at risk.
Both examples have 1000 possible hands.

 

Because in multiline each hand isn't completely independent. You're playing with the same held cards on multiple hands.

 

Yep, and I have been looking a good chunk of the afternoon looking for any more info on how to actually calculate multi-line variance, but I think you just have to grind through all of the possibilities and there is no shortcuts.

Unfortunately the Wizard's page is one of the best pages on multi-hand video poker variance. But it's bit dated I think because of the "gimmick poker era". In a game like Super Times Pay, which I pointed out to OP is one of the best games PHo has for quarters or less, I am questioning if multiline STP play is even worse variance than standard multiline games because the multiplier is always given to all the hands that have the same dealt cards. So the multiplier is correlated with the hands as well, yes? Unfortunately every Video Poker calculator I have encountered just calculates variance for a single hand game.

Other than trying to code a VP calculator, I have no way to figure this out though. I will probably have to bother to ask the Wizard himself and/or his "VPGenius" webmaster, JB, for a better, more detailed explanation.

 

I appreciate all the insight!

 

The variance would be higher on multiline STP, whether that is worse or not depends on your preference. Simply put if you increase any payouts of a game in a nonlinear fashion you'll increase its volatility. As an extreme example if I doubled the payout on a royal on JoB it would increase the variance by 4x. But obviously you would play that game (it'd be +EV anyway). It's essentially the same as saying on every Nth hand the payout increases as it does in STP.

If you have the breakdown of the variance for both the dealt cards and the draw cards in any single line game you can easily compute the variance for a multiline version. Same with STP since the multiplier's effect on variance would already be baked into the single line numbers and the same multiplier is spread across all hands.

 

Right, but I don't know of any calculator that actually breaks down variance by deal and draw. I'm only aware of calculators that give the game's total variance. And I dunno if I have the effort in me to actually create a program for that...lol

And as a suggestion to grosx2, I probably wouldn't wager more on DDB STP than you typically do, the standard deviation of 1-line 9/5 DDB STP is 8.1865 betting units/hand, which is in line with slot machines of moderate variance. So if you like the swings of slot machines, this is a decent game. Without STP, the SD is 6.4936 betting units/hand.

If you like a little less swing then you would want to play 7/5 Bonus w/STP as it only has a standard deviation of 5.7675 betting units/hand (w/o STP 4.5556 betting units/hand) so bankroll swings will be much less. This is mainly due to Bonus Poker paying 2 for 1 on 2 pair. Two pair happens a lot and help keeps you a float. Conversely, you only get 1 for 1 for 2 pair in DDB, so you need to depend on quads more to help keep you in the game. And if you end up playing STP, hitting the multipliers and hitting hands while having them is obviously also very important to winning sessions.