# RTP, Variance and sample sizes explained

#### Rusty

##### Banned User - repetitive flaming
This is a continuation from the ChuChu titan threa but I did not want to derail that so I have opened a new thread.
I think this may help people better understand how slots work and if they are getting a fair game.

The portion of RTP represented by RJ is about 1.5% according to Dogboy.

So, a slot with a RJ attached will pay out 1.5% less in reel/bonus wins than one without a RJ.

224k spins is a big number, but the actual combinations possible on the slots would have to be known - it may be in the millions so the 224k might only represent a fraction of the 'cycle'. Of course, playing different slots complicates things even more. However, Chu is right in saying that player should be closer to the RTP than someone with half that number of spins.

Takethemoney is also right when they say that different players will experience different RTPs over the same number of spins......and here comes that variance thing again lol.

As I said, its not just the RTP that one should consider when choosing a slot - in fact, its not the most important at all.

Chu - hopefully some will learn about how to present an argument without sounding like a lunatic from that thread, but I wouldnt hold your breath.

The actual combinations on real series slots are many millions.
Even a slot with 30 symbols flat on each reel will have over 24 million combinations.
But this is tempered greatly by the fact that players play more than 1 line and that winning combinations are repeated many times within this figure.

So assume a player plays 10 lines and not 1 - now we cycle through total combinations in 2.4 million spins not 24 million.

Consider then that the bulk of the combinations from these spins is made up from repeating symbol combos* that give small returns of 2 and 3 of a kind which barely return your bet (I would guestimate that the most common win combination would be repeated a few hundred thousand times and we see the figure is not so daunting when considering variance and RTP.

So I would expect samples of 220K to be very close to the average RTP of the reel series slots played. (add on 1.5% for RJ)
Of course you would take out any outliers from the data to give a truer picture.

Consider that a player plays 250K spins flat betting \$1 playing 20 lines.
They would actually have played through the equivalent of 5 million spins playing a single line.
Assume the 91% return and they would lose \$22,500.
Now as they have played 5c a line lets throw in a theoretical jackpot win of 5000 times bet into the data and see what happens.
5000*0.05c = \$250 how does that affect our RTP?
Well now our RTP has gone up from 91% to erm 91.1%
It didn't even move the needle!

So let's say they get lucky and hit 10 jackpots in 10 spins
so an extra \$2,500 returned!
What happens after this impossible run of luck?
We push our RTP up to 92%

So you can see the above clearly demonstrates that a Casinos protestations that you were unlucky and such numbers are too small for clear picture are bunk.

*Explanation (this assumes no wilds)
say a slot has a symbol repeated 5 times on each reel, to know how many times 3 of a kind of this symbol will occur in a complete cycle of spins (this how we back engineer variance and theoretical RTP) we need to work out our combinations for 3 of a kind of this symbol which are;

5/30, 5/30, 5/30, 25/30, 30/30 = 93,750 instances in 24,300,000
The reason the 4th number is 25/30 is because we are excluding 4 of a kind so we take all the combos where the 4th reel is not our symbol.
The 5th reel 30/30 because any symbol is valid once we know the 4th reel breaks our sequence.

If I have made any mistakes in the above which is always possible in posts such as this then apologies and please correct.

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#### AussieDave

##### Banned User
Hi All,

Having experienced endless numbers of losing streaks and winning streaks too, all made up from online slots play since 97, I've played literally millions of spins.

From my understanding (correct me if I'm wrong) the true RTP is calculated by the money put through the slot against the money won (paid out by the slot).

There has been a lot of talk about MGS and other casino slots not paying what they used to before the UIGEA.

My reasoning for this now is:
• MGS, RTG..ect..ect have many more slots
• With so many extra slots, the amount of money being played through each slot is less

Hypothetically if 500 players were play ABC slot before the UIGEA and 100 players were playing that same slot after the UIGEA came into affect, the number of cold slot sessions would increase because of less players playing ABC slot.

Hence there would be more losers and less winners.

Someone commented (think it was VWM), you need a BIG bankroll these days to ride out the cold slot streaks.

That would certainly seem feasible given my above points.

I've seen a lot of chatter about RTP, variance...ect..ect but I haven't seen peeps comment on what I've outlined above.

Cheers

Dave

#### Rusty

##### Banned User - repetitive flaming
Hi Aussie

It depends on what your starting premise is.

If you feel slots have algorithms that control RTP and/or variance then there may be some truth to what you express above unless the controls are platform wide.
There is only such a thing as "due to pay" if the slot is designed specifically to take in X and payout Y

If however the slots were not weighted and had no controls then the above would certainly not matter as there is no such thing in this instance as a streak before it has happened.
In other words you would be as likely to win on spin 1 as spin 1 million so assuming all games were equal random and fair you would still get the expected RTP playing each game consecutively only 1 spin at a time.

Therefore if it could be shown that a players RTP was lower than previously it would be a fair conclusion that the RTP of the slot was lower whichever way we feel about how the slots operate.

#### zap987

##### Meister Member
PABnononaccred2
It really depends on which slots are played. If someone plays 250.000 spins on Honey to the Bee or some similar low variance slot and gets 91% return without hitting any random jackpot, it would be safe to say it's set to 92% payout or so.

If someone plays for example Triple Twister for 250.000 spins and gets 91% return then it's much harder to say. These slots have 'jackpots' at 50000x line bet so having bad luck here and getting fewer \$2500 wins than expected will have a big impact.

#### Rusty

##### Banned User - repetitive flaming
It really depends on which slots are played. If someone plays 250.000 spins on Honey to the Bee or some similar low variance slot and gets 91% return without hitting any random jackpot, it would be safe to say it's set to 92% payout or so.

If someone plays for example Triple Twister for 250.000 spins and gets 91% return then it's much harder to say. These slots have 'jackpots' at 50000x line bet so having bad luck here and getting fewer \$2500 wins than expected will have a big impact.

This is not as true as you might initially think.
Be mindful that such events occur so infrequently as to be considered anomalous data.
When was the last time you saw a 50,000 X line bet win? Ever?
I don't think I have ever seen one posted here and that is over Billions of collective spins.

As I have outlined in the initial post even including a 50,000 line bet win, which would be a huge anomaly in a data set of 250K spins, would only raise the RTP by 1% from 91% to 92% using the example I set out.
That fact remains unchanged.

#### takethemoney

##### Banned User - Chargebacks at Slotastic
So maybe there is no way to know if you're getting a fair game until you've played out 2 million spins / hands or whatever. I can also see where this is a really tough one to measure. Who is gonna keep track of 2 million spins?

What I do know is my RTG play does not last as long as it did 2 years ago. I used to be able to just deposit a \$100 and play for a day, or sometimes two. Now it seems like most of the time it's a couple hours at best.

#### Rusty

##### Banned User - repetitive flaming
So maybe there is no way to know if you're getting a fair game until you've played out 2 million spins / hands or whatever. I can also see where this is a really tough one to measure. Who is gonna keep track of 2 million spins?

What I do know is my RTG play does not last as long as it did 2 years ago. I used to be able to just deposit a \$100 and play for a day, or sometimes two. Now it seems like most of the time it's a couple hours at best.

Well what I am trying to point out is just the opposite but things like this are never easy to explain in simple terms.

Remember the theoretical RTP should be made up from total combinations possible divided by total winnings in those combinations.
Basically the variance is how many individual wins you have to make up the total winnings.
so a slot with 1 million combinations will take in 1 million coins in a complete cycle at 1 coin and 1 line bet.
Total winnings from each of these combinations might be 950,000 coins which would represent a theoretical RTP of 95%

Now if you had only 1 winning combination that paid 950,000 coins the variance would be high to the extreme because there would be 999,999 dead spins to 1 winning spin.
So slot designers choose to have lots of winning combinations that pay smaller amounts for playability.
The variance is increased upward by having more high paying wins and downward by having more low paying spins while keeping the total winnings the same thus the variance is changed but the theoretical RTP remains 95%
Obviously with bonus slots and wilds and scatters things are more complex but that is the basic principle.

With that understanding the most important things to grasp when comparing real life results and considering sample sizes are,

A) That you play multiple lines so if you play 20 lines you are in effect cycling through 20 combinations in 1 spin - it is the equivalent of playing 20 spins at 1 line in that respect.

B) That many combinations are repeated many thousands of times within a complete cycle of possible combinations.
This means with reel map and paytable knowledge we can make reasonable evaluations of actual RTP against claimed theoretical RTP with much smaller samples than the Casinos pretend.

and to a lesser extent
C) The variance of the slot but please note the variance would have to be exceptionally high to skew results over 250,000 spins at 20 lines which is what I have tried to point out in my reply to Zap.

I hope I have explained that ok

#### zap987

##### Meister Member
PABnononaccred2
This is not as true as you might initially think.
Be mindful that such events occur so infrequently as to be considered anomalous data.
When was the last time you saw a 50,000 X line bet win? Ever?
I don't think I have ever seen one posted here and that is over Billions of collective spins.

As I have outlined in the initial post even including a 50,000 line bet win, which would be a huge anomaly in a data set of 250K spins, would only raise the RTP by 1% from 91% to 92% using the example I set out.
That fact remains unchanged.

I was thinking of the cap on wins at 50000x line bet of which there are plenty of screenshots in the winner screenshot thread from mostly the newer real series slots with stacked wilds and such.

#### Rusty

##### Banned User - repetitive flaming
I was thinking of the cap on wins at 50000x line bet of which there are plenty of screenshots in the winner screenshot thread from mostly the newer real series slots with stacked wilds and such.

Plenty of screenshots of 50,000Xline bets?

I went a lot of pages and found nothing like so perhaps you are mistaken?

Remember to check for how many coins are played as well you need to divide the line bet win with this number and also remember that the total win shown is from all lines (especially stacked wilds wins) and not just one line.
When you include these necessary calculations get back to me when you find a genuine 50,000 X line bet win.
I'm not saying that they can not exist just that they are so rare that they cold be discounted as anomalous data in a small sample size.

Also don't lose sight of what is pertinent to the discussion which is even if a 50,000X line bet was won (which would be a massive positive outlier in our data) it would only increase the RTP by 1% in our example.

#### Tengil

##### Senior Member
Seriously if some of you think that 224k spins should give a close estimate of the RTP (+-1%) you are wrong. 3 standard deviations accounts for ~99,7% of the results. So for that amount of spins to give a close estimate the slot would need to have a variance of ~1,578 standard deviations which is way too low for a slot.

Even on a slot with a variance of 3 SD( I doubt they are any slots like that) you would need 810 000 spins.

And +3 SD losses happens all the time, my worst that I have calculated is 4,0 on Baccarat.

#### KasinoKing

##### WebMeister & Slotaholic..
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From my understanding (correct me if I'm wrong) the true RTP is calculated by the money put through the slot against the money won (paid out by the slot).
You're wrong.
I'll let Rusty explain it:
Remember the theoretical RTP should be made up from total combinations possible divided by total winnings in those combinations.

Also;
Plenty of screenshots of 50,000Xline bets?

I went a lot of pages and found nothing like so perhaps you are mistaken?
It depends on his definition of "plenty" as to whether he is mistaken or not.
I would say a "few", but there are definitely some max-out screenshots in there somewhere.
(No, I am NOT volunteering to go find them! )

KK

#### Simmo!

##### Moderator
Staff member
An aside: RTG used to be 40,000 x line bet max payout. Has that changed to 50,000 recently?

#### KasinoKing

##### WebMeister & Slotaholic..
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An aside: RTG used to be 40,000 x line bet max payout. Has that changed to 50,000 recently?
I think that 20-liners are 40,000 and 25-liners are 50,000 - but I could be wrong.
Can someone confirm?

KK

#### kakata

##### Banned User - hyper flamming
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what I know 4 sure is..that when I used to play a lot..,.I would spin well over 250K spin a month.
multiply that for 12 and for 8 it will be 24 million spins....so I think I can see the difference....and there is a lot of it .( Im sure Ive made more than 50 million)

Im not the only one who have noticed it and wont be the last one...
Now , among us(gamblers) there are some "gamblers" whom do defend the theory of : bad luck, bad shit, bad run.bad whatever....." and do NOT want to admit that something has changed for the worse...pretty f'''kkin worse.

Why they do it?
I dont know for sure
and I dont care for sure

I know what I know ....and believe me, what I know is MY truth, which count to me more than all the (BS) I ,sometime, read.

#### Rusty

##### Banned User - repetitive flaming
Seriously if some of you think that 224k spins should give a close estimate of the RTP (+-1%) you are wrong. 3 standard deviations accounts for ~99,7% of the results. So for that amount of spins to give a close estimate the slot would need to have a variance of ~1,578 standard deviations which is way too low for a slot.

Even on a slot with a variance of 3 SD( I doubt they are any slots like that) you would need 810 000 spins.

And +3 SD losses happens all the time, my worst that I have calculated is 4,0 on Baccarat.

We do not have the data and without a PAR sheet for an average slot such as Cleopatra's Gold there is not much point in exploring standard deviation on theoretical variance.
However by using the Cleopatra's Gold paytable (a fairly standard RTG slot) and an assumed sample of 225,000 spins at 20 lines with some educated guesses on variance lets see if your conjecture on the variance of slots and your statement that a reasonable idea of RTP can not be gauged over such a sample holds up.

First of all,
225000*20 lines= 4,500,000 total combinations. That is the figure we should use - not the 225,000 spins as we are looking at RTP over total combinations played against theoretical RTP over total combinations.

Judging by your post you are good at maths, admittedly not my strong suit, so take a look at this loose example and see what you think.
I am open to being corrected and if I'm wrong I'm wrong.

Since a slot such as Cleopatra's Gold has around 12 symbols and the symbols are paired in value we can cancel that down to 6 instances. I have looked at the paytable and I have personally played well over 200,000 spins on this slot playing 9 lines so I feel I can make a pretty good educated guess on the variance.

If each reel has around 35 symbols there would be over 50 million combinations but in these combinations outcomes are repeated.
Therefore can we cancel down by the least likely outcome to simplify?

Unfortunately this is 1/1 the Wild symbol in this case but since it only pays x10,000 and occurs only once it is only 0.02% of our RTP over 50 millions spins so we can leave that aside without skewing our figures?

The next highest win is x2000 and I would guess there are at least 1000 instances of this. So we could divide our 50 million by this number which would mean a 1 in 50,000 probability of the least likely event which makes up only 4% of the RTP.
So now can we use our 4500,000 combinations to theoretically play through our total possible combinations 90 times?
I am sure you see the importance of this technique but do you consider it invalid?

Anyway that would mean an average of 90 instances in our sample size.
Lets say only 60 instances appear. 30x2000 = 600,000
This would only change our RTP by 1.3% and we are using an example with the highest paying symbol occurring over 30% less frequently than expected!

I think these slots are much lower variance than what you think.

Obviously these figures are quite loose but which part of it do you disagree with in principle?

#### Tengil

##### Senior Member
Will try to answer in the beginning of next week. Statistics and probability theory isnt really a strong field for me and specially explaining it in English.

But what would be more interesting to speculate on is when you have extremely bad runs with a decent sample.

I think that the slots have lets say a RTP of 95%. But are they truly random? For example a BJ game returning 99,65% over a sample of 2 million hands doesnt mean its random, "fair" maybe.
I have my doubts as I have experienced some horrible runs. You know those balance busting streaks when you lose your 300-400xbetsize bankroll with RTPs ranging from 30-50.

Actually had a "nice" streak once on Achilles, ~1700 spins flatbetting 2/spin and losing roughly 1800.

#### diamondale

##### Banned User
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Its SLOT mACHINE

There is no way you know what its going to do. I have played and hit 20 bonuses almost in a row and sometimes nothing its called luck ive bitched in the past but i gave up if its your day to win you will, enough with the theories already!

#### Tengil

##### Senior Member
There is no way you know what its going to do. I have played and hit 20 bonuses almost in a row and sometimes nothing its called luck ive bitched in the past but i gave up if its your day to win you will, enough with the theories already!

If one would know the variance you would know exactly "what goes on". And with attitudes like that AP/UB and EH would never had get caught.

And remeber it was the players that busted them. And its not like anyone is forcing you to read these kind of threads.

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