Is variance fact or opinion?

[Valhalla]

Is variance fact (programmed into games) or opinion (we decide for ourselves what variance we believe a game to be).
Is this an industry thing or a gambler's term?

I remember recently declaring my belief that, for example, DoA is low variance. Because of the many many small wins you get and very rare big wins. But another member told be that "most people would say it's a high variance bastard of a slot".
Am I wrong, or is it debatable? DoA is just one example, and remembering the above statement prompted me to write this thread.

I'm just curious where the term variance actually came from. I know (or assume, rather) the developers create a game's RTP, but is variance just a by-product of the paytable, or is variance taken into account in development?

 

[spintee]

It boggles my mind when people mention about variance ect, I no that the variance and rtp is totally different,

To me high variance is shit payouts but can get big wins, low is a good paytable but rarely big wins, I tend to not even think about it, Just spin away and hope for the best,

 

[Valhalla]

spintee - I'm the same mate
I'm just wondering though whether variance is something we (the players) created, or if it's actually an industry word/creation.

 

[mathsboy1975]

spintee - I'm the same mate
I'm just wondering though whether variance is something we (the players) created, or if it's actually an industry word/creation.

Variance is a statistical measure that essentially gives you an idea of how spread out or dispersed the observed values are around their mean (average) value - in the case of slot machines each observed value is one of the possible payout values and the "mean" would be the average return per spin. It is not a made up quantity and it is not an industry term - it is grounded in the theory of statistics.

By definition it is the sum of the squared differences between every possible payout and the mean (average) payout per spin. A similar measure you might have heard of is the Standard Deviation which is the square root of the variance statistic.

A low variance slot therefore will result in a larger number of payouts being "closer" to the mean payout than for a high variance slot. This would most likely be satisfied by a lower number of possible high payouts than lower payouts. Higher variance will see some much larger values that are a long way from the average payout. As no payout can be negative, this usually means that higher variance slots must have the ability to return larger payouts than lower variance slots (or possibly higher probabilities of hitting larger/mid range payouts). It is hard to quantify specifically without some concrete examples, but some members here have performed some analysis of a number of slots and if you dig around on the forum you might come up with some actual measured values.

In every day terms, consider a group of 100 people who have a mean (average) weight of 80kg and a variance of 5kg compared with another group with the SAME mean (average) weight 80kg and variance of 10kg. The second group will contain people that have a wider RANGE of weights than the first group. The variance measures how widely dispersed values are around their mean value.

As a very crude example, consider a slot with a 95% RTP and a variance of zero. With a stake of 1£ per spin, this would result in a payout of £0.95 returned on EVERY spin. You would literally lose 5p per spin, EVERY spin - the least entertaining slot in the world.

 

[zanzibar]

Variance is neither something gamblers invented nor an industry creation. It is a mathematical term that describes the distribution of a set of numbers. High variance means that the numbers are widely spread apart, while low variance means they are all close together. If the numbers were all the same then the variance would be zero. Here is more info but most of it is way over my head.

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So in relation to games of chance and most particularly slots, when people talk about variance they mean the distribution of wins on the game. If you have a slot that pays a lot of smaller wins like 0.5x, 1x, or 2x your bet, then occasional huge wins of 2000x or more then you would say the variance is high. If the difference between the biggest and smallest win is only something like 50x then you would say the variance is low. Most card and table games are low variance. Video poker can be high variance. Slots are generally high variance compared to every other type of casino game, but obviously some slots are much higher variance than others.

And yes, variance has nothing at all to do with RTP.

 

[K2C]

Is variance fact (programmed into games) or opinion (we decide for ourselves what variance we believe a game to be).
Is this an industry thing or a gambler's term?

I remember recently declaring my belief that, for example, DoA is low variance. Because of the many many small wins you get and very rare big wins. But another member told be that "most people would say it's a high variance bastard of a slot".
Am I wrong, or is it debatable? DoA is just one example, and remembering the above statement prompted me to write this thread.

I'm just curious where the term variance actually came from. I know (or assume, rather) the developers create a game's RTP, but is variance just a by-product of the paytable, or is variance taken into account in development?

Both variance and RTP are by-products of the paytable and/or game rules and do not need to be specifically "programmed into". Furthermore, both concepts existed long time before computer programming. They existed from beginning of the time I would say. In application to gambling they appeared when the very first game of chance was introduced.

RTP shows how much you are expected to lose on average
Variance shows how far you may go from that average loss.

RTP = 0.95, Variance = 0.000001 -----> You will lose 5% of each bet, or very close to 5%
RTP = 0.99, Variance = 100 ----> You will lose 1% of each bet on average in the long run, but on individual bets you may win a lot or lose the full bet.

Every programmed game would have some RTP and some Variance. It is also possible to tweak the paytable to specifically achieve the desired values for RTP or Variance, e.g. a round number, or some fun number, or a small number or a big number. So yes, a casino may specifically program a high-variance game, but not every high-variance game was designed with this thought in mind.

 

[dunover]

Let's simplify it in terms most players will understand:

Reel maps decide the chance of each possible result and all permutations of those reel maps once would give the game's TRTP of say 96%.

We know due to the law of large numbers and via testing that the games will pay pretty bang-on their TRTP over a million or so spins, although not guaranteed.

Let's say over those million spins there was 1 result of 960,000 x stake and 999,999 paid zero. Imagine the reel maps of the slot showing 16 positions over 5 reels of which 15 were zeroes and one a diamond. The chances of getting 5 diamonds on the one payline would be just over a million to one 16*5. (for simplicity's sake ignore multiple pay lines/ways and features).

So, in the above scenario you'd have the ultimate high-variance game whereby over 1 million spins only ONE spin would be needed to meet the game's TRTP, like a Netent nightmare...

Imagine the opposite scenario whereby 5 diamonds was the only possible LOSING combination, and any 1,2,3,4,or 5 zeroes paid a win - this would be the ultimate low-variance game, more boring than even St*rb*rst.

So, add more symbols on the reels, 8 of some, 6 of others and only 2 of the highest-paying ones and assign values to them according to their chances of hitting and totalling the game's TRTP.

If the game had some symbols that only appeared once or twice these would give accordingly very high values x stake while the remainder were appearing 7 or 8 times and paid less than 1 x stake you'd have a high-variance game.

If the game had one or two symbols appearing say twice on a reel and the rest 4-6 times you'd have a medium variance game where most wins were not fractions of a credit but low multiples thereof.

To summarize the pay table is related to reel maps whether these are computer-generated or physical reels. The spread and frequency of symbols on the reel maps decides the variance of the game, and over time whichever degree of variance you compute the reel maps to will equal the TRTP.

Spintee - yes, TRTP is static for games, variance isn't.

As a footnote a software provider can give an exact RTP for a simple 1-line or multi-line game with no random feature (like free-spins, as opposed to pre-selected 'pick me' rewards which are non-random.) Where the feature is random like free-games or the free game reels are enhanced, you tend to get a 'range' figure for RTP like 94.11 - 95.98% for example. This because testing over all possible reel outcomes plus feature outcomes is nigh on impossible so you get a range from various cycles of millions of test pulls on the RNG.

 

[KasinoKing]

As a footnote a software provider can give an exact RTP for a simple 1-line or multi-line game with no random feature (like free-spins, as opposed to pre-selected 'pick me' rewards which are non-random.) Where the feature is random like free-games or the free game reels are enhanced, you tend to get a 'range' figure for RTP like 94.11 - 95.98% for example. This because testing over all possible reel outcomes plus feature outcomes is nigh on impossible so you get a range from various cycles of millions of test pulls on the RNG.

This last point you made is the only thing I don't understand about slots.

Even given that you have some random picking feature, free-spins or whatever - these features still must have calculable occurrence and maximum limits, so therefore you should still be able to work out what the average return is over infinite spins and therefore give a fixed TRTP for these features which can be added to the TRTP for the base game.
i.e. What I'm saying is that the designers should be able to calculate the exact TRTP without having to trial the slot at all.

KK

 

[quber]

I agree KK, all outcomes are calculable for the majority of slots, Netent give a precise figure for their games and look at all that is going on in them with the likes of Eggomatic, Attraction and Wishmaster for example.

Some games will have a range like the new Nemos Voyage which has a varying RTP depending which wild feature is active and no set time to be in each area. when the player is descending the RTP can be worked out by the odds of the pressure gauge landing but on the way up the time is dependent on the speed that the player spins at it is a constant ascent so the players speed affects the RTP.

 

[Jono777]

The bottom line with every slot game is that they are a computer program designed to make money.

Like land based machines they exist as a business to make money for the owners.

The 'reels' are just eye candy and could be removed and when you 'click to spin' you balance either goes up or down.

A percentage is returned to the players which is written into the code/program

Yes its a lot more in depth than this but that's the basics

 

[quber]

The bottom line with every slot game is that they are a computer program designed to make money.

Like land based machines they exist as a business to make money for the owners.

The 'reels' are just eye candy and could be removed and when you 'click to spin' you balance either goes up or down.

A percentage is returned to the players which is written into the code/program

Yes its a lot more in depth than this but that's the basics

The percentage is not written into the code, the RTP is a mathematical result of the paytable and reels, to change the RTP all you have to do is add or remove a symbol or change the payout of a of a set of symbols

Each spin of the reels is totally random and independent of any previous spin or bet size.

Pretty much like a physical roulette wheel, it is spun randomly, the ball is thrown randomly, it doesn't have any idea of what bets have been placed yet the game returns an RTP of 97.3%


Now UK pub slots, that is a totally different game and is fixed in the code.

 

[dunover]

This last point you made is the only thing I don't understand about slots.

Even given that you have some random picking feature, free-spins or whatever - these features still must have calculable occurrence and maximum limits, so therefore you should still be able to work out what the average return is over infinite spins and therefore give a fixed TRTP for these features which can be added to the TRTP for the base game.
i.e. What I'm saying is that the designers should be able to calculate the exact TRTP without having to trial the slot at all.

KK

There is also the factor of multiple reel sets (not allowed in some US states for example) plus the offering of different math models like for example with RTG games. As quber says you also have enhanced features in play that are optional too. You can remove a pay-out too like Cleopatra in some land based casinos won't pay 2x stake for 2 scatters thus reducing RTP by a few %. As you say for any slot without a second or third layer of randomness built in, there should be an exact TRTP offered by the developer.

 

[Valhalla]

Whilst I really do appreciate all the very detailed and well thought out replies, I wasn't exactly asking what variance is, rather I was asking if variance (when applied to slots mainly) is something that just happens to exist due to the nature of the games. OR if games are designed with variance in mind by the producers.

Like... did Microgaming start to design Break da Bank Again, and say to themselves (in a board meeting or whatever) "let's make this game really high variance", or did they design the game with it's paytable, and the high variance factor was just a by-product of said paytable?

Does that make sense? I know what variance is, I'm just asking if it's intentional or if it's organic (if that's the right word)...

 

[K2C]

Let's simplify it in terms most players will understand:
.....
To summarize the pay table is related to reel maps whether these are computer-generated or physical reels. The spread and frequency of symbols on the reel maps decides the variance of the game, and over time whichever degree of variance you compute the reel maps to will equal the TRTP.

That was a good and simple explanation, indeed.

Spintee - yes, TRTP is static for games, variance isn't.

No, that is not true. Variance is just as "static" as RTP for any game. And it is calculated the same way: by recording a large number of results and applying a formula to the array. Only that the Variance formula is a bit more complicated. Also, if you fully know the game mechanism you can calculate the exact RTP and exact variance mathematically.

As a footnote a software provider can give an exact RTP for a simple 1-line or multi-line game with no random feature (like free-spins, as opposed to pre-selected 'pick me' rewards which are non-random.) Where the feature is random like free-games or the free game reels are enhanced, you tend to get a 'range' figure for RTP like 94.11 - 95.98% for example. This because testing over all possible reel outcomes plus feature outcomes is nigh on impossible so you get a range from various cycles of millions of test pulls on the RNG.

That's not true either. Yes, those features complicate the mathematical calculations and also they require bigger sample in the sample-based calculations but still you can come up with the exact numbers for RTP and Variance.

For example, if the feature is based on selecting 3 boxes out of 5, each containing a random prize, there is a limited number of possible prizes and their combinations, just like there is a limited number of symbols on each reel and their combinations. It will be an RTP within RTP and variance within variance (the convolution of probability distributions) but still both measures are calculatable.

 

[dunover]

Whilst I really do appreciate all the very detailed and well thought out replies, I wasn't exactly asking what variance is, rather I was asking if variance (when applied to slots mainly) is something that just happens to exist due to the nature of the games. OR if games are designed with variance in mind by the producers.

Like... did Microgaming start to design Break da Bank Again, and say to themselves (in a board meeting or whatever) "let's make this game really high variance", or did they design the game with it's paytable, and the high variance factor was just a by-product of said paytable?

Does that make sense? I know what variance is, I'm just asking if it's intentional or if it's organic (if that's the right word)...

It's definitely intentional. Making most symbols on the reels scarce and thus making a few possible combinations pay out the majority of the game's RTP, and paying small amounts for the more common symbols like BDBA you stated.

 

[K2C]

Like... did Microgaming start to design Break da Bank Again, and say to themselves (in a board meeting or whatever) "let's make this game really high variance", or did they design the game with it's paytable, and the high variance factor was just a by-product of said paytable?

Both instances are possible, depending on the instructions given to the designer/programmer. It can be that he was asked "to produce a game with a 95.43 RTP, payouts as high as x1500 and some gold coins on the reels" and nobody cared about the variance. It is also possible that he was given the instruction to design a game with a variance higher than in Game X or even with a variance equal to a specific number. The latter is highly unlikely in my opinion (cause that would be a lot of work for no good reason), but possible.

Theoretically, the same is aplicable to RTP, i.e. a game can be designed without caring of what the RTP will be, but in practice it is not possible, unless the casino is extremely stupid

 

[K2C]

It's definitely intentional. Making most symbols on the reels scarce and thus making a few possible combinations pay out the majority of the game's RTP, and paying small amounts for the more common symbols like BDBA you stated.

But it's more complicated than that unless we are in your simplified example. Most slots have multiple payout lines and the variance is affected not only by highest and lowest ones, but also by the ones in the middle, as well as their respective probabilities. Here is a hypothetical with only 5 payouts (all slots in the example have an RTP of 96.5%)

Slot 1

Payout Probability
120 0.001
15 0.010
4 0.050
2 0.100
1 0.295
0 0.544

Variance = 17.213775

Slot 2

Payout Probability
40 0.001
15 0.005
7 0.050
4 0.120
2 0.010
0 0.814

Variance = 6.203775

The second slot is paying in 18.6% spins which is 2.5 times scarcer than the first slot. But the Variance for Slot 1 is almost three times as high than for Slot 2 . Now you may probably argue that this because the top payout for Slot 1 is much higher than for Slot 2. Okay, here is another slot:

Slot 3:

Payout Probability
65 0.001
30 0.005
20 0.025
2 0.120
1 0.010
0 0.839

Variance = 18.283775


Now, the top payout is closer to that of Slot 1 than it is to Slot 2, but the variance is actually even higher than for Slot 1

You can play with it in Excel just as I did now.

 

[Valhalla]

K2C... you're just blowing my mind

 

[dunover]

But it's more complicated than that unless we are in your simplified example. Most slots have multiple payout lines and the variance is affected not only by highest and lowest ones, but also by the ones in the middle, as well as their respective probabilities. Here is a hypothetical with only 5 payouts (all slots in the example have an RTP of 96.5%)

Slot 1

Payout Probability
120 0.001
15 0.010
4 0.050
2 0.100
1 0.295
0 0.544

Variance = 17.213775

Slot 2

Payout Probability
40 0.001
15 0.005
7 0.050
4 0.120
2 0.010
0 0.814

Variance = 6.203775

The second slot is paying in 18.6% spins which is 2.5 times scarcer than the first slot. But the Variance for Slot 1 is almost three times as high than for Slot 2 . Now you may probably argue that this because the top payout for Slot 1 is much higher than for Slot 2. Okay, here is another slot:

Slot 3:

Payout Probability
65 0.001
30 0.005
20 0.025
2 0.120
1 0.010
0 0.839

Variance = 18.283775


Now, the top payout is closer to that of Slot 1 than it is to Slot 2, but the variance is actually even higher than for Slot 1

You can play with it in Excel just as I did now.

But the bit I've bolded in example 3 is plain ridiculous and you wouldn't see it on a normal slot unless the designer had really messed up. So 1 (at 0.010) is 12 times less common than the pay-out 2 (at 0.120) above it??

 

[K2C]

But the bit I've bolded in example 3 is plain ridiculous and you wouldn't see it on a normal slot unless the designer had really messed up. So 1 (at 0.010) is 12 times less common than the pay-out 2 (at 0.120) above it??

Of course my slots are just as unrealistic as your hypothetical "Diamonds and Zeros" machine is. Just like it, they were designed to illustrate the point. The point in my case being that the variance does not just depend on the highest payout and the no-pay probability, rather it is a function of the payout table and the accompanying vector of probabilities in their entirety.