About multi strike 9/6 JOB

Discuss proper hold strategies and "advantage play" and ask questions about how to improve your play.
catalina2021
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About multi strike 9/6 JOB

Post by catalina2021 »

I know the 9/6 jacks or better pays 99.79%. I have some questions about this game.

1. Assume no royal flush occurs on neither X4 nor X8 multipliers, what would be the return of this game?

2. Since you bet 20 credits per hand, so the average multiplier is slightly more than X4. But often you play only one hand out of 4 if you can’t move up. So, what is the average number of hands per game you actual play?

3. What is the variance of this game?

Thank you.

dinghy
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Post by dinghy »

catalina2021 wrote:
Sat Nov 06, 2021 4:31 pm
1. Assume no royal flush occurs on neither X4 nor X8 multipliers, what would be the return of this game?
According to Wizard of Odds video poker analyzer, the royal is worth roughly 0.5% on each level, so if you run dry on the top two levels, you'd drop off 1%, reducing the return to about 98.8%.
3. What is the variance of this game?
Analyzer says 20, 41, 81 and 167 on levels 1, 2, 3 and 4 respectively. Each level contributes approximately the same 25% EV to the 99.8% total, so you could maybe maybe not average the variances.

advantage playe
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Post by advantage playe »

Thanks for the very interesting data on this game !!

catalina2021
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Post by catalina2021 »

Ok so royal on X4 happens every 165520 main hands, and on X8 it’s like every 316972 main hands.

This is truly a 98.8% game.

Carcounter
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Post by Carcounter »

True story about defying the odds. When Borgata opened, I think in 2002, I started playing the 9/6 JOB multi strikes. In the first 18 months, I hit 3 top line 8k royals, and none on the bottom 3 lines. Since then, no top line royals, although I have seen other players hit them. What are those odds?

olds442jetaway
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Post by olds442jetaway »

I guess it depends on how many total hands you have played that made it up to the top row.

New2vp
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Post by New2vp »

Playing perfect max-EV Multi-Strike strategy, the odds of the first 3 royals being only on the top line are about 3110 to 1. Because the top line is only played about one-eighth of the time that the bottom line is played (actually closer to 12.74%), only 6.85% of the royal flushes are expected on the top line. The other probabilities are 13.12% for the 4x line, 27.05% for the 2x line, and 52.98% on the bottom line.

The odds could be considerably different if you were not playing perfect max-EV Multi-Strike strategy.

olds442jetaway
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Post by olds442jetaway »

Yes, there are a number of very tricky holds or discard decisions in this game. I am surprised myself until I really think about it.

advantage playe
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Post by advantage playe »

can anyone compute the variance of multi strike full pay job ? Maybe New2vp can since he is a silicon based life force , just kidding New2vp lol . I am not smart enough to compute it !!

New2vp
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Post by New2vp »

advantage playe wrote:
Fri Nov 19, 2021 7:59 am
can anyone compute the variance of multi strike full pay job ? Maybe New2vp can since he is a silicon based life force , just kidding New2vp lol . I am not smart enough to compute it !!
Hey AP, no silicon, just a hobbyist arguably devoting too much time to video poker. If this were any other base game, I may only venture to give a rough estimate of the variance, but I put together a spreadsheet for the variance of MS 9-6 JoB some time ago, so I'm happy to share.

I remember being enamored with this game (maybe 20 years ago?) when Bob Dancer suggested how to put strategies together more or less by hand using WinPoker adding 6, 4, and 2 coins to the 1x, 2x, and 4x non-free-pass level win amounts. Later, with other software that would accept non-integer amounts, I calculated that add-ons of 5.9367, 3.9560, and 1.9909 were a bit more precise to use for a max-EV strategy.

It takes some time to calculate variance using Excel and four instances of the Wizard of Odds Strategy Calculator. There may be other ways to calculate it, but the way I did it requires a listing of all the possible total wins (summing the wins on the four lines) along with their corresponding probabilities. If I didn't make any errors, I found 1921 possible outcomes. Only 185 of those possibilities have more than one chance in a million of occurring on any one bet. These 185 values are responsible for more than 99.99% of all amounts to be won (including zero coins) on a single bet.

Also, in specifying the variance, I think it is more instructive to make comparisons with respect to regular 9-6 JoB than just to state a number. You can probably find 19.5147 for the variance of regular 9-6 JoB. Lots of software and practitioners have computed this, so it may be a good place to start. For MS 9-6 JoB, my calculation of variance is only 20.9959. Hmmm ... when thinking about the relative bankroll swings between the two games, it may seem that such a number is not nearly large enough, but let's examine the units involved. In each case, the units are the somewhat cryptic "squared bets." If we want to have a better understanding, we may want to factor in the difference in bet size, 5 coins vs. 20 coins. But since we are dealing with "squared" units, the comparison is actually between 25 squared coins and 400 squared coins.

Regular JoB variance in terms of "squared coins" is 5^2 x 19.5147 = 487.8669 squared coins. This can be contrasted with MS JoB variance of 20^2 x 20.9959 = 8398.3535 squared coins, more than 17 times bigger. I think squared units are a bit difficult for most intuitions to grasp, so I would suggest using standard deviations in coins to compare relative volatility between two games because the units for standard deviations are just plain old "coins." Doing that (by taking the square root of the previous numbers), you will get 22.0877 coins for regular 9-6 JoB and 91.6425 for MS. That comparative ratio is 4.15, which is just a little more than the ratio of the bet sizes, 5 coins to 20.

Hope this makes your day better ... best of luck.

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