Question about Multi-Line Games

[FloridaPhil]

I haven't played many multi-line machines, but I'm thinking about it.  If a J/B Royal supposedly happens on a single line machine about every 45,000 hands. Does playing a 3 line game count the same as three times the plays on a single line game?  In other words, does playing a multi-line machine increase your Royal chances by the number of lines?  I realize these are just averages.  As they say "Your results may not be the same"...

[Eduardo]

Yes*.
 
*For a more detailed response including comments on variance and other details that may actually make my answer incorrect, see the upcoming post by New2Vp or Shadowman.

[onemoretry]

In other words, does playing a multi-line machine increase your Royal chances by the number of lines? 

Over time, the average should still work out to around once every 40400 total hands or so (not 45000).  But, you will have played those hands, in all liklihood, a lot faster, as that represents about 13470 original deals.
 
And, don't forget that you will be playing for three times as much per deal, so when you do hit a royal, it will not pay off at 800 times your total bet (unless you're lucky enough to hit three at once).
 
I really like playing multiline - to me it's simply a lot more exciting.
 
The downside is that when it turns ugly, and you experience a lengthy period of poor quality deals - it can drain your credits (or bankroll) very, very fast.

[New2vp]

Yes*.
 
*For a more detailed response including comments on variance and other details that may actually make my answer incorrect, see the upcoming post by New2Vp or Shadowman.I really wanted to skip this post, but I can't disappoint Eduardo.  Intuition would say that he is right, but the 2nd sentence in my next paragraph also should be right by that same intuition.  When you consider both of these, you can see that one of these has to be wrong.You can expect to see fewer than 1/3 as many hands containing royals when you play triple play as you would when playing single line with the same strategy.  The TOTAL number of expected royals will be 3 times as many, but a very few of those hands will contain multiple royals, so for things to balance out, there are a few more hands with zero royals.In the following, I'll use 9/6 Jacks or Better, computer perfect strategy and show cycle lengths to 5 significant digits.Single line--Freq. of hands with at least one royal: 40,391Triple Play--Freq. of hands with at least one royal: 14,147(If we saw hands with royals 3 times as often with triple play, the frequency would be 13,463)     Freq. of hands with exactly one royal:          14,569     Freq. of hands with exactly two royals:   1,973,400     Freq. of hands with exactly three royals:   648,270The last number contains both dealt royals and the infrequent triple drawn royal, which is expected to occur about every 287,390,000 games.I've never had either double or triple royals with the same dealt hand in triple play.  Considering the rarity of multiple royals on triple play, I concede that we have to give Eduardo at least partial credit for his answer, especially considering both his brevity and his predictive skills.

[Eduardo]

All numbers aside, I think the most important thing is that your good will be better, and your bad will be worse. Think in extremes, like 100 play.
 
Say you get dealt 4 to a royal on 100 play. That's a lot of opportunities for that royal at once. You will probably hit one or two, maybe more. You will play single hand a loooooong time before you get dealt 4 to the royal 100 times, and each time is going to be hard to get that 5th card. In 100 play, the odds at a royal with that hand are great. It's similar on 3 or 10 play, just to a smaller degree.
 
Then of course you have to remember the poor hands, with nothing good at all. Multiply that by 3, 10 or 100 and it can hurt. It is more expensive to earn a good starting hand.
 
So you hope for a good starting hand much more than in single hand because it matters 100 times more.
 
When I played multi-hand recently, the biggest difference in whether I would last seemed to come on "average" hands where you have that chance at a full house or straight and instead of one shot, you have multiple chances to pick it up. The throw away hands were awful, but that dealt quad on 10 play... so so sweet. Let's face it, I would never have 10 quads in a few minutes playing single hand.
 
So it's a wild ride to some extent, but more opportunities to win when you do have some decent cards can make it fun. As long as you have the bankroll to make it work.
 
I am a small-time gambler so I only make it work because I set aside part of my bankroll for "high risk, high pay" games for fun, and use the remainder for "smarter" and more conservative play. I was lucky enough to get ahead early on this last trip which gave me the chance to get some real play in on these machines. Usually it is short lived and I go back to what I know.

[onemoretry]

[QUOTE=Eduardo]Yes*.
 
*For a more detailed response including comments on variance and other details that may actually make my answer incorrect, see the upcoming post by New2Vp or Shadowman. The TOTAL number of expected royals will be 3 times as many, but a very few of those hands will contain multiple royals, so for things to balance out, there are a few more hands with zero royals.
[/QUOTE]

To me, a hand is just that - one hand, i.e., 5 cards.
 
Playing multiline, each deal consists of one dealt hand, repeated several times.
 
I would agree with your statement if it read: "....but a very few of those deals will result in multiple royals".....

[New2vp]

I'm glad that you were able to figure out the gist.

[onemoretry]

All numbers aside, I think the most important thing is that your good will be better, and your bad will be worse. Think in extremes, like 100 play.
 

Here's an example of this from my most recent trip to Seneca Niagara.
 
Monday morning, I played 5 line, 50c ,8/5 bonus poker.  I loaded $125 in freeplay into the machine, and played for a little over 2 hours without having to go into my wallet.  I cashed out $850.  My coin-in was about $17500.
 
Tuesday morning, same player, same machine, same game, down $800 in about 35 minutes!  Coin-in was only about $4550, so my return for that truly ugly session was 82.4%.  If you're going to play multiline, you have to be prepared for sessions like this one.

[Eduardo]

Very good example.
 
I think we can all agree that the first session is a lot more fun.

[onemoretry]

 
I think we can all agree that the first session is a lot more fun.

It sure was.  I forgot to mention that there were no royals.  The session was just a lot of good results (straight flushes,quads, bonus quads, full houses, etc), and very few of those dreaded  0, 5, or 10  credit win streaks.
 
What made it even better was the fact that my wife, playing beside me, was enjoying a similar session.