Super Times Pay Bell Curve

[Voodoo111]

Hi all,

Reading through the recreational forum I came across a post by New2vp.

http://forum.videopoker.com/forum/forum ... p?TID=9482

On the first page, he lists a bell curve for expected win/loss for .25 cent JOB for 1000 hands. Really good stuff.

My wife and I typically play single line $1 9/6 JOB, or several different variations of 3 line .25 cent STP. To calculate for 1$ JOB in the same format was simple enough. Multiplied the numbers in the table by 4.

Calculating the math is way beyond me, but I'm interested in the same bell curve application for these games:

1000 hands of 3 line STP totaling $4.50 per spin. $4500 coin in total.

.25 cent 3 line 9/5 JOB STP
.25 cent 3 line 9/5 DDB STP
.25 cent 3 line 9/6 DDB STP

Again, this is way beyond my computation skill, but this would really help in understanding small sample expected W/L and help to understand the variance to an extent.

Any assistance would be greatly appreciated. Great forum here, lots of good info!!

[New2vp]

Hi all,

Reading through the recreational forum I came across a post by New2vp.

http://forum.videopoker.com/forum/forum ... p?TID=9482

On the first page, he lists a bell curve for expected win/loss for .25 cent JOB for 1000 hands. Really good stuff.

My wife and I typically play single line $1 9/6 JOB, or several different variations of 3 line .25 cent STP. To calculate for 1$ JOB in the same format was simple enough. Multiplied the numbers in the table by 4.

Calculating the math is way beyond me, but I'm interested in the same bell curve application for these games:

1000 hands of 3 line STP totaling $4.50 per spin. $4500 coin in total.

.25 cent 3 line 9/5 JOB STP
.25 cent 3 line 9/5 DDB STP
.25 cent 3 line 9/6 DDB STP

Again, this is way beyond my computation skill, but this would really help in understanding small sample expected W/L and help to understand the variance to an extent.

Any assistance would be greatly appreciated. Great forum here, lots of good info!!

Hey Voodoo,  the distribution that you referred to as a bell curve was if I recall 1000 hands of single line 9/6 Jacks of Better.  To do this requires what mathematicians call "convolving" the possible outcomes and their probabilities 1000 times.  With most Jacks or Better games that have the same payout for quads regardless of their rank, there are only 10 outcomes to "convolve."  We have the 9 payouts from a paying pair, two pairs, trips, on up to the royal flush and then one more outcome that is "no win" with 0 coins returned.When you go to Triple Play, now there are 10 x 10 x 10 = 1000 possible outcomes since theoretically each of the 3 lines could have any of the 10 outcomes that you see in single line.  For the calculations that you have in mind, it would not matter what order the outcomes appear, so that reduces down to 220 possible combinations.  For example, we don't need to account for any difference between an outcome that is [Quads on Line 1, Full House on Line 2, and Trips on Line 3] vs. an outcome that is [Full House on Line 1, Quads on Line 2, and Trips on Line 3].  I know I didn't explain how the answer is 220 but there is one more step anyway to pare these outcomes down to 114 in the case of 9/5 Jacks or Better.  The number ends up being lower than 220 because of examples that have equivalent payoffs for the sum of all 3 lines, like an outcome of [1 straight, 1 flush, and 1 no win] pays the same as an outcome of [1 full house and 2 no wins].  Both payments are 45 coins.If that were all, we would then need to convolve 114 outcomes through the 1000 hands, quite a bit more work without specialized software than doing this for only 10 outcomes.  But you also requested Super Times Pay which has 6 possible multipliers (2x, 3x, 4x, 5x, 8x, and 10x) plus the default no multiplier, which is essentially 1x.  So that means we now have a possible 7 x 114 = 798 possible outcomes.  These can also be pared down to consolidate those outcomes like 5 x 15 and 3 x 25, which both yield the same number.  But I think that is still 554 outcomes for 9/5 Jacks or Better, 993 possible outcomes for 9/5 DDB, and 970 for 9/6 DDB.All this is to say that this is a lot of calculating.  The software available at this website (VPFW) does most of the heavy lifting and actually works well for triple play, 5-play, and 10-play.  It also works with STP and MultiStrike combined with multiplay.  But it doesn't work for example with Double Super Times Pay or something like Quick Quads.  So if you are (or anyone else is) interested in looking at distributions or figuring out how much you need to be safe for a given amount of play, it may be worth your investment.Following is what I did for you based on the games that you chose.  Rather than try and show all the humps, bumps, and positions of the distributions (or series of exponentially decaying bell curves), I've taken a chance that showing you how much money you should take if you want to play 1000 hands and finish all 1000 hands before busting 95% of the time is the most helpful information for you..25 cent 3 line 9/5 JOB STP:  $576.50
.25 cent 3 line 9/5 DDB STP:  $932.75
.25 cent 3 line 9/6 DDB STP:  $889.00For my own memory, I gave the software a parameter that I was going to quit if at anytime I reached $1000 above my starting bankroll, but I don't think that could affect the answers by even as much as a $1.There really is no easy out-of-the-box formula to do these calculations.  I've heard of something called Dunbar's Risk Analyzer but I have never seen it in action, so I don't know if it works on STP.  I presume it will do calculations like this with minimal user intervention for the games that it does have. I had to do a lot of trial and error to get the numbers above with VPFW, so while it's not rocket science it does take some time to do anything like this.As I close, I'll suggest what many might see intuitively but at least some might not.  These numbers are not linear.  That is to say, if you wanted to see how much you would need to play 2000 hands instead of 1000 hands it would be a mistake to simply double the amount.  You would actually need a lot less than double.  If you wanted to see how much you would need to play 500 hands, it would be an even bigger mistake (if you were most concerned about running out of money too soon).  For 500 hands, you will need more than 1/2 the amounts suggested above.Below is an illustration of what I'm saying for the .25 cent 3 line 9/6 DDB STP game you asked about.  The amounts are what would be necessary to assure play through the end of the given number of hands at least 95% of the time:  500 hands  $   554.501000 hands  $   889.002000 hands  $1,407.753000 hands  $1,831.50So for 50% fewer hands than 1000, you will require 62% of the bankroll necessary for 1000 hands.  For 100% more hands than 1000, you only need 58% more bankroll.Hope this helps.  For more, you might want to invest in some software.  That would be much more efficient in getting you the answers that are most helpful to you.

[Tedlark]

Excellent work New.

[DaBurglar]

What are the discretionary High points and low points (losses) that the player is abiding by here.....this seems like an incredibly over worked analysis.    I have not heard the term "Convolve"  since Modern Econometrics back in 1988 working with differential equations, something FAR more complex than simple video poker "what ifs?"I mean if you want to go to this trouble that's your business.....but again, a central component of this whole discussion is something that differs and changes from person to person, i.e.  at what point do I want to quit when I am either winning or losing.    And this question is one that never ceases to come up in ANY serious VP thread.

[Voodoo111]

Thanks for the work New!

Those numbers are in line with my experiences. I have a good "feel" for when I am losing/winning more than the norm based on number of hands played. I do think I will purchase VPFW and run some simulations. I have run 40,000+ hand trials to get a small sample of expected W/L on this website, but a simulator will give me more long term data, as it pertains to the short term highs and lows.

Burglar >>

We typically spend about 20-30 days in Vegas a year. Last year we had around 700-800k coin in at mainly Boyd and Station casinos. Difficult to get exact numbers, as Boyd doesn't provide coin in numbers to my knowledge, just W/L statement. Station Casinos does give coin in numbers.

On a single trip last year I experienced the high end of the variance curve hitting a 10x, a 5x, and a 3x royal. The odds of hitting a 10x royal are pretty astronomical, let alone following it up with a 3x and a 5x.

Obviously, this is far from the norm and an unbelievable rush. We've been going to Vegas the last 20 years, but only in the last 3 years have we dedicated our trips to full time Video Poker.

9/6 DDB STP is difficult to find, particularly if you are averse to uprights. While the game does not have to be 100% payback for me to play, I do like to keep my threshold around 99.5%. Herein really lies the basis for my discussion. I'm looking for the differences of what can be expected in a single short term sitting, usually a sitting for us at a STP pay machine is 2500-3000 hands.

While it's easy to calculate expected return over 100,000+ hands, I'm more interested in the math for the short term variance.

In short, basically I'm trying to figure out what a normal day would be for my wife when she runs off to play a 9/5 DDB STP machine, while I'm stuck at the boring JoB machine.

(she doesn't care much about the math, she just likes to get spinners and hit the buttons!

Thanks again for the help.