cmlotito
cmlotito
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December 10th, 2021 at 3:47:11 AM permalink
There seems to be a major difference in using Tom Skis strategy master program vs Wizard's strategy maker for JoB Multi Strike.

I followed the recommendation of adding 6 to each pay out for level one on both programs. There is a major difference for 4 card flushes. Tom Ski's Video Poker Strategy Master lumps all 4 card flushes together. The Wizards strategy maker on the website splits up 4 card flushes. There are a few other differences on other levels but the 4 card flushes on all levels seem to be the biggest discrepancy.

I think Wizards' strategy of splitting up flushes makes more sense depending on number of high cards involved vs lumping them all together on Tom Ski's strategy master.

Thoughts?
Wizard's strategy maker https://wizardofodds.com/games/video-poker/strategy/a-1-b-74-c-1-d-0-d-7-d-8-d-9-d-10-d-12-d-15-d-31-d-56-d-806/
Tom Ski's Strategy https://wizardofodds.com/games/video-poker/tables/multi-strike/appendix/2/
Last edited by: cmlotito on Dec 10, 2021
100xOdds
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December 10th, 2021 at 6:39:18 PM permalink
Quote: cmlotito

There seems to be a major difference in using Tom Skis strategy master program vs Wizard's strategy maker for JoB Multi Strike.

I followed the recommendation of adding 6 to each pay out for level one on both programs. There is a major difference for 4 card flushes. Tom Ski's Video Poker Strategy Master lumps all 4 card flushes together. The Wizards strategy maker on the website splits up 4 card flushes. There are a few other differences on other levels but the 4 card flushes on all levels seem to be the biggest discrepancy.

I think Wizards' strategy of splitting up flushes makes more sense depending on number of high cards involved vs lumping them all together on Tom Ski's strategy master.

Thoughts?
Wizard's strategy maker https://wizardofodds.com/games/video-poker/strategy/a-1-b-74-c-1-d-0-d-7-d-8-d-9-d-10-d-12-d-15-d-31-d-56-d-806/
Tom Ski's Strategy https://wizardofodds.com/games/video-poker/tables/multi-strike/appendix/2/
link to original post

Welcome back!

You at Borgata?
How's Noir status treating you this year?
Think MGM will let you keep it for next year?
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
cmlotito
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December 11th, 2021 at 3:47:32 AM permalink
Quote: 100xOdds

Quote: cmlotito

There seems to be a major difference in using Tom Skis strategy master program vs Wizard's strategy maker for JoB Multi Strike.

I followed the recommendation of adding 6 to each pay out for level one on both programs. There is a major difference for 4 card flushes. Tom Ski's Video Poker Strategy Master lumps all 4 card flushes together. The Wizards strategy maker on the website splits up 4 card flushes. There are a few other differences on other levels but the 4 card flushes on all levels seem to be the biggest discrepancy.

I think Wizards' strategy of splitting up flushes makes more sense depending on number of high cards involved vs lumping them all together on Tom Ski's strategy master.

Thoughts?
Wizard's strategy maker https://wizardofodds.com/games/video-poker/strategy/a-1-b-74-c-1-d-0-d-7-d-8-d-9-d-10-d-12-d-15-d-31-d-56-d-806/
Tom Ski's Strategy https://wizardofodds.com/games/video-poker/tables/multi-strike/appendix/2/
link to original post

Welcome back!

You at Borgata?
How's Noir status treating you this year?
Think MGM will let you keep it for next year?
link to original post



National Harbor is basically dead to me. No decent games left. (I don't consider plain 9/6 DDB decent) Last thing I was playing was 9/5 DSTP JoB 98.95%. Continued my streak of non multiplied royals and called an end to it a couple months ago.

Noir at Borgata is head and shoulders above National Harbor. Many more places and shops to use comps at. Borgata actually has 24 hour places to eat vs National Harbor. Also has a wider variety of video poker to play. 9/6 JoB Multi Strike to play and 9/5 SDB to use free play on.

Comps and slot dollars earned (what they call free play) for the one trip I had in October in one gaming day was:


I played just $2 JoB Multi Strike the entire trip. This was all contained in one gaming day 6am to 5:59am.

I used the Wizards strategy generated from his strategy maker program with the major difference of 4 card flushes being split up vs Tom Ski's program that lumps them all together. Can anyone confirm which way is correct?

Wizard links to Tom Ski's program strategy yet contradicts it with his own strategy maker. Which is correct???
ThatDonGuy
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December 11th, 2021 at 9:57:10 AM permalink
Quote: cmlotito

There seems to be a major difference in using Tom Skis strategy master program vs Wizard's strategy maker for JoB Multi Strike.

I followed the recommendation of adding 6 to each pay out for level one on both programs. There is a major difference for 4 card flushes. Tom Ski's Video Poker Strategy Master lumps all 4 card flushes together. The Wizards strategy maker on the website splits up 4 card flushes. There are a few other differences on other levels but the 4 card flushes on all levels seem to be the biggest discrepancy.

I think Wizards' strategy of splitting up flushes makes more sense depending on number of high cards involved vs lumping them all together on Tom Ski's strategy master.

Thoughts?


I use 5.23 as the addition instead of 6, but I do think the Wizard is correct, at least with holding onto a high card if it is the unsuited card with 4/flush but not if it is part of the 4/flush itself.

"Where does 5.23 come from?"
First, play standard 9/6 JoB with payouts multipled by 8; the ER is 7.963512
For Level 3 without a free ride, play standard 9/6 with payouts multiplied by 4 and then 7.96 added to each one; the ER is 6.15234.
Multiply this by 93.6% (the probability of not getting a free ride on Level 3), add 6.4% x (7.96 + the standard ER when the payouts are multiplied by 4), and you get a true Level 3 ER of 6.523087.
For Level 3 without a free ride, play standard 9/6 with payouts multiplied by 4 and then 6.52 added to each one; the ER is 4.991379. Adding the "free ride ER" gets a true Level 2 ER of 5.23796.
GaryJKoehler
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December 12th, 2021 at 4:17:56 AM permalink
For the game 9-6 Jacks with Free Rides of 0.077, 0.070 and 0.064 giving an EV of 99.79% and variance of 20.90, using exact expected values (not a +6 approximation), here are some cases:

Level 1:
3-5-7-10 of Clubs with a 6 of Hearts: Hold the 4-Flush, EV = 2.2858.
3-5-7-10 of Clubs with a 10 of Hearts: Hold the Pair of 10s. EV = 2.5284.
3-5-7-10 of Clubs with a Jack of Hearts: Hold the Jack. EV = 2.4756.

Level 2:
3-5-7-10 of Clubs with a 6 of Hearts: Hold the 4-Flush, EV = 3.8129.
3-5-7-10 of Clubs with a 10 of Hearts: Hold the Pair of 10s. EV = 3.9192.
3-5-7-10 of Clubs with a Jack of Hearts: Hold the 4-Flush.

Level 3:
3-5-7-10 of Clubs with a 6 of Hearts: Hold the 4-Flush, EV = 6.1207.
3-5-7-10 of Clubs with a 10 of Hearts: Hold the 4-Flush.
3-5-7-10 of Clubs with a Jack of Hearts: Hold the 4-Flush.

It looks like 4-Flush holds depend on the Level and the 5th card.
cmlotito
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December 12th, 2021 at 7:28:24 AM permalink
Quote: GaryJKoehler

For the game 9-6 Jacks with Free Rides of 0.077, 0.070 and 0.064 giving an EV of 99.79% and variance of 20.90, using exact expected values (not a +6 approximation), here are some cases:

Level 1:
3-5-7-10 of Clubs with a 6 of Hearts: Hold the 4-Flush, EV = 2.2858.
3-5-7-10 of Clubs with a 10 of Hearts: Hold the Pair of 10s. EV = 2.5284.
3-5-7-10 of Clubs with a Jack of Hearts: Hold the Jack. EV = 2.4756.

Level 2:
3-5-7-10 of Clubs with a 6 of Hearts: Hold the 4-Flush, EV = 3.8129.
3-5-7-10 of Clubs with a 10 of Hearts: Hold the Pair of 10s. EV = 3.9192.
3-5-7-10 of Clubs with a Jack of Hearts: Hold the 4-Flush.

Level 3:
3-5-7-10 of Clubs with a 6 of Hearts: Hold the 4-Flush, EV = 6.1207.
3-5-7-10 of Clubs with a 10 of Hearts: Hold the 4-Flush.
3-5-7-10 of Clubs with a Jack of Hearts: Hold the 4-Flush.

It looks like 4-Flush holds depend on the Level and the 5th card.
link to original post



Looks like you agree with Wizard's strategy maker over Tom Ski's program.
100xOdds
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December 12th, 2021 at 8:38:28 AM permalink
Quote: GaryJKoehler

For the game 9-6 Jacks with Free Rides of 0.077, 0.070 and 0.064 giving an EV of 99.79% and variance of 20.90, using exact expected values (not a +6 approximation), here are some cases:

Level 1:
3-5-7-10 of Clubs with a 6 of Hearts: Hold the 4-Flush, EV = 2.2858.
3-5-7-10 of Clubs with a 10 of Hearts: Hold the Pair of 10s. EV = 2.5284.
3-5-7-10 of Clubs with a Jack of Hearts: Hold the Jack. EV = 2.4756.

Level 2:
3-5-7-10 of Clubs with a 6 of Hearts: Hold the 4-Flush, EV = 3.8129.
3-5-7-10 of Clubs with a 10 of Hearts: Hold the Pair of 10s. EV = 3.9192.
3-5-7-10 of Clubs with a Jack of Hearts: Hold the 4-Flush.

Level 3:
3-5-7-10 of Clubs with a 6 of Hearts: Hold the 4-Flush, EV = 6.1207.
3-5-7-10 of Clubs with a 10 of Hearts: Hold the 4-Flush.
3-5-7-10 of Clubs with a Jack of Hearts: Hold the 4-Flush.

It looks like 4-Flush holds depend on the Level and the 5th card.
link to original post


how did you get var = 20.9?
Wiz has this for var:
lvl 1 = 19.9, lvl 2 = 40.8, lvl 3 = 80.6, lvl 4 = 167.2
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
100xOdds
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December 12th, 2021 at 8:46:26 AM permalink
Quote: cmlotito



I played just $2 JoB Multi Strike the entire trip. This was all contained in one gaming day 6am to 5:59am.

1.7M tier credits?
Congrats on staying Noir!

and yeah, mgm national harbor sucks for vp (and slots)!
but i think they still have $5 9/7 db? (99.1%)
it's $35 coin-in per tier credit for that game.

anyway, at Borgata, what's the return on Multi-strike deuces wild?
And do you know how much coin-in for 1 tier credit at Borgata for Multi-strike?
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
ThatDonGuy
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December 12th, 2021 at 9:19:38 AM permalink
Quote: ThatDonGuy

"Where does 5.23 come from?"
First, play standard 9/6 JoB with payouts multipled by 8; the ER is 7.963512
For Level 3 without a free ride, play standard 9/6 with payouts multiplied by 4 and then 7.96 added to each one; the ER is 6.15234.
Multiply this by 93.6% (the probability of not getting a free ride on Level 3), add 6.4% x (7.96 + the standard ER when the payouts are multiplied by 4), and you get a true Level 3 ER of 6.523087.
For Level 3 without a free ride, play standard 9/6 with payouts multiplied by 4 and then 6.52 added to each one; the ER is 4.991379. Adding the "free ride ER" gets a true Level 2 ER of 5.23796.
link to original post


Hmmm...when I enter the numbers this morning, I get this:

Level 4 ER: 7.963512 (8 x 99.5439%)
Level 3 without Free Play ER: 7.634618
Level 3 overall ER: 7.910500
Level 2 without Free Play ER (using 7.91 as the Level 3 ER): 5.637264
Level 2 overall ER: 5.935717
Level 1 without Free Play ER (using 5.93 as the Level 2 ER): 3.743208
Level 1 ER: 3.98824 (99.706%)

The strategy differences for different 4/flush values is the same.
cmlotito
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100xOdds
December 12th, 2021 at 10:19:46 AM permalink
Quote: 100xOdds



anyway, at Borgata, what's the return on Multi-strike deuces wild?
And do you know how much coin-in for 1 tier credit at Borgata for Multi-strike?
link to original post



I may be going next weekend if I can get Sunday off from work. I was going to tag along with a guy I know from work and a friend of his. If I don't have to drive that is a huge win in my book. I won't be going all out at $2 level since the last time I went I got my ass handed to me. Have gone 5 times to Borgata this year. 4 wins and 1 loss. But the loss was most of what I won the previous 4 trips combined. Oh well. Still ahead for the year there. I'll stick to 50 cent with an occasional trip into the dollar range.

I have a friend who says he will only play dueces wild games next year so I have to scout out all the versions they have of it there. Multi Strike, Ultimate X, DSTP, Royal Hunt is all I can currently think of. It's 2022 next year so you can guess why he wants to do that.

My 1 trip in October generated these December offers:
I will be able to double dip the $600 offer in one trip. It cuts off at 6am then next offer kicks in at noon. Plus I earned $601 in bounce back slot dollars last trip. So that's $1801 in free play I get just for tagging along. Not too shabby.

I'll see if I can figure out coin in for 1 tier credit on Multi Strike and post it.
GaryJKoehler
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December 12th, 2021 at 10:25:24 AM permalink
Quote: 100xOdds

[
how did you get var = 20.9?
Wiz has this for var:
lvl 1 = 19.9, lvl 2 = 40.8, lvl 3 = 80.6, lvl 4 = 167.2
link to original post


Methodology is in an academic paper on:
https://www.playperfectllc.com/about

The EV and Variance are for Level 1. Where are you seeing the Wiz reporting 19.9 for the variance?
ChesterDog
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December 12th, 2021 at 12:31:19 PM permalink
Quote: 100xOdds

...
anyway, at Borgata, what's the return on Multi-strike deuces wild?...




Here's a photo of a quarters pay table taken on 11/27/21 at Borgata. The Wizard of Odds has 25/16/13/4/3/2 at 97.27% return.

The same machine has denominations of half dollars, dollars, and two dollars, but I only checked quarters.

100xOdds
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December 12th, 2021 at 2:13:35 PM permalink
Quote: GaryJKoehler

Quote: 100xOdds

[
how did you get var = 20.9?
Wiz has this for var:
lvl 1 = 19.9, lvl 2 = 40.8, lvl 3 = 80.6, lvl 4 = 167.2
link to original post


Methodology is in an academic paper on:
https://www.playperfectllc.com/about

The EV and Variance are for Level 1. Where are you seeing the Wiz reporting 19.9 for the variance?
link to original post

His VP analyzer:
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
100xOdds
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December 12th, 2021 at 2:18:00 PM permalink
Quote: ChesterDog

Quote: 100xOdds

...
anyway, at Borgata, what's the return on Multi-strike deuces wild?...

Here's a photo of a quarters pay table taken on 11/27/21 at Borgata. The Wizard of Odds has 25/16/13/4/3/2 at 97.27% return.

The same machine has denominations of half dollars, dollars, and two dollars, but I only checked quarters.


link to original post

wow.. that bad pay table is surprising since they offer 9/6 JoB multistrike at quarters.
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
GaryJKoehler
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December 13th, 2021 at 2:52:53 AM permalink
Quote: 100xOdds

Quote: GaryJKoehler

Quote: 100xOdds

[
how did you get var = 20.9?
Wiz has this for var:
lvl 1 = 19.9, lvl 2 = 40.8, lvl 3 = 80.6, lvl 4 = 167.2
link to original post


Methodology is in an academic paper on:
https://www.playperfectllc.com/about

The EV and Variance are for Level 1. Where are you seeing the Wiz reporting 19.9 for the variance?
link to original post

His VP analyzer:

link to original post


I'm guessing he's adding the expected value of the next level to his outcomes, doing so for the Free Ride and no Free Ride cases and then combining them. This gives the correct EVs but doesn't take into account the fact that when he adds the next level EVs, they have a variance too. They aren't fixed values. Taking such into account will increase the overall variance.

Perhaps the wiz can weigh-in.
Wizard
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December 13th, 2021 at 11:44:54 AM permalink
I've been asked to comment.

The formula for each row of the variance column is (win-ER)^2, where:

win = the gross win for that hand, measured as the ratio of money won to money bet. For example, for a royal it would be 800.
ER = expected return. In the case of 9/6 jacks, it is 0.9954...

If anyone thinks I am in error about the variance of multi-strike, please let me know, preferably with links.

Thank you.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
GaryJKoehler
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December 13th, 2021 at 12:41:21 PM permalink
Quote: Wizard

I've been asked to comment.

The formula for each row of the variance column is (win-ER)^2, where:

win = the gross win for that hand, measured as the ratio of money won to money bet. For example, for a royal it would be 800.
ER = expected return. In the case of 9/6 jacks, it is 0.9954...

If anyone thinks I am in error about the variance of multi-strike, please let me know, preferably with links.

Thank you.
link to original post


Can't argue with boiler-plate definitions. I see that the Wiz's calculator does give the stats for the entire set of outcomes, so his variance has to be correct. I'll check my code.
drrock
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December 13th, 2021 at 3:52:52 PM permalink
Quote: Wizard

I've been asked to comment.

The formula for each row of the variance column is (win-ER)^2, where:

win = the gross win for that hand, measured as the ratio of money won to money bet. For example, for a royal it would be 800.
ER = expected return. In the case of 9/6 jacks, it is 0.9954...

If anyone thinks I am in error about the variance of multi-strike, please let me know, preferably with links.

Thank you.
link to original post

Hey Wiz, thank you for the tool. I have used it a lot in the past. And I think I reverse engineered how the variance calculation works a while ago. It indeed is based on "(win-ER)^2". You probably meant to include the probability for that win in your explanation of the calculation, so each line would be (win sub i -ER)^2 * p sub i. And then you could sum over i to get the entire variance of the game. That is a standard way to calculate variance, for video poker or any other random variable, for any list of mutually exclusive and exhaustive numerical outcomes. And your tool works that way for the standard games.

I don't have any links to give you, but, in the case of the Multi-Strike calculations, that is not how that column is currently being calculated, at least for the Jacks 9-6 case. It is currently simply (win sub i )^2 * p sub i, unless the ER that is being referenced is zero. You can check out any one of the lines to see which of those two formulae allows you to replicate the value given by the tool. It is probably easiest to see that there is a problem by looking at one of the Win-zero lines where you will see that the variance component is also shown as zero. That can't happen for a win of zero unless the ER is zero or the probability of a win of zero happens to be zero itself.

But even if you put in an ER, I'm currently at a loss as to how you would make this calculation work in that format without putting in a lot more lines. Would you put in the ER for one of the four Multi-Strike lines? Or for the overall game? The issue here is that you have the individual wins for each line listed, but this is not a list of the mutually exclusive and exhaustive outcomes for the entire game.

You have the entire list for Level 1 (the sum of the probabilities in its lines are 1.0000), and parts of the entire list for each of the other Levels. In order for those lists to be complete you need to have another line that has a value of zero 49.0310% of the time for Level 2, 74.2869% of the time for Level 3, and 87.2574% of the time for Level 4. Those probabilities are to account for the percentage of time when you never reach that line.

But, unfortunately, even then you would simply have 4 mutually exclusive and exhaustive lists, one for each level instead of one overall list. In order to calculate the variance in the manner that your tool uses for the other games, you need a single list that delineates all the possible win totals and their corresponding probabilities.

I believe there are 1921 different possible values in that list. I am not advocating that you do that at all. One methodology would be just to blank out the column that currently shows variance to avoid confusion. I was able to determine the 1921 values by using the current output of your tool. If instead, you had given me the list of 1921 values, I would not have been able to go backwards and see the underlying results on each line that generated those 1921 different values.

Thanks for the great tools and blogs over the years. Sorry I wasn't able to meet up with you this year at the G2E. It would have been great to get together, but my girlfriend and I had a wonderful time both on our Vegas stay and driving to and fro.
Last edited by: drrock on Dec 13, 2021
drrock
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December 13th, 2021 at 4:39:43 PM permalink
Quote: GaryJKoehler

Quote: Wizard

I've been asked to comment.

The formula for each row of the variance column is (win-ER)^2, where:

win = the gross win for that hand, measured as the ratio of money won to money bet. For example, for a royal it would be 800.
ER = expected return. In the case of 9/6 jacks, it is 0.9954...

If anyone thinks I am in error about the variance of multi-strike, please let me know, preferably with links.

Thank you.
link to original post


Can't argue with boiler-plate definitions. I see that the Wiz's calculator does give the stats for the entire set of outcomes, so his variance has to be correct. I'll check my code.
link to original post

Hey Dr. Koehler, I've appreciated your posts, papers, and programs over the years. Until this column came out, I was unaware that you had decided to put the Multi-Strike game calculations in a paper. When I flipped to it, courtesy of your inclusion of the hyperlink, I was relieved to see that I was only a month or so out of date, since your paper looked to have a date of last month.

Some time ago I had used the Wizard's tools to calculate optimal strategy for each of the four levels and the resulting game (or in this case "level") statistics associated with those strategies for 9-6 MultiStrike Jacks or Better. Then I got a little ambitious with an Excel spreadsheet and calculated what I thought was a list of all the possible win totals, from 0 to the never-in-this-universe total of 4000 + 8000 + 16000 + 32000 = 60000 coins. As a sidenote, I have that max-value probability as 3.46954E-19, while the probability of being shutout on any drop of 20 coins is 0.511959918.

So, when I read your first 12/12/21 post, I wanted to check if my calculations squared with yours. The number that I got, back then is close but a little higher than what you listed: 20.9959*. When I checked your paper, I was surprised at the brevity of the section that explained variance, not seeing any covariance terms, and was troubled by the explanatory lines:

"Now, the variance on Level3 is influenced by the variance on Level 4. The influence is independent, since the outcomes on Level 4 do not depend on decisions of Level 3, so we can ignore co-variances."

For simplicity, if we just consider the random variable that is the sum of the Level 3 outcome plus the Level 4 outcome, for any Level 3 outcome other than zero, it is true that all the Level 4 outcome probabilities are the same. But if the Level 3 outcome happens to be zero, you can predict that the Level 4 outcome will also be zero more than 97% of the time. So, the random variable representing the Level 3 outcome is clearly not independent of the random variable representing the Level 4 outcome, so you cannot do a handwave and ignore the covariances entirely. They do appear to be fairly small but positive, though I have only tried to calculate one of them.

Certainly with Excel, I think it is simpler with less chance for calculation blunders to just calculate a mutually exclusive and exhaustive list of the totals than to calculate 6 covariances that you need, but I imagine with your programming skill either way would work fine. And with covariances, the formulae in your paper will get more "academic."

Best of luck.

*For anyone surprised that 20.9959 is not that much bigger than the variance associated with regular 9-6 Jacks (19.5147), it is helpful to remember that the units here in both cases are bets-squared. Since the MultiStrike bet is 20 coins instead of the standard 5-coin bet, we can show the two variances in a different light in units of coins-squared to be 487.8669 (19.5147 x 5^2) for standard Jacks vs. 8398.3535 (20.9959 x 20^2) for MultiStrike Jacks.
Last edited by: drrock on Dec 13, 2021
cmlotito
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December 14th, 2021 at 12:47:09 AM permalink
Getting back to my original question, Is Wizard's strategy maker the correct way of splitting up 4 card flushes vs Tom Ski's strategy maker that lumps them all together?

I think Wizard is correct I would just like a second or third opinion.

Thank you.
drrock
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December 14th, 2021 at 3:48:02 AM permalink
Quote: cmlotito

Getting back to my original question, Is Wizard's strategy maker the correct way of splitting up 4 card flushes vs Tom Ski's strategy maker that lumps them all together?

I think Wizard is correct I would just like a second or third opinion.

Thank you.
link to original post

Given the options you presented, I would prefer the strategy that you got from the Wizard's strategy maker. Both methods use approximations to calculate their final output, so calling either one of them "correct" will also be an approximation. But when choosing strategies, ease of use to the player using the strategy is clearly an important factor. For me, the more "correct" strategy would be similar if not exact to what That Don Guy has been indicating. Instead of adding 6, I added 5.9367 to each of the winning lines on Level 1, and put together a strategy from the Wizard's strategy maker that incorporated his entire list of Basic Strategy Exceptions. I don't recall whether I checked to see if adding more decimal points to that specific add-on (e.g., 5.93672 or 5.936717) would result in any additional strategy change.

TomSki's Video Poker Strategy Master calculated the EVs for one typical representation of each of the holds it considered. For some holds, it was a penalty free hold; for others, it was the hold with a specific combination of penalty cards. So, VPSM compared a typical representation of one hold vs. a typical representation of another hold. It was correct on most of its comparisons and as I recall always correct on at least one typical hand that contained the two holds.

The Wizard's Strategy Maker looks at the EV of each of the 134,459 unique hands and makes a determination of what is the max-EV hold on each of those hands. So, when comparing two holds against one another, some of those hands will have a higher EV with hold 1 than hold 2; while for a similar comparison (when at least one of hold 1 or hold 2 has a different penalty situation than in the first example), the EV for hold 2 can be greater. Putting together its Basic Strategy is a challenge when sometimes hold 1 is better while other times hold 2 is. And it is even more complicated when simultaneously considering 3 or even more holds that are bunched together. But that is where applying its Basic Strategy Exceptions enters the picture. And then it is generally a matter of taste whether you want to play a strategy that is more accurate but also more complicated or a strategy that is less accurate but also simpler to apply.

In the case of MultiStrike, where decisions made at Level 1 result in different probabilities of advancing to the higher levels, it is even more complicated to make comparisons between Basic and Computer Perfect Strategies. Using a Computer Perfect Strategy at each level will result in a Computer Perfect Strategy for the entire game.

But taking each of the 4 Computer Perfect Strategies and transforming them to 4 Basic Strategies for each of the 4 Levels may not result in the overall "best" set of Basic Strategies for the entire game. I wouldn't advise that level of calculation to get an approximate result when much less calculation would result in an exact result.

Best of luck no matter which set of strategies you eventually decide to employ.
GaryJKoehler
GaryJKoehler
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December 14th, 2021 at 7:55:57 AM permalink
Quote: drrock

When I checked your paper, I was surprised at the brevity of the section that explained variance, not seeing any covariance terms, and was troubled by the explanatory lines:...And with covariances, the formulae in your paper will get more "academic."


Wow! As usual, your clear-thinking and rigor have cut through the noise and resolved the issues. And, you caught an important “hand-wave” on my part. I always hated covariances and look for any excuse to ignore them! My bad. Interesting, as you surmised “they do appear to be fairly small but positive” leading to a variance of 20.9959 instead of my 20.8952 for 9-6 Jacks. I'll revise the paper once I get my code working.

Thanks for all you do for the community.
GaryJKoehler
GaryJKoehler
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December 14th, 2021 at 9:16:06 AM permalink
Quote: drrock

I believe there are 1921 different possible values in that list.


I just confirmed there are 1,921 unique win amounts for 9-6 Jacks.
GaryJKoehler
GaryJKoehler
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December 15th, 2021 at 9:17:44 AM permalink
Quote: GaryJKoehler

Quote: drrock

I believe there are 1921 different possible values in that list.


I just confirmed there are 1,921 unique win amounts for 9-6 Jacks.
link to original post


Also confirmed your three other values:

Probability of RSF on each line = 3.4695353719696e-19
Probability of a zero win = 0.51195991750753
Variance = 20.995883678538
drrock
drrock
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December 15th, 2021 at 10:34:32 AM permalink
Thumbs up! Quick work!
GaryJKoehler
GaryJKoehler
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December 15th, 2021 at 10:41:48 AM permalink
Revised paper is up too. Paper is on:

https://www.playperfectllc.com/about
3for3
3for3
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December 18th, 2021 at 8:09:41 AM permalink
Have you looked at Ultimate X Gold?
GaryJKoehler
GaryJKoehler
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December 18th, 2021 at 10:25:50 AM permalink
Actually, working on it. So, yes.
cmlotito
cmlotito
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December 19th, 2021 at 3:04:42 AM permalink
Quote: 100xOdds

Quote: cmlotito



I played just $2 JoB Multi Strike the entire trip. This was all contained in one gaming day 6am to 5:59am.

1.7M tier credits?
Congrats on staying Noir!

and yeah, mgm national harbor sucks for vp (and slots)!
but i think they still have $5 9/7 db? (99.1%)
it's $35 coin-in per tier credit for that game.

anyway, at Borgata, what's the return on Multi-strike deuces wild?
And do you know how much coin-in for 1 tier credit at Borgata for Multi-strike?
link to original post


Just did $77,140 coin in and earned 25,970 tier credits playing only multi strike in one day at Borgata.
Hunterhill
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December 19th, 2021 at 7:44:59 AM permalink
Cm is there anything good to spend your comps on in the gift shops at Borgata, are the prices 2 for 1 with comps?
The mountain is tall but grass grows on top of the mountain.
cmlotito
cmlotito
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December 19th, 2021 at 8:33:17 AM permalink
Quote: Hunterhill

Cm is there anything good to spend your comps on in the gift shops at Borgata, are the prices 2 for 1 with comps?
link to original post


They say its 2 for 1 but I don't think it is. I bought $160 in candy at gift shop for people at work and it deducted 160 comp dollars. It might be 2 for 1 at the high end shops but that crap doesn't interest me so I can't verify.
100xOdds
100xOdds 
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December 19th, 2021 at 11:02:46 AM permalink
Quote: cmlotito

Quote: 100xOdds

1.7M tier credits?
Congrats on staying Noir!

and yeah, mgm national harbor sucks for vp (and slots)!
but i think they still have $5 9/7 db? (99.1%)
it's $35 coin-in per tier credit for that game.

anyway, at Borgata, what's the return on Multi-strike deuces wild?
And do you know how much coin-in for 1 tier credit at Borgata for Multi-strike?
link to original post


Just did $77,140 coin in and earned 25,970 tier credits playing only multi strike in one day at Borgata.
link to original post

$3 coin-in per TC?!
wow!!!
F U MGM-NH!!
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
cmlotito
cmlotito
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December 19th, 2021 at 3:34:24 PM permalink
Quote: 100xOdds

Quote: cmlotito

Quote: 100xOdds

1.7M tier credits?
Congrats on staying Noir!

and yeah, mgm national harbor sucks for vp (and slots)!
but i think they still have $5 9/7 db? (99.1%)
it's $35 coin-in per tier credit for that game.

anyway, at Borgata, what's the return on Multi-strike deuces wild?
And do you know how much coin-in for 1 tier credit at Borgata for Multi-strike?
link to original post


Just did $77,140 coin in and earned 25,970 tier credits playing only multi strike in one day at Borgata.
link to original post

$3 coin-in per TC?!
wow!!!
F U MGM-NH!!
link to original post


Wait, I made a mistake. Disregard those numbers. I thought I had taken a before picture of my tier credits but there was some other action involved. I will get it right next time I go.
cmlotito
cmlotito
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December 22nd, 2021 at 4:11:43 PM permalink
Just made another trip to Borgata and can confirm that at Noir level I earned 4,711 tier credits by doing $16,400 coin in only playing Multi Strike.
100xOdds
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December 23rd, 2021 at 6:23:54 AM permalink
Quote: cmlotito

Just made another trip to Borgata and can confirm that at Noir level I earned 4,711 tier credits by doing $16,400 coin in only playing Multi Strike.
link to original post

$3.5 per tc.
Still ALOT better than MGM-NH's $35 per tc!

hm.. i think i was Gold (+20% tier credit) when I calc $35 per tc.
so noir is +40%.

too early for math but whatever the Gold equivalent rate is still MUCH better than MGM-NH!
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
cmlotito
cmlotito
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December 25th, 2021 at 9:43:46 AM permalink
Quote: 100xOdds

Quote: cmlotito

Just made another trip to Borgata and can confirm that at Noir level I earned 4,711 tier credits by doing $16,400 coin in only playing Multi Strike.
link to original post

$3.5 per tc.
Still ALOT better than MGM-NH's $35 per tc!

hm.. i think i was Gold (+20% tier credit) when I calc $35 per tc.
so noir is +40%.

too early for math but whatever the Gold equivalent rate is still MUCH better than MGM-NH!
link to original post


Going thru my records at National Harbor i once ran thru $48,140 playing triple play ddb in high limit and dstp at the bartop. I earned 5,680 tier credits. Not sure if they earn tier credits at same rate or not. Thats about $8.50 a tier credit. With no competition for National Harbor its not surprising the rate is awful.
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