Thoughts For Beginners

[asteroid]

Absolutely. I am just saying that just as we use our computers for very simple calculations such as opening up Excel just to get a square root when we could do it with logarithms or a hand calculator, so it will be with quantum computers where we will be swatting a fly with a sledgehammer - we don't need another significant figure or even to do a Fisher's Exact Test when the the sample size of a Chi-Square test converges on the exact answer (with 10000 data points), but when all we need to do is turn on the quantum computer, plug in the sample data and have the quantum processor perform billions of calculations simultaneously due to the superposition of quantum states and come up with an answer we will do so. I guess that you are implying that IGT uses numerical/empirical statistical and mathematical methods to come up with these games like Ultimate X and they don't have a quantum computer in the back room to formulate new games
[QUOTE=asteroid]
That's where qubits come in sir - I have faith in quantum computers . . .I'm sure the future of qubits is super "qu-ool."  It is not my field of expertise, but even if it becomes possible, it is generally not worth doing 10^100 times the work to gain a decimal place or two in hypothesis testing.  If you want to know whether someone is over 6 foot tall and you can measure their height with a yardstick as 6 foot 6, it really doesn't matter if you are off by the width of an atom or two.  No sarcasm intended as that is a fairly accurate analogy  to these statistical tests.  You just want to see whether a statistic is greater than a particular measure.  If the numbers are so close as to require 5 or 6 decimal place accuracy to discern which is larger, the tests are essentially inconclusive anyway as to whether one would reject a hypothesis of randomness.I can think of other video poker problems that would benefit from faster computing.  Calculating perfect strategy for all 352,716 possible states in 10-play TDB Ultimate X Bonus Streak or calculating the exact variance for Spin Poker are a couple that come to mind.Please be sure and keep us up to date on how the future of computing can benefit our play.  I know you will have to put up with a naysayer or two here since they already don't like the amount of math involved in advanced video poker play. [/QUOTE]

[Vman96]

Absolutely. I am just saying that just as we use our computers for very simple calculations such as opening up Excel just to get a square root when we could do it with logarithms or a hand calculator, so it will be with quantum computers where we will be swatting a fly with a sledgehammer - we don't need another significant figure or even to do a Fisher's Exact Test when the the sample size of a Chi-Square test converges on the exact answer (with 10000 data points), but when all we need to do is turn on the quantum computer, plug in the sample data and have the quantum processor perform billions of calculations simultaneously due to the superposition of quantum states and come up with an answer we will do so. I guess that you are implying that IGT uses numerical/empirical statistical and mathematical methods to come up with these games like Ultimate X and they don't have a quantum computer in the back room to formulate new games [QUOTE=New2vp]
[QUOTE=asteroid]
That's where qubits come in sir - I have faith in quantum computers . . .I'm sure the future of qubits is super "qu-ool."  It is not my field of expertise, but even if it becomes possible, it is generally not worth doing 10^100 times the work to gain a decimal place or two in hypothesis testing.  If you want to know whether someone is over 6 foot tall and you can measure their height with a yardstick as 6 foot 6, it really doesn't matter if you are off by the width of an atom or two.  No sarcasm intended as that is a fairly accurate analogy  to these statistical tests.  You just want to see whether a statistic is greater than a particular measure.  If the numbers are so close as to require 5 or 6 decimal place accuracy to discern which is larger, the tests are essentially inconclusive anyway as to whether one would reject a hypothesis of randomness.I can think of other video poker problems that would benefit from faster computing.  Calculating perfect strategy for all 352,716 possible states in 10-play TDB Ultimate X Bonus Streak or calculating the exact variance for Spin Poker are a couple that come to mind.Please be sure and keep us up to date on how the future of computing can benefit our play.  I know you will have to put up with a naysayer or two here since they already don't like the amount of math involved in advanced video poker play. [/QUOTE]
[/QUOTE]

As far as I know, IGT does as much as they can to analytically determine returns of slot and VP games. They did do it for the original Ultimate X. An analysis of analytically determining the return has been written by Gary J. Koehler, an Information Systems and Operations Management Professor at Florida that was interested in verifying IGTs original work. He occasionally posts at the "Wizard of Vegas" as well.

Ultimate X Return Analysis

And speaking of IGT, I'm pretty sure they threw my resume in the trash this past week.   

[New2vp]

I've seen Mr. Koehler's analysis of Ultimate X. The 10-play version has only around 108 states (for multiplier totals between 10 and 120, inclusively, with 119, 117, and 115 being impossible IIRC) and therefore 108 different sets of strategy. You may reread his paper to see how ungodly long it took for his analysis to run. There is a technique to calculate it a couple orders of magnitude quicker, though I have only tested the proof of concept with Excel for single line play rather than 10-play.

I was referencing the newer game Ultimate X BONUS STREAK, which has 352,716 possible states as compared to Ultimate X's 108. Some of Bonus Streak's states share a common strategy, buy it still has about 3 and a half orders of magnitude more complexity than Ultimate X.

I can see a way to have computed an upper bound for Bonus Streak's EV using the quicker method. I haven't seen Koehler's take on the newer game, but I believe his Ultimate X technique will be fairly impractical unless he comes up with some more "shortcuts."

Also, Ultimate X has a single strategy that JB and others have computed that gets within a few hundredths of a percent of optimal. That same technique misses optimal for Bonus Streak by over 1/2% on single line play, so it is more important practically to alter strategy depending on the combination of bonus steaks that you are faced with, including anticipating the probabilities of the streaks you will see on the next hand, the one after that, and so on.

[asteroid]

 

And speaking of IGT, I'm pretty sure they threw my resume in the trash this past week.    Indeed (I thought I did OK in the in person interview - answering several probability questions correctly but  . . .):Hello xxxxxxxxxxx,

Thank you for interviewing with IGT to discuss your qualifications on behalf of job 9903BR - Mathematician PA I.
We
were fortunate to have several qualified applicants apply for this
position. We interviewed each of the top applicants and after careful
consideration determined that the credentials of another applicant are a
better match to the needs of the department.
If you have continued interest in other opportunities available at IGT, please visit our website on www.IGT.com/careers and apply online should you feel your qualifications match an open position.
Please accept our best wishes and thank you for your interest in IGT.
Cordially,



The IGT Recruitment Team

[onemoretry]

If you play a 99.54%game like 9/6 JOB your long term results will always be dependent on whether you hit an average,below average, or higher than average number of royals. I can definitely attest to that. A major disappointment in my video poker play was my results over 11 years of play at Casino Rama, here in Ontario.

Most of the play was 3 or 5 line 9/6 JOB for 50c. There was some 10 line 25c denomination mixed in, as well. Overall, my total coinin was $8,468,775. The total number of hands was 4,004,868.

Statistically, I "should" have scored 99 royal flushes. But, I was 22 short, at 77, and my return for the 99.54% game was reduced to just a touch shy of 99%. My loss, on the game itself, was $86,241. Because of cashback and bonus cash my net loss was a lot less than that, but it was a loss, nevertheless. And, it was a positive game when those two items were factored in.

Had I not been unlucky, and had the "right" number of royals (99), my loss on the game would have been reduced to around $49000, and the game return increased to 99.42%, which is still a bit on the low side, but a lot better than the 99% number. And, I would have been a net winner on the game when cashback and bonus cash were included.

And, of course, had I been lucky and been 22 royals above average, my overall result over the 11 years would have been about plus $40,000.

The bottom line, in my opinion, is that you do not have to be particularly lucky to come close to a game's theoretical return over an extended amount of play - but, you can't be unlucky.

[billryan]

When playing multi line machines,shouldn't you only count the first line? For example, let's take a ten play machine. If on the drawer, one holds a pair, then it's impossible to draw a Royal on all ten hands.
On a single line machine, you can still draw a Royal on any of the next nine hands.
Not sure how to factor it in, but it has to effect hand totals. Just as drawing a Royal on the bottom line on a ten play will.

[alpax]

I can definitely attest to that. A major disappointment in my video poker play was my results over 11 years of play at Casino Rama, here in Ontario.

Most of the play was 3 or 5 line 9/6 JOB for 50c. There was some 10 line 25c denomination mixed in, as well. Overall, my total coinin was $8,468,775. The total number of hands was 4,004,868.

Statistically, I "should" have scored 99 royal flushes. But, I was 22 short, at 77, and my return for the 99.54% game was reduced to just a touch shy of 99%. My loss, on the game itself, was $86,241. Because of cashback and bonus cash my net loss was a lot less than that, but it was a loss, nevertheless. And, it was a positive game when those two items were factored in.

Had I not been unlucky, and had the "right" number of royals (99), my loss on the game would have been reduced to around $49000, and the game return increased to 99.42%, which is still a bit on the low side, but a lot better than the 99% number. And, I would have been a net winner on the game when cashback and bonus cash were included.

And, of course, had I been lucky and been 22 royals above average, my overall result over the 11 years would have been about plus $40,000.

The bottom line, in my opinion, is that you do not have to be particularly lucky to come close to a game's theoretical return over an extended amount of play - but, you can't be unlucky.



Personally amazed at the level of details you've kept on your playing sessions all these years.

I think it must mean you are over royaled at Seneca.

I know there are folks that will point out that there are no guarantees to win, but not me, I'll take those playing conditions all the time if it still existed even if I go down tens of thousands of dollars.

[alpax]

I was referencing the newer game Ultimate X BONUS STREAK, which has 352,716 possible states as compared to Ultimate X's 108. Some of Bonus Streak's states share a common strategy, buy it still has about 3 and a half orders of magnitude more complexity than Ultimate X.

I can see a way to have computed an upper bound for Bonus Streak's EV using the quicker method. I haven't seen Koehler's take on the newer game, but I believe his Ultimate X technique will be fairly impractical unless he comes up with some more "shortcuts."

Also, Ultimate X has a single strategy that JB and others have computed that gets within a few hundredths of a percent of optimal. That same technique misses optimal for Bonus Streak by over 1/2% on single line play, so it is more important practically to alter strategy depending on the combination of bonus steaks that you are faced with, including anticipating the probabilities of the streaks you will see on the next hand, the one after that, and so on.

Do you know where I can find the analysis of the Ultimate X Bonus Streak game? I was wondering how the strategy approach ended up to be.

[onemoretry]

When playing multi line machines,shouldn't you only count the first line? For example, let's take a ten play machine. If on the drawer, one holds a pair, then it's impossible to draw a Royal on all ten hands. Playing multiline is really playing the same dealt hand several times in a row. Granted, if that dealt hand does not provide a royal draw opportunity, none of the draws will produce a royal. Doesn't that happen in single line play as well - you go many, many consecutive hands with no royal draw opportunity?

The other side of that coin is being dealt three or four to the royal, and having multiple chances to hit. Over time, I think, this clumping of dealt hand types and draw opportunities resulting from multiline play will smooth out, and the overall opportunities per deal will be similar to single line. This is particularly so with respect to my results from in the neighbourhood of 750,000 individual deals. I do not, however, have a strong enough math and statistical background to back this opinion up.

In any event, at the end of a playing session, I take note of my total play, how much I won or lost, and royals, if any. I don't much care which hand they were on.

All of the foregoing was, I guess, a long way of replying: I don't think so.

I believe you often attend Bob Dancers classes. It might be interesting to put this question to him, and get his opinion.

[billryan]

I am going to ask him today. I'm not sure he will discuss it during class, but if not, perhaps by email.