Variance on multi-play JOB

[Mikeinri]

Can someone give me the variance numbers for the following 2 9/6 Jacks or Better games?1. nickel fifty-play ($12.50 a spin)2. 2 cent hundred-play ($10 a spin)I am, of course, looking for the game with the LOWER variance/risk of ruin.Assume I am cycling 100 thousand dollars.

[Eduardo]

Geez, on 100 grand bankroll with 9/6 JOB, I'd imagine the variance there is going to be almost insignificant if you play it right on nickels or 2 cents. It would take a lot of play before you "ruin" yourself on that one.  If you play it right.


 
Also is there any cash back on play? That would help tremendously, even if it's only half a  percent.
 
To answer your question between the two, I would think hundred play at the lower denomination would always be lower variance. But I'm really not sure how significant.

[New2vp]

The winner of the low variance contest is 50-play at nickels.To evaluate the variance for multi-play games, you need what is called the covariance for the game, which is rarely available but happens to be listed for a few games, including 9/6 Jacks or Better, on Jazbo's home page.  He lists the variance and covariance for 9/6 Jacks or Better as 19.510 and 1.966, respectively.  The variance is actually closer to 19.515.Assuming that his covariance calculation is correct and using the correct variance for single play 9/6 jacks, the variance for 50-play is 115.8487 bets squared (19.51468 + 49 x 1.966) and the variance for 100-play is 214.1487 bets squared (19.51468 + 99 x 1.966).  Since your bet sizes differ you need to multiply these by the bet size squared to get your answer.  You end up with a variance of 18,101 dollars squared on 50-play at $12.50 per play (multiplying by 156.25, which is 12.5 squared) vs. 21,415 dollars squared on 100-play at $10.00 per play (multiplying by 100, which is 10 squared).If you were super concerned about variance, you could play $5 single-line Jacks or Better ($25 per bet) and have lower variance than either of your listed options at 12,197 dollars squared.  Of course that might not be as much fun as watching all the hands unfold on multi-play!Your risk of ruin is 100% on both games unless you have some comps to overcome the house edge of 0.4561%.  Risk of ruin calculations end up under 100% only when you have an edge.  Even if you received enough cash back, as Eduardo suggests, to overcome the edge, the calculations here would be daunting.However, depending on your profit goal, you might have some reasonable chance of reaching it and quitting before losing your bankroll.  Again however, I am not certain of an easy way to calculate those odds for 50- or 100-play.  But with $100K at your disposal, you would get to play for a long time!

[Mikeinri]

The winner of the low variance contest is 50-play at nickels.To evaluate the variance for multi-play games, you need what is called the covariance for the game, which is rarely available but happens to be listed for a few games, including 9/6 Jacks or Better, on Jazbo's home page.  He lists the variance and covariance for 9/6 Jacks or Better as 19.510 and 1.966, respectively.  The variance is actually closer to 19.515.Assuming that his covariance calculation is correct and using the correct variance for single play 9/6 jacks, the variance for 50-play is 115.8487 bets squared (19.51468 + 49 x 1.966) and the variance for 100-play is 214.1487 bets squared (19.51468 + 99 x 1.966).  Since your bet sizes differ you need to multiply these by the bet size squared to get your answer.  You end up with a variance of 18,101 dollars squared on 50-play at $12.50 per play (multiplying by 156.25, which is 12.5 squared) vs. 21,415 dollars squared on 100-play at $10.00 per play (multiplying by 100, which is 10 squared).If you were super concerned about variance, you could play $5 single-line Jacks or Better ($25 per bet) and have lower variance than either of your listed options at 12,197 dollars squared.  Of course that might not be as much fun as watching all the hands unfold on multi-play!Your risk of ruin is 100% on both games unless you have some comps to overcome the house edge of 0.4561%.  Risk of ruin calculations end up under 100% only when you have an edge.  Even if you received enough cash back, as Eduardo suggests, to overcome the edge, the calculations here would be daunting.However, depending on your profit goal, you might have some reasonable chance of reaching it and quitting before losing your bankroll.  Again however, I am not certain of an easy way to calculate those odds for 50- or 100-play.  But with $100K at your disposal, you would get to play for a long time!
Oh, no.  I don't have 100 grand to blow! What I mean is 100 grand cycled through one time only.Within that finite universe  is the nickel 50-play still a lower variance and risk of ruin than the 2 cent 100 play?The play is in Reno-and with slot club and the free room and "goodies" promised by the host it is well over 100% for me.

[New2vp]

The variance for the 50-play nickel machine is the
same and still lower than the 100-play 2-cent machine.We must
have a communication gap when discussing "risk of ruin" since I understand that term to mean "the probability of losing one’s entire
starting
bankroll with infinite play."  If I modify that to mean "the
probability of losing one’s entire starting
bankroll while playing it through only once," we have essentially
a meaningless term, since it is virtually impossible to lose the entire
bet on each play.If you are playing $100,000 through one time
only, you will get 8000 deals with the 50-play game and 10,000 deals
with the 100-play game.  It is fairly hard to lose your entire
bet on even one deal at either 50-play or 100-play.  Your best chance of
that occurs when drawing one card to a 4-card inside straight with no high
cards, 6xx2-Txx6, and even then you will hit at least one hand on 50-play 99% of
the time, increasing to 99.99% of the time on 100-play.  (And if you
play your cards right with 9/6 Jacks or Better, you would never make
this play!  When tossing away all 5 low cards like T9765 with 4 suits
and the T5 suited, the odds are more than 1/2 million to one against
losing it all on 50-play and more than 281 billion to 1 against losing
it all on 100-play.  And you only get bad deals like that a little more
than 3% of the time.)So, the odds of losing the entire bankroll
while playing good strategy for 8,000 to 10,000 deals are much more than
astronomical.If by "risk of ruin" you mean the odds of losing some given portion of the original $100K, I think you can use variance to help with your evaluation.  The expected winnings from either machine are going to be $99,544.  If you were unlucky and had results 2 standard deviations below the mean, with the 50-play, you would win only $75,476, but you would be worse off with the 100-play machine at $70,276.  Of course, the offset is that the upside is lower on the 50-play machine.  Two standard deviations above the mean on the 50-play machine is $123,611 compared to $128,812 on the 100-play machine.  (You can't really use a normal bell-shaped curve here to evaluate exactly how often you will be within 2 standard deviations, but it will no doubt be a fair amount of the time.)NO MATTER WHAT YOU DO, IT SOUNDS LIKE YOU HAVE A GREAT SETUP IN RENO!  BEST OF LUCK!

[Eduardo]

So I was wrong, what else is new.

[New2vp]

Eduardo, I wouldn't say that.  I would certainly at least give you partial credit for saying,  "It would take a lot of play before you "ruin" yourself on that one.  If
you play it right."

 
and also questioning the existence of comps to make it a positive play.  Plus your answer was a lot quicker and more readable than mine.----------------------------------------------------------------------------------The intuition on understanding the considerably higher variance on 100-play comes about by first thinking of it as two 50-plays with the same dealt hand and comparing that to two different 50-plays, one with the same dealt hand as before and one with a different dealt hand.On the former you are "stuck" with that first deal.  If it's a good deal you will tend to get higher results than the latter; if it's bad you will tend to get lower results than the latter.  Either way, the latter with two different deals will be a smoother ride tending more towards an average result.
 

[Eduardo]

Plus your answer was a lot quicker and more readable than mine.

 
Yes, once again... "what else is new?"


 
I love your responses.

[videos00]

It seems intuitive to me that .02 100 play would have a lower dollar variance than .05 50 play.  -  only .10 rides on each individual draw instead of .25- a greater sample size gives you a better chance of reaching the expected result (99.54%)