What Would It Take???

[Frank Kneeland]

Extra FeatureIn the strategy dependent section of the utility we'll be recording the occurrence of straights and higher and the total number of hands played. With this data it is very simple to add a feature that tells you how you would have done if you played a machine with a slightly different pay-table, if the strategies are close enough. In other words, it's a way to track the daily cost of how much a lesser or greater pay  on the Full-House or Flush would cost or save you. It will be an optional feature. ~FK

[moneyla]

Frank, I'm sorry but I totally missed the entire point you were making.  In fact, if I were shooting a rifle I would have missed the broad side of the barn, so to speak.   I thought you were coming up with something that everyone could use to compile results so we could determine if machines are random, either individually or as a group. So now I am completely lost.  What the heck are you coming up with??

[Frank Kneeland]

Frank, I'm sorry but I totally missed the entire point you were making.  In fact, if I were shooting a rifle I would have missed the broad side of the barn, so to speak.   I thought you were coming up with something that everyone could use to compile results so we could determine if machines are random, either individually or as a group. So now I am completely lost.  What the heck are you coming up with??I making something for people to use themselves for themselves to test whatever theory they'd like to test. Some people are currently making conclusions on both sides of the discussion without the benefit of any first hand information or use of the math specifically designed for the task, either because they don't know it, or it's too much work to implement. I'm trying to save them some steps and make it more accessible to all.So the answer is, it will be for individual use.~FK

[moneyla]

OK Frank.  Well, speaking as individual player, my concern is about the 1/47 draw for a royal.  That hand comes rarely enough and can be idenfitified easily enough that I can easily keep track of how many times I hit a royal with a 1/47 draw. The reality is I have kept track and I don't hit royals 1/47 times when I have a 1 card draw.  In fact I have a miserable record of hitting royals when it was a one card draw.  But most of my royals were hit on two card draws, and twice I was dealt a royal, and once on a five card redraw. So since the royals are not hitting 1/47 times when I have a one card draw does that mean the game is "off" or not random?  Of course it doesn't mean that. So again, what is the point of this exercise?

[New2vp]

I don't know if Frank's software will come up with exactly the same number, but in order to test whether the probability of hitting a royal flush when holding 4 to the royal is less than 1/47, you can employ the following test.Ignoring past results, start now.  If you go 215 straight 1-card draws, holding 4 to the royal, with no royal, you can conclude that the probability is less than 1/47.  If this is your test and you do get those results, you still have an 0.98% chance that your conclusion would be wrong, that the probability was indeed 1/47, and you just had an unlucky streak.The idea here is to give guidance to just how many trials are necessary to reach a conclusion.  Someone else might come up with the same conclusion after 140 straight draws with no royal, but in making that conclusion, they would have a 4.92% chance of making an error, because there is nearly a 5% chance of seeing a streak that long simply by chance when the probability in fact is exactly 1/47.Someone making the conclusion after a streak of only 94 (2 cycles) might be right, but they would have a 13.24% of actually coming up with an incorrect conclusion.  And of course, you might have actually hit some royals but had many more draws such that you feel you have hit less than "your share."The idea is to give guidance as to just what type of data is needed to form statistically significant conclusions.

[moneyla]

Aha !!!  Thanks New2vp... now Im getting more of an understanding. But this looks like ti will be a life long project for me if I wanted to study my one card royal flush draws.

[Frank Kneeland]

Aha !!!  Thanks New2vp... now Im getting more of an understanding. But this looks like ti will be a life long project for me if I wanted to study my one card royal flush draws.Because the Royal is a rare hand the corresponding number of trials it takes to determine the frequency from results is great. If that's your particular concern then you have a long road ahead of you. One can test for more common hands and individual card occurrence in a very reasonable number of hands that's doable in perhaps a week.The utility will have a track for 1 card draws to the RF.~FK

[Tomcat1569]

OK Frank.  Well, speaking as individual player, my concern is about the 1/47 draw for a royal.  That hand comes rarely enough and can be idenfitified easily enough that I can easily keep track of how many times I hit a royal with a 1/47 draw. The reality is I have kept track and I don't hit royals 1/47 times when I have a 1 card draw.  In fact I have a miserable record of hitting royals when it was a one card draw.  But most of my royals were hit on two card draws, and twice I was dealt a royal, and once on a five card redraw. So since the royals are not hitting 1/47 times when I have a one card draw does that mean the game is "off" or not random?  Of course it doesn't mean that. So again, what is the point of this exercise?
 From personal experience, I agree that most of my royals have occurred on more than one-card draws. For example, my last three royals have been 3, 2 and 2-card draws. I can't remember the last time I hit a one-card draw, in fact, although I know there have been a few instances. Just the other day I was dealt four to a royal on a triple-play BP machine at Bally's AC and whiffed again. A few days earlier I got dealt two such hands at Parx and missed those, too. So my guesstimate is also that the occurrence of successful one-card royal draws for me is below average. For whatever reason, I seem to be dealt four to a royal an above-average amount, so it would not be hard to assemble a statistically significant sampe size in a relatively short time frame. That being said, watch me hit a 4-to-royal dry spell!

[Frank Kneeland]

From personal experience, I agree that most of my royals have occurred on more than one-card draws. For example, my last three royals have been 3, 2 and 2-card draws. I can't remember the last time I hit a one-card draw, in fact, although I know there have been a few instances. Just the other day I was dealt four to a royal on a triple-play BP machine at Bally's AC and whiffed again. A few days earlier I got dealt two such hands at Parx and missed those, too. So my guesstimate is also that the occurrence of successful one-card royal draws for me is below average. For whatever reason, I seem to be dealt four to a royal an above-average amount, so it would not be hard to assemble a statistically significant sample size in a relatively short time frame. That being said, watch me hit a 4-to-royal dry spell!That's interesting. And you'll be able to use the utility to test forward from this point on to check if anything is amiss. Here's why you can't use your preexisting data.Tests like Chi Squared are designed to determine how unlikely a particular run is, but not after the fact. If let's say getting as few Royals on 1 card draws as you did is a once in 1000 occurrence, then we'd expect 1 in a thousand people to have results just like yours...and we'd expect the other 999 people to be silent. Unless all the people playing VP everywhere, even the ones not reading this post and not using the test chime in (impossible) with their results, we have no way of knowing the base rate information. This is known as base rate neglect, and it's very common.You can't wait until something unlikely has already happened and then see how unlikely it was, because after the fact it's not unlikely, it's guaranteed (it already happened).Imagine you created a survey with the purpose of seeing how unlikely it was to be struck by lighting and made it voluntary...and after putting it out in the community the only people that were interested enough to use your survey were those that had been struck or knew someone that had. If you used their prexisting data you might come up with being hit by lighting as a near guarantee. It would be fine to use them in your study, but only if you tracked if they get hit from the time they take your survey forward, especially if having been hit is what got them in the door.~FK

[moneyla]

Based on what happened with American Coin and its fraud, if a company is going to rig machines to not be random they are not going to mess with common hands.  They are going to rig the big winners, which is why I am most concerned with the 1/47 royal draws.  American Coin rigged the royals when all five coins were played, and it made sense that they did rig just that hand to boost their profits.  It's unlikely anyone would rig a game for lesser more common hands that would be more easily detected because they come up more times.  Im not really concerned with fifth card flipovers on stragiths or flushes or even full houses -- as important as those hands are to being a winner.  But show me that royals are rigged and I will be very interested.