Optimum # of multi-plays?

[Julius Caesar]

I'm new to this forum (signed up today) and exclusively a DW player.I'm curious about the peculiar way that video poker machines handle multiple game playing.  The way I have observed it is that a single hand is dealt then replicated to all the multiple play hands.  Each hand is then given its own copy of the remaining 47 card deck for the draw.I know that everything is supposed to even out in the end but, while playing over a period of time, I have casually observed that ten multiple plays provide a better overall return than either a single play or, a great number of plays (say, 50 or 100).  What I suspect is that there might be a bell curve lurking here. Has anyone investigated this?  Has anyone written a model to test it?  I'm a retired programmer and surely someone has already done some ground-breaking workThanks!  J. C. 

[rascal]

It is an interesting question. I have long wondered about the obvious modification necessary to the RNG process when you duplicate the initial hand yet then shift into individual, or singular, draws from supposedly isolated decks.
 
In general, my own casual observation is that there is a lesser overall return proprotionate to the number of hands compared to a single play, but I always attributed this to the sometimes lesser paytables on a multiple play machine.

[shadowman]

The return of all multi-play games is exactly the same as single line. The variance is a little higher since dealt hands have a bigger short term influence.
 
The RNG situation could be handled many ways. Each separate deck could be handled by having a different seed. The RNG would loop on all the seeds while waiting instead of just one.

[Minn. Fatz]

The return of all multi-play games is exactly the same as single line. The variance is a little higher since dealt hands have a bigger short term influence.
 
Another way to try and understand this is that the actual return of a given dealt/initial hand in a multi-play game trends closer to its theoretical long-term return as the number of lines played increases.
 
In fact, if the number of lines were the same as (or some multiple of) the number of possible draws, and each line resulted in a different possible final hand (or some multiple), the actual return of any initial hand would be identical to the theoretical long-term return. Same difference if "infinite" lines are played.
 
So the actual return on that 4-card flush draw is going to be more consistent at 100-play than at Triple Play. The rub is that if you don't get dealt enough hands with good expected values at 100-play you are a lot more likely to run through your roll more quickly than at Triple or single play.
 
I think it's been stated somewhere here that the return on n-line Spin Poker is identical to the return on n-line multi-play; I haven't seen that proved mathematically yet but that seems to be the case, though I'd guess the SP variance would be even higher than multi-play.

[njmike37]

The odds are exactly the same no matter how many hands that you are playing at one time, but the more hands you are playing, the higher the variance.  As others have stated, the multi-hand games are highly dependant on the deal in the short term, so if you go through a stretch of hands where you are getting very bad deals, you can go through a lot of money very quickly.  However, if you do happen to get a great deal, such as 4 to a royal, trips or quads, it is very nice having more than 1 shot at hitting a monster hand.
For me personally, I compared 3-hand, 5-hand, and 10-hand play with my sessions, and I tend to last longer with 5-hand.  3-hand play just doesn't have very much draw power compared to the others.  10-hand play is way too dependant on the deal for me, so I try to stay away from it unless I am in a hurry (see my post in Video Poker stories for my hit on 10-play.)  5-hand play gives me a decent number of hands for my bankroll, and good drawing power when I do get dealt those possible monster hands.  
Just a sidenote, I never play 50-play or 100-play, as I have never done really well on those games.  You go through money so quickly unless you get a good deal, and even if you do happen to catch a decent hand from a crappy deal, such as the following scenario in 100-play.. you get dealt a pair of 5's and catch 10 trips, 10 2-pairs, 1 full house, and 1 quad.. you are still behind in 100-play since you are betting 500 credits for max bet.  I don't like that idea..
 
Mike

[Julius Caesar]

I think it's been stated somewhere here that the return on n-line Spin Poker is identical to the return on n-line multi-play; I haven't seen that proved mathematically yet but that seems to be the case, though I'd guess the SP variance would be even higher than multi-play.Glad you mentioned Spin Poker; it is another peculiar departure from the norm!In the normal single play world, each hand is represented by a deal and a draw.  However, in Multi-play and Spin Poker multiple hands are based on just one deal.  Spin Poker introduces yet another aberration by basing up to nine hands on a single deal and just three draws!Regardless of the purity of the RNG and it's methodical re-seeding, bias has to be introduced when you reduce the number of cards in your population.  Consider this:Nine single plays use 45-90 randomly selected cards.Nine multi-plays use 5-50 randomly selected cards.Nine Spin Poker plays use 5-15 randomly selected cards.To what degree does this reduction of randomness affect the outcome?  In my experience, DW Spin Poker and multi-play are money makers while single plays are losers.  I'm hoping that someone out there has written a model and might share it or portions of it.

[shadowman]

I think your bias only effects short term results and is the basis for the higher variance. Over the long term it has little effect. In games like VP being "more random" is not important.
 
My own personal results have been poor at multi-hand games and good at single line games. For example, at 3-play deuces this year I'm averaging 4 deuces once every 11,000 hands. For 5-play I've had exactly ZERO royals over 150K hands.

[Minn. Fatz]

Nine single plays use 45-90 randomly selected cards.
Nine multi-plays use 5-50 randomly selected cards.
Nine Spin Poker plays use 5-15 randomly selected cards.

To what degree does this reduction of randomness affect the outcome? 
 
Ave Caesar!
 
My working hypothesis is that even though Spin Poker (SP) uses fewer cards, so you'd expect to hit fewer draws, when you do hit those draws they pay off more. For instance, a one-card draw, say to a flush, in SP will hit around 1/3 as often as a "straight" 9-line game but will pay off, on average, 3 times as much. So it seems to be a wash as far as expected value is concerned, but I'd be surprised if it didn't increase variance.

[njmike37]

Minn. Fatz,
 
Very true.  If you happen to get dealt 4 cards to a jackpot in Spin Poker, it is impossible to only get paid for 1 line if you connect.  If you happen to get lucky enough to get dealt 4 to a jackpot and you need the middle card to complete it, connect on the middle row on the draw, you get it 5 times.
 
Mike

[Julius Caesar]

Some interesting new discoveries!If you have Win Poker or Video Poker For Winners, you already have a modeling/simulating program that will compare video poker game payouts and can help you gather data on variance and bias too.I ran tests the last two days on single and multi-play draw poker games, ranging from 10,000 to 16,000 hands at a time and both programs performed very closely to the payout tables I had loaded.  Shadowman and Minn. Fats were on the money about this.  Win Poker is the fastest running program by a mile but, VPW additionally reports on Spin Poker and other variants.If anyone is interested, I will publish some instructions for running your own simulations.  This is undocumented in VPW and barely mentioned in Win Poker.  Maybe the author(s) will add some help topics later.PS: After testing, I'm just going to walk by the Spin Poker machine and spend the day at a multi-play!