Slot probabilities - From observation

Hey folks,

This is really a math/probability question, so apologies for asking here rather than dusting off some old math books.

I'm currently trying to analyze a slot machine. The end goal is to determine when the progressives might make it APable, somewhat similar to the ongoing thread about 88 fortunes.

The thing about this machine is it's a lot simpler. For the sake of argument, consider the following:
* Single pay line.
* 10 different pays.

In my feeble mind, this makes it a lot more realistic to "analyze". I don't care about the real layout and positions, as to me that just adds unnecessary detail, since outcome is ALWAYS either
* 1 of 10 different pays.
* no pay.

I currently have several thousand plays logged on this machine, and I'm curious at what point I can reasonably start deriving probabilities for the different pays.

For instance, let's say I have the following:

* 2000 spins
* 200 pay1 (smallest win)
* 150 pay2
* 40 pay3
* 5 pay 4
* 1 pay 6

I'm not under any illusion that the above means pay 6 will happen roughly 1 in 2000 spins, but how many samples/spins would I need to say with a reasonable certainty that pay 1 happens in roughly 1 in 10 spins? 1000? 100.000?

The problem in my mind can really be generalize as:

What's the confidence level and "buffer" for concluding that probability of an event happens in X / Y spins, given a sample size of Y (spins) and X (desired outcomes)?

As an example, if I did 1,000,000 spins, and had a specific outcome in 100.007 times, it would probably be reasonable to conclude that the event has ~10 chance of happening. Maybe it's really 11% or 9%, but I'm pretty sure it's neither 2% nor 30%.


EDIT: I think I found my answer here. (not sure why the link won't show up. if you start a reply by quoting you should see it.).

I think I get what you’re asking. First of all, 2000 spins is a big enough sample size according to some slot experts. Slot Kingz recommended observing 1000-2000 spins in one podcast of Gambling With an Edge (GWAE), and as little as 100-200 spins in another, to derive probabilities.

My Excel function skills are not up to par, but I believe if you tinker around with that or some other online tool (I believe you say you have found one?), you may be able to derive more valuable statistics like the confidence intervals, etc.

The way I personally approach questions like this is I find PAR Sheets for similar (e.g. volatility, paytable, etc) profile games to the one I’m analysing and I look at the confidence interval tables in them to extrapolate roughly how precise my data could be based on the number of spins I have observed. Of course, with any slot machine you don’t start seeing close convergence until around 100,000 spins or more, but depending on your risk tolerance, you should be able to glean some useful information from the sample you have collected. After all, if experts who do this for a living say it’s enough, it probably is.

Also, as a side note. It may be worth your while reaching out to Ross Bybee (Ross Slots) on Facebook. I know 88 Fortunes is a game he has collected thousands, if not ten’s of thousands, of spins worth of data for, including how many wilds need to land to get the pot to shut on different bet levels (on average - there’s no predetermined amount obviously).

I cannot guarantee he will share his data with you, or even answer you, but it might be worth a try. It would certainly save you a few dollars in collecting the data yourself.

Quote: Mukke

EDIT: I think I found my answer here. (not sure why the link won't show up. if you start a reply by quoting you should see it.).
link to original post

Blessing the link.
Links are disabled for members with a low post count, as an anti-spam measure.

I get that you want to simplify things but...

Modern 5 reel games have a minimum of 60 symbols per reel. This means that the possible number of unique outcomes is north of half a billion. With 2000 spins your sample isn't statistically significant. As mentioned, you need the reel compositions or a PAR sheet or both to be able to confidently state your chances of landing any given outcome. I had the same levels of curiosity (regarding Lighting/Dragon Cash games) and so created an AI bot that reads the reels from actual games and spits out the reel compositions. Once you have those, you have all of your answers. I'm not sure that you can get the same observationally.

Quote: p13man

I get that you want to simplify things but...

Modern 5 reel games have a minimum of 60 symbols per reel. This means that the possible number of unique outcomes is north of half a billion. With 2000 spins your sample isn't statistically significant. As mentioned, you need the reel compositions or a PAR sheet or both to be able to confidently state your chances of landing any given outcome. I had the same levels of curiosity (regarding Lighting/Dragon Cash games) and so created an AI bot that reads the reels from actual games and spits out the reel compositions. Once you have those, you have all of your answers. I'm not sure that you can get the same observationally.
link to original post

That sounds fascinating. Do you know what the odds of hitting any of the progressives are?

Quote: p13man

I get that you want to simplify things but...

Modern 5 reel games have a minimum of 60 symbols per reel. This means that the possible number of unique outcomes is north of half a billion. With 2000 spins your sample isn't statistically significant. As mentioned, you need the reel compositions or a PAR sheet or both to be able to confidently state your chances of landing any given outcome. I had the same levels of curiosity (regarding Lighting/Dragon Cash games) and so created an AI bot that reads the reels from actual games and spits out the reel compositions. Once you have those, you have all of your answers. I'm not sure that you can get the same observationally.
link to original post

I honestly think you are making it more complicated than it has to be.

I understand that this idea probably makes sense on multiline machines where there are tons of different combinations (win 5 cent from lines 23,24 and 29, 10 cents from lines 9, 42 and 43 and 200 cents from line 59). But for a single line basic machine with few outcomes, it doesn't really matter.

To show my point, imagine a slot machine that has 9 reels. Each real has numbers. Real 1-4 has the numbers *2,4,6,8,10", reel 5-8 has numbers *1,3,5,7,9". Finally, real 9 has numbers 1-10. And let's say the first 8 reels has each number twice, so all reels has exactly 10 stops.

This means there are quite a few unique outcomes, (10^9 though with some repeat combination).

Let's also say that the machine has 2 types of pay: An even total results in $1.99 win. An odd total results in no win (-$1).

I would argue you don't have to anaylyze/observe all plays, because realistically there are only 2 outcomes. You don't care what makes up the outcome (the actual reels) just the outcome. So observing on how many spins you won (even), you could quickly find out the probabilities of pay.

Now as a kicker, the machine I have in mind is actually in WA, where the rules are slightly different. The reel stops are not random, the outcome is (ish). The reels will just land on whatever is needed to give the pay the the outcome dictates. That makes looking at the reel composition even less relevant. However, I would argue my observation above would apply equally to Vegas style machines.

In case anyone else is curious about the viability of AP like this, some stats:

After 6000 fully tracked spins, my RTP % is 99.4%. Almost exactly half of my return is from progressives and half is from regular pays.

This is with me playing when the state is not necessarily fully ap-able, as so far I have opted for taking a slight hit to the EV in favor of getting more data.

Some conclusions so far:

* This machine is definately APable (if I played slightly more conservative, I would be +EV
* Including cash back and comps impact of additional play, the EV goes up
* This will likely not have enough +EV to pay for rent :)
* It's a good filler between other APs.
* Insight gained is useful for the high roller versions of this machine, where I can be more conservative, play less but have relatively significant EV, assuming I can deal with the variance.

And since there might have been some confusion: This is NOT about 88 fortunes. I've experimented a bit with 88 fortunes but honestly I don't think it's APable. The amount of return from progressives vs non-progressives is too low in my opinion to overcome the house edge.