# Slot Statistics - Critiques Requested

#### Jasminebed

##### Game old gal
I like to think of Variance in terms of how big a bankroll will I need to get close to the theorhetical RTP. For games that a very large part of the payback is on bonus rounds, if the bonus round doesn't usually trigger in around 140 spins or so, that means it is pretty high variance.

For games which produce decent line wins, you might play a few hundred spins and still be close to even, without a bonus round.

Let's take a page from one of Enzo's past posts, and use a slot machine with every spin costing \$1 and paying back .99 cents. That would be the ultimate in low variance, but guarantees every session will be a losing session.

At the other end of the spectrum is a slot that costs \$1 to play, and pays a jackpot of \$99,000 on average once every 100,000 spins, and no other wins are possible. But because of it's random nature, you might hit that Jackpot win on the very first spin, and you might hit it again the very next spin even. Or you could spin 200K times and never hit it.

If it was \$1 a spin and hit on average once every 100 times and paid \$99, that would be very medium variance IMO, but another player might consider it low variance. If I usually only play with \$10, I might feel it's high, if I have \$1,000 bankroll, I'm sure I would consider it low..

All the above examples produce payback of 99%

Of course few games play quite that way, offering intermediate wins that keep you playing. The more smaller wins you have to increase the number of spins you get to hit that jackpot or hit that bonus round, the lower the variance as I see it.

Oh, and by the way, I don't have that big a problem with "winning" 60 cents when I bet \$1. I spent the \$1 to take a chance to win, and winning 60 cents is better than nothing.

#### binary128

##### Dormant account
Jasminebed,

Thank you VERY MUCH for taking the time to provide all of those words.

I've discovered that slot variance is such a subjective thing - player to player, game to game (day to day?). And 10 years (20 years?) of history has led to the creation of a whole lot of words to try to describe this subjective thing.

But all slots have a variance value that is a number - a calculated, hard, nothing-subjective-about-it number. It would appear that Galewind Software is the first in line to actually publish those numbers.

So we find ourselves in the difficult position of publishing hard numbers into a well-developed "subjective words dictionary" world. I've published a variance number of 35. What does that mean? It's not in the dictionary.

I've decided, for the time being anyway, that it doesn't mean anything at all. Hmm. Let me re-phrase that. It means whatever anyone wants it to mean.

Again, thank you for all of your words.

I assume that your final paragraph was in reference to my "rant" on "WIN!" displays. Well, it's a pet peeve of mine - we've all got 'em. Each to his own I guess.

Chris

#### Jasminebed

##### Game old gal
Even if it is subjective whether a player views a slot's variance as low medium or high, the numbers will provide a guideline to allow a player to know if a game (especially an unfamiliar one) is higher or lower than others.

#### binary128

##### Dormant account
Even if it is subjective whether a player views a slot's variance as low medium or high, the numbers will provide a guideline to allow a player to know if a game (especially an unfamiliar one) is higher or lower than others.

Jasminebed,

I agree. I plan to publish this page (the one that has been linked in this thread) shortly, so the numbers will be publicly available (to that small percentage of Players that use the Help system anyway).

What I have decided not to do, for now, is to assign any words to those numbers. That is, Crazy 8 Line has a variance of 23, Gems of Isis is 51, and Silver Spurs is 106. I'm not going to jump the gun and assign words to those numbers until I feel more comfortable that any word association I make is consistent with something/anything.

But, to repeat, the numbers are going to be published and available.

Chris

#### binary128

##### Dormant account
ChopleyIOM,

BTW, the changes that you suggested concerning our choice of words regarding the wild symbol not appearing on reel 1 during Free Spins (remove the "There are no multiple wild stops in a free spin" part) is up on both the popup paytable graphics as well as in the Help file text.

Again, thanks for that. You were right - it did sound harsh.

Chris

#### Jufo

##### Dormant Account
I noticed being mentioned in this thread so I thought I pop in and say my two cents worth.

First of all, I find it great that Chris did all this work to increase transparency of their slots performance to players. In his previous thread about Return percentages a few people wanted slot variance data to be published and it shows a great deal of devotion to players that he then spent all the time and money to deliver this data to players. I haven't seen a software provider to cater for player's wishes in this way before, so kudos for that!

I am a bit disappointed though, because I have read all those threads and long discussions by several members on this forum wishing that casinos increase their transparency and now that something like that is finally done in this thread, most of these posters haven't even bothered to come here to reply (VWM where are you lurking?)

Like Chris mentioned, based on our discussions he added a couple of new details to the slot performance help-page. Now would be also the perfect opportunity for the people here to suggest an interesting slot stat they would like to see published. So is there some other statistic you would like to see on the help-page that hasn't been mentioned yet? Perhaps Chris will be open to adding it to the page as well.

#### Jufo

##### Dormant Account
I'll cover some issues that have been discussed in the thread.

To the topic of: What is the real meaning of standard deviation / variance value and can you assign some descriptive words to it?

Like it was mentioned it is difficult to compare variances of slots and assign words to these values because these haven't been published for other softwares (I'll state the variance values of two Microgaming slots below though). But for most other game types standard deviations are known and you could compare the standard deviations of slots to these games. For example, Jacks or Better video poker has a standard deviation of 4.42, so if you play a slot with standard deviation close to 4.4, in a way you'd expect the same amount of swings than playing Jacks or Better at the same bet size.

It's important to note here that many quite different kinds of games can have similar standard deviation value, so the standard deviation or variance value by itself may not accurately describe the "feel of the game". For example the following bets:

1) Playing single-zero roulette by betting \$5 on single number every spin
2) Playing Joker Poker video poker betting \$5 per hand
3) Playing Galewind's Lucky Lantern slot at \$5 per spin

All of the above bets have a standard deviation value close to 6, ie. the standard deviation of the above bets is ~\$30 per round. But the games are quite different and the "feel" is also quite different between them. Yet, in a somewhat abstract sense, they all deliver the same amount of "swings" as the variance between them is nearly the same. The point is that it would be overly optimistic to think that the "whole feel" of the game could be captured in a single value called variance.

Now the topic of comparing Galewind's slot variance data to other softwares.

Unfortunately there's not much info available on the subject (as other sw providers haven't published these). However, I have been working on a slot simulator tool which enables me to measure variance values for any slot that I have obtained the reel layouts for. So far I have done this for only two Microgaming slots but I guess this is better than nothing. The results are:

Loaded slot [2x multiplier choice in free spins, maximum 25 lines]: Standard deviation based on 10 million simulated spins = 5.0
Thunderstruck Slot [maximum 9 lines]: Standard deviation based on 10 million simulated spins = 6.5

So now we have some reference values about two MG slots. People are more familiar with these slots than Galewind's slots, so do you consider these two slots as low, medium or high variance? One reference: KasinoKing's website (
) describes 'Loaded slot' as Medium variance and 'Thunderstruck slot' as Low variance. There is inconsistency here in KK's assignments, as Thunderstruck has larger standard deviation than Loaded Anyway if the general consesus is that, for example, both of these slots are Medium variance, then we would at least have a starting point to assign descriptions to standard deviation values, such as: "slots with standard deviation between 5-7 fall to Medium variance category."

More to come later...

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#### binary128

##### Dormant account
Something else about which I have been thinking since I first started to organize all of this data:

- A 20-line bet, \$1 per line, one line wins and pays \$5.

- A 20-line bet, \$1 per line, five lines win, each paying \$1 for a total return of \$5.

I'm pretty sure (I rechecked the Variance equation in my first post) that there is no difference in Variance here. Or rather, if there were a sufficient number of these types of conditions within the sample set, there would be no impact on the resulting Variance calculation/result.

However, I think that there would be a big difference in how the Player perceives the Variance. I think that the single-line win would be perceived as a higher Variance, and the multi-line win would be perceived as a lower Variance.

Obviously, a sample of 1 would have little if any impact. But if, purely by coincidence, a number of these samples occurred, especially if they occurred within a short span of time, then I think that would impact the Player's opinion.

"You know, the first time I played this slot I thought that it was Low Variance, but I just played it again and now I'm thinking that maybe it is more Medium Variance."

Here is the list, sorted by the Standard Deviation lowest to highest:

Take It or Leave It: 4.1

Hot Peppers: 4.7

Crazy 8 Line: 4.8

Diamonds Wild: 4.8

Lucky Lanterns: 6.1

Gems Of Isis: 7.1

Golden Goal: 7.4

Bowl-a-Palooza: 7.7

The Red White & Blue: 8.0

Silver Spurs: 10.3

Bells & Whistles: 16.2

Chris

#### binary128

##### Dormant account
Unfortunately there's not much info available on the subject (as other sw providers haven't published these). However, I have been working on a slot simulator tool which enables me to measure variance values for any slot that I have obtained the reel layouts for.

So far I have done this for only two Microgaming slots but I guess this is better than nothing. The results are:

Loaded Slot: Standard Deviation (SD) = 5.0, Variance = 25.

Thunderstruck Slot: SD = 6.5, Variance = 42.

So now we have some reference values about two MG slots. People are more familiar with these slots than Galewind's slots, so do you consider these two slots as low, medium or high variance?

KasinoKing describes Loaded (Variance = 25) as Medium Variance and Thunderstruck (Variance = 42) as Low Variance.

There is inconsistency here in KK's assignments, as Thunderstruck has larger standard deviation than Loaded.

Anyway if the general consesus is that, for example, both of these slots are Medium variance, then we would at least have a starting point to assign descriptions to standard deviation values, such as: "slots with standard deviation between 5-7 fall to Medium variance category."

More to come later...

I have reformatted your post so that I might better understand its significant points.

What is your level of confidence in the accuracy of the reel layouts for the 2 MG slots which you reference?

@KK - What criteria did you apply which resulted in your assigning a Low Variance to Thunderstruck and a Medium Variance to Loaded? I confess that I am unfamiliar with the site which Jufo has linked, but I will head over there shortly.

Chris

#### Jufo

##### Dormant Account
What is your level of confidence in the accuracy of the reel layouts for the 2 MG slots which you reference?

I'd say my confidence is moderately high. The reel layouts for different Microgaming slots were originally "cracked" in this thread dating back to 2007. These reels also produce the exact same RTP that the software provider has published.

@KK - What criteria did you apply which resulted in your assigning a Low Variance to Thunderstruck and a Medium Variance to Loaded? I confess that I am unfamiliar with the site which Jufo has linked, but I will head over there shortly.
Chris

What makes Thunderstruck to have higher variance is the restriction to maximum 9 lines. This means fewer line hits that are larger in magnitude. I think the "default" approach in ranking slots according to their variance would be assuming that maximum number of lines are always played as most players prefer to play maximum lines. However, if you only played 9 lines in Loaded (rather than the maximum 25), Loaded seems to have about the same standard deviation value (~6.5) as Thunderstruck with 9 lines.

#### binary128

##### Dormant account
I was confused by the last paragraph, so here is more data:

Game: SD: Line Count

Take It or Leave It: 4.1: 27

Hot Peppers: 4.7: 20

Crazy 8 Line: 4.8: 8

Diamonds Wild: 4.8: 1

Lucky Lanterns: 6.1: 20

Gems Of Isis: 7.1: 20

Golden Goal: 7.4: 20

Bowl-a-Palooza: 7.7: 9

The Red White & Blue: 8.0: 1

Silver Spurs: 10.3: 9

Bells & Whistles: 16.2: 5

I don't see any correlation between line count and SD.

#### Jufo

##### Dormant Account
I was confused by the last paragraph, so here is more data:

Game: SD: Line Count

Take It or Leave It: 4.1: 27

Hot Peppers: 4.7: 20

Crazy 8 Line: 4.8: 8

Diamonds Wild: 4.8: 1

Lucky Lanterns: 6.1: 20

Gems Of Isis: 7.1: 20

Golden Goal: 7.4: 20

Bowl-a-Palooza: 7.7: 9

The Red White & Blue: 8.0: 1

Silver Spurs: 10.3: 9

Bells & Whistles: 16.2: 5

I don't see any correlation between line count and SD.

The above list seems to assume maximum number of possible lines played in every slot. The last paragraph in my previous post addressed how the SD value of the slot increases when you play fewer than maximum number of lines. The correlation between # of lines and standard deviation was actually going to be my next topic. I'll get back to it tomorrow.

#### binary128

##### Dormant account
Jufo,

But if you're going where I think you're going:

1. Your result will be more confusion than clarification.

2. You're going to have trouble reconciling the SD for my two single-line slots.

Chris

#### Jufo

##### Dormant Account
What I was getting at in my previous posts was the relationship between slot's SD value and the number of lines. Chris, you might think this is adding confusion, but IMO this is relevant and needs to be addressed. I hope discussing this clears the confusion you had from my previous posts.

In the helpfile, Galewind's Hot Pepper slot is listed to have SD of 4.7 with maximum 20 lines played. Below are the SD values of this slot with different number of lines played, obtained from the slot simulator by simulating 20 million spins for each choice of # of lines. (I hope Chris that it is ok to post these):

Hot Pepper Slot - 15 lines = ~4.9
Hot Pepper Slot - 10 lines = ~5.3
Hot Pepper Slot - 5 lines = ~6.6
Hot Pepper Slot - 3 lines = ~8.7

'~' means "approximately". I had to use this notation because even in 20 million spins the estimated standard deviation values have decent margin of error.

Chris, you can verify the above numbers with the copy of the sim I sent you. (Shame on you if you haven't tried it already!)

What the above results show is that if you play Hot Pepper slot with only 3 lines it changes from lower-variance slot to much higher-variance slot. In fact you would have larger swings than by playing 20 lines in Gems of Isis (SD 7.1). This is of course assuming you keep the total bet size constant.

So what I was getting at in my previous posts, was that if you would rank the slots by choosing, say, 9 paylines for every slot (exluding those slots with fewer than 9 lines) then the order of the slots according to their variance might be completely different than what you have right now. Therefore your assignment for the number of lines affects the result of ranking. I wrote before that the "default" (most sensible) assignment would be to always choose max. lines when comparing variances but it's not the only possible choice.

I wrote before that Microgaming's Loaded slot has SD of 5.0 with max. 25 lines but SD of 6.5 with 9 lines. Thunderstruck has SD of 6.5 with 9 lines (=max.lines). I was just trying to see if the number of chosen lines explains KK's assignment of Thunderstruck being lower-variance than Loaded but the numbers didn't support this, so KK's assignment seems to be simply wrong.

This brings us to the topic of how players can control their variance

Even though players cannot influence how the slot operates and have to take it's behaviour as given, they do have plenty of control over the variance which is the topic of this thread. They have two parameters to control the variance: bet per line and number of lines. And these work differently.

Standard deviation is linear in terms of total bet size, so to have linear control over the variance, the players can simply lower or increase their bet size to get the desired variance.

For example, playing Gems of Isis (20 lines) \$1 per spin gives a standard deviation of \$7.1 per spin. Doubling the bet size to \$2 per spin doubles also the standard deviation to \$14.2 per spin. Notice however, that doubling the bet size quadrubles (not doubles) the variance.

However, players may seek higher variance but aren't comfortable with increasing their total bet per spin. They can accomplish this by switching from a lower variance slot to a higher variance slot, but they could also simply reduce the number of lines while keeping the total bet size constant. Like shown above, even a lower variance slot like Hot Pepper becomes rather high variance slot when you reduce the number of lines from 20 to 3. This means that despite the slot's behaviour being "cast in stone" there's a plenty of room for players to obtain a desired level of variance.

However, I often hear that players are not very willing to play fewer than maximum number of lines. This seems to relate to the feeling of frustration if there happens to be a big payout on a payline that wasn't chosen. But at the same time they don't consider that playing fewer than maximum lines also saves them money every time nothing hits on those paylines, so it all evens out.

I threw this out here because it would be interesting to hear opinions from players why they like/don't like to play fewer than maximum lines.

#### binary128

##### Dormant account
Well, the first thing I'm going to have to do is to add the qualifier to the Slot Stats file that all Standard Deviation and Variance values are based on the use of max lines wagered, min bet per line wagered.

Also, it is completely OK for you to publish any numbers that you wish concerning the Hot Peppers slot.

And yes, I hang my head in shame that I have not yet tried your sim. I offer no excuses.

Now, as to my statement that you will create more confusion than clarification:

Consider that the objective in all of this is to create for the Player some way to compare the Variance of all of the slots in a collection.

That is, a "recreational" Player who wants to maximize their spin time but is on a limited budget is going to want to play a slot with a lower variance. Someone with a larger stake who is looking for the "big score" and can afford the potential spin time needed to get it is going to be looking for a higher Variance slot.

Since both of your modifications (line bet count and line bet amount) increase the slot's Variance from its Theoretical Minimum, then one can say that the most effective way to allow a Player to compare one slot to another is to publish the minimum variance values, which will be realized with minimum bet amount and maximum line count.

I Started a Thread on this, and (perhaps by coincidence) this was the default - on load - configuration which won the vote.

It just occurred to me - perhaps I should refer to my currently published SD and Variance values as:

Theoretical Minimum Standard Deviation

Theoretical Minimum Variance.

Your data (modify the line count, modify the line bet) demonstrates how you can change an orange into an apple.

1. I agree it is relevant.

2. I agree that it is interesting, especially given the fact that with your sim, and absolute confidence in at least the Hot Peppers reel layout, you can play around with all sorts of different configurations and quickly see the quantitative impact.

3. If you think that this hasn't added a layer of confusion for the "recreational slot Player" then you, my friend, have been spending way to much time with that sim.

Why I agree that it is relevant. There were a couple of statements earlier in this thread by zap987 concerning the Gems of Isis slot:

Depends on the reel layout but the max possible win if you hit the top symbol is going to be about 700-1000xbet and that is the best you can ever hope for. Of course 1000x bet is a very good win and variance isn't only in how big wins you can get but also how often they happen and having played a lot of spins in fun mode it just feels like low to medium variance compared to real high variance slots. Just too much of the RTP in small hits and not enough in the big wins.

Sadly that does mean that it's another low variance slot ...

Both of these seem to indicate that zap987 is looking for a high-variance slot, and the default configuration of Gems is not meeting that requirement. Your numbers clearly demonstrate that he can achieve that increased variance in Gems by doing either of the modifications you've suggested above.

BTW, the one time that I suggested (even just as a question, rather than a statement or a directive) dropping the line count, I got Thoroughly Spanked by VWM.

Chris

#### Jufo

##### Dormant Account
I don't have much to add except a couple of short comments.

Consider that the objective in all of this is to create for the Player some way to compare the Variance of all of the slots in a collection.

That is, a "recreational" Player who wants to maximize their spin time but is on a limited budget is going to want to play a slot with a lower variance. Someone with a larger stake who is looking for the "big score" and can afford the potential spin time needed to get it is going to be looking for a higher Variance slot.

Since both of your modifications (line bet count and line bet amount) increase the slot's Variance from its Theoretical Minimum, then one can say that the most effective way to allow a Player to compare one slot to another is to publish the minimum variance values, which will be realized with minimum bet amount and maximum line count.

I Started a Thread on this, and (perhaps by coincidence) this was the default - on load - configuration which won the vote.

Yes I agree, Max lines (or Minimum Variance like you put it) seems to be the best way to rank slots according to their variance. Mostly because this is the setting that the vast majority of players are using anyway.

It just occurred to me - perhaps I should refer to my currently published SD and Variance values as:

Theoretical Minimum Standard Deviation

Theoretical Minimum Variance.

I don't think that's necessary. Many people wouldn't see the connection to max lines and would be confused what the above words refer to.

3. If you think that this hasn't added a layer of confusion for the "recreational slot Player" then you, my friend, have been spending way to much time with that sim.

Heh maybe my last bit did add confusion. But since I finally came here to write to this thread I thought that I will try to bring some new concepts to the table, even with the risk that the discussion is going to get a bit more involved. I wonder if anyone besides me and you is even reading this thread anymore

Both of these seem to indicate that zap987 is looking for a high-variance slot, and the default configuration of Gems is not meeting that requirement. Your numbers clearly demonstrate that he can achieve that increased variance in Gems by doing either of the modifications you've suggested above.

BTW, the one time that I suggested (even just as a question, rather than a statement or a directive) dropping the line count, I got Thoroughly Spanked by VWM.
Chris

Actually, I forgot to add to my last post that there is one crucial difference between increasing variance by increasing bet size and increasing it by dropping line count. If you increase the variance by doubling your bet size, the house edge per spin will double as well. At \$1 per spin, each spin costs you 3 cents on average, but at \$2 per spin each spins costs you 6c on average. However by dropping line count you can keep the bet size and house edge per spin constant and achieve increased variance for free. Therefore it's more "cost-efficient" to do it by dropping lines than by increasing bet size. This observation relates to the same concept mentioned earlier in this thread that a gambler should sometimes seek to minimize "house edge/variance" rather than house edge only. However, people value many different things when playing, such as the longitude of game play, and mathematically the most "effective" way of playing (that seeks to minimize long-term losses) is usually not the most entertaining.

#### binary128

##### Dormant account
OK, I added the line bet/lines bet disclaimer to the top of the file.

You may be right - we're the only ones in this conference room. Well, screw it - let's get a keg in here.

In addition to seeing it in the equations, I can also intuitively understand the increase in Variance associated with a decrease in paylines wagered.

However, I can't see the same thing with the bet amount. The SD applies to the RTP. RTP is a ratio. That is, bet 1000 and lose 100 is the same as bet 10 and lose 1. So, I can't intuitively understand how increasing the bet per line increases the SD.

I can see that it increases the absolute value of win/loss. Again, the example above - lose 100, or lose 1.

However, since SD (and thus Variance as SD squared) is relative to RTP, and RTP is not affected by bet size (as above) - explain to me what I'm missing here.

Chris

Edit: Reminder to self. Do the HE/Variance calculations to determine Galewind's "best" slot.

#### Jufo

##### Dormant Account
OK, I added the line bet/lines bet disclaimer to the top of the file.

You may be right - we're the only ones in this conference room. Well, screw it - let's get a keg in here.

In addition to seeing it in the equations, I can also intuitively understand the increase in Variance associated with a decrease in paylines wagered.

However, I can't see the same thing with the bet amount. The SD applies to the RTP. RTP is a ratio. That is, bet 1000 and lose 100 is the same as bet 10 and lose 1. So, I can't intuitively understand how increasing the bet per line increases the SD.

I can see that it increases the absolute value of win/loss. Again, the example above - lose 100, or lose 1.

However, since SD (and thus Variance as SD squared) is relative to RTP, and RTP is not affected by bet size (as above) - explain to me what I'm missing here.

Chris

Edit: Reminder to self. Do the HE/Variance calculations to determine Galewind's "best" slot.

Hmm there seems to be some severe misunderstanding of concepts here as I don't understand too much of your post. Well, since I am a teacher let's try to go forward...

Referring to your post above, house edge and variance/SD are independent parameters. They don't relate to each other. So I don't understand or agree with the statement "The SD applies to the RTP".

For example, the SD value of 4.7 for Hot Pepper slot (with 20 lines) means: standard deviation relative to unit wager, in other words unitary or normalized value. If you bet \$1, the SD is \$4.7 per spin (notice that the value will have a unit of dollar, it's not a unitless parameter). If you bet \$2 a spin, the SD is obviously \$2*4.7 = \$ 9.4 and so on. The unit SD value never changes, ie. it is always 4.7 but you obviously multiple this 4.7 by your bet size (\$1, \$2 or whatever). This means that if you double your bet, the standard deviation value of the bet (\$4.7 or \$9.4) doubles, while the "SD per unit bet" 4.7 always remains constant.

In contrast, when decreasing the number of lines, the "SD per unit bet" 4.7 is not a constant anymore, but varies according to number of lines. So these two settings (total bet amount and number of lines) affect the actual SD of the bet in two different ways.

Some examples of different bets in Hot Pepper slot:

#1
20 lines, \$5 bet per spin (\$0.25 per line):

SD = \$5*4.7 = \$23.5 per spin

#2
5 lines, \$3 bet per spin (\$0.60 per line):

SD = \$3*6.6 = \$19.8 per spin

#3
15 lines, \$15 bet per spin (\$1 per line):

SD = \$15*4.9 = \$73.5 per spin

It's these SD values that the player will observe (expressed in dollars), not the "SD per unit"-values in the help-file.

Now I am not sure if this was the exact thing what you tried to address in your post, but if it was, I hope this clears it up.

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#### ChopleyIOM

webby
You may be right - we're the only ones in this conference room. Well, screw it - let's get a keg in here.

I'm still reading, although the maths is starting to go over my head a bit

#### TheLastCylon

##### Banned User - violation of rule 1.19
You may be right - we're the only ones in this conference room. Well, screw it - let's get a keg in here.

No. I'm in here, too. So you may want to buy a second keg. I can really put it away.

#### binary128

##### Dormant account
Jufo,

For ease of access, Link Removed ( Old/Invalid) to the page in question.

Note my Definition of Terms for Standard Deviation. What you have just described completely contradicts everything in here. I'm OK with the contradiction. My goal is an accurate publication.

(Technically, we did not calculate the SD. We calculated the Variance (using the equation in my first post), and then just took the square root of that for the SD.)

Assuming SD as it applies to a normal distribution curve, what are your X and Y axis labels?

20 lines, \$5 bet per spin (\$0.25 per line): SD = \$5*4.7 = \$23.5 per spin. Given that 1 SD is "66% of the area under a normal curve", are you saying that 66% of the time your win on this spin will fall between what? 0 and \$23.5?

Chris

#### Jufo

##### Dormant Account
Jufo,

For ease of access, Link Removed ( Old/Invalid) to the page in question.

Note my Definition of Terms for Standard Deviation. What you have just described completely contradicts everything in here. I'm OK with the contradiction. My goal is an accurate publication.

(Technically, we did not calculate the SD. We calculated the Variance (using the equation in my first post), and then just took the square root of that for the SD.)

Ok I am trying to see what you mean. No, what I described doesn't really contradict what's in the page, it's more like what I described is not mentioned in the page.

What it says at the top:

"Please Note: The Standard Deviation and Variance values reported are based on using the minimum bet amount per payline, and the maximum payline count per slot."

This line should say something like

"Please Note: The Standard Deviation and Variance values reported are based on using unit bet size, and the maximum payline count per slot.

Now if you choose 20 lines at 0.05 coin (minimum coin) each spin happens to be at unit bet size, so your definition is accidentally correct but this is not what the published SD values really mean.

Note, that in the equation to calculate variance in the first post you are dividing the sum of payouts by total bet size, so in other words you are normalizing variance relative to unit bet size in that calculation. The equation in the first post is precisely the same one as the one my simulator uses for calculating the variance (and SD).

A bit further down it reads:

"The Standard Deviation values are associated with the Theoretical RTP values. They are an indicator of how far above or below these Theoretical RTP values your results might be given a reasonably large sample size."

This is correct in the sense that you can use the combination of both T-RTP and SD to measure how far the actual results will be from T-RTP in a sample. But SD and T-RTP are still independent parameters even though you can use them together to perform such a calculation.

I think it might be a good idea to alert Jacobsson and/or the Wiz to this thread, because they might be able to clear the confusion. They might have a different interpretation of these definitions than what I have presented.

Assuming SD as it applies to a normal distribution curve, what are your X and Y axis labels?

20 lines, \$5 bet per spin (\$0.25 per line): SD = \$5*4.7 = \$23.5 per spin. Given that 1 SD is "66% of the area under a normal curve", are you saying that 66% of the time your win on this spin will fall between what? 0 and \$23.5?

Chris

To use normal distribution curve requires that the result is normally distributed in the first place. The result of one spin is definitely not normally distributed, so you can't apply "66% of the area under a normal curve" to one spin, you can only do it to a sample of relatively large number of spins (
)

It's funny because this was exactly the topic that I was going to address next, ie. answer the following questions: how to use the known SD values to determine the range of results for a sample of N spins and how large sample (variable N) is needed so that the resulting distribution is close enough to normal distribution, so that such determination is mathematically valid? I warn though that the number of readers of this thread might drop to negative numbers.

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#### binary128

##### Dormant account
Jufo,

You are having fun with that sim, aren't you?

Actually, it was Eliot that wrote the section on Standard Deviation. It was also Eliot that suggested the addition of the chart in the Line Pay Hit Frequency section. (Your suggestions resulted in the addition of 2 more columns to this chart.)

If you could explain to me what "Unit Bet Size" means, then maybe I can make a modification to that introductory sentence that doesn't use that phrase, so that the average reader can understand.

It is my understanding that SD has to be associated with something. Example:

Measure the height of 10,000 men, then plot the results on a graph where the x axis is count and the y axis is height. (Assume a Standard Distribution, which is a reasonable assumption.) The peak of the curve is the mean, and 1 SD either way means that 33% of the sample is less than the mean and 33% of the sample is greater than the mean. (Total of 66% of the area under the curve.)

So, in this case SD is associated with the distribution of Height values.

If I publish SD values, what is the SD associated with? SD is associated with a distribution of values - to what distribution of values is this SD associated?

Re: your last paragraph. You're right - if ever there was a thread killer then that sounds like it. Personally, I'm going to vote that the required number will be smaller than expected. For Hot Peppers - 6,478. (Of course, that depends on the definition of "close enough to normal distribution".)

Chris

#### Jufo

##### Dormant Account
Jufo,

You are having fun with that sim, aren't you?

I don't follow you. In my previous post I clarified the confusion and severe lack of understanding you have with basic concepts, and explaining these concepts to you has absolutely nothing to do with the sim. So I really don't get or appreciate the above remark.

Actually, it was Eliot that wrote the section on Standard Deviation. It was also Eliot that suggested the addition of the chart in the Line Pay Hit Frequency section. (Your suggestions resulted in the addition of 2 more columns to this chart.)

There is nothing wrong with that section if you are trying to explain a complicated subject in two sentences. But it doesn't mean that all there is to be said about variance is there. You should still alert Eliot to this thread if you want to have assurance that what I have written is accurate, because you certainly seem to question it at every turn.

If you could explain to me what "Unit Bet Size" means, then maybe I can make a modification to that introductory sentence that doesn't use that phrase, so that the average reader can understand.

Sigh, what else can I say? "Unit bet size" is a bet of one unit. If I go to foreign exchange and change 100 euros to 150 dollars then the unit conversion rate is 1.5. It's not 150 even though I got 150 dollars and not 1.5 dollars. Are you being thick here on purpose?

It is my understanding that SD has to be associated with something. Example:

Measure the height of 10,000 men, then plot the results on a graph where the x axis is count and the y axis is height. (Assume a Standard Distribution, which is a reasonable assumption.) The peak of the curve is the mean, and 1 SD either way means that 33% of the sample is less than the mean and 33% of the sample is greater than the mean. (Total of 66% of the area under the curve.)

So, in this case SD is associated with the distribution of Height values.

If I publish SD values, what is the SD associated with? SD is associated with a distribution of values - to what distribution of values is this SD associated?

The SD is associated with the distribution of payouts that a single spin generates. When you play one spin you can win 0, or 10, or 200, or 2000 or 50000. SD measures how wide this range of possible payouts is, and the SD values in your help-file measure the range of payouts relative to unit bet size.

On further thought variance is always measured around the mean value (or average value) so in this sense, what I wrote before about SD and RTP being completely independent paramaters is inaccurate. Since variance is centered around the mean (or RTP), it's definitely correct to say that "variance is associated with RTP". So I stand corrected, that part of my previous post was wrong.

Re: your last paragraph. You're right - if ever there was a thread killer then that sounds like it. Personally, I'm going to vote that the required number will be smaller than expected. For Hot Peppers - 6,478. (Of course, that depends on the definition of "close enough to normal distribution".)
Chris

If you expect the number to be 6478 then why did you try in your previous post use normal distribution approximation to one spin? Some of stuff you write just don't make sense.

Upon further thought, the results in the next topic might actually be interesting to regular players. The results will, for example, answer the following question: If I play 2000 spins at specific slot, what is the probability that I will be ahead after those 2000 spins? I will calculate this probability both by using the normal distribution curve (= measuring the number of SDs from the T-RTP) but also by using the simulator. I anticipate that the simulator will give results that will shock you, and make a section of your help-file questionable if not plain wrong.

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#### binary128

##### Dormant account
Jufo,

First of all, I sincerely apologize for obviously really pissing you off. I don't know what else to say. I'm sorry.

I said "having fun with that sim" because I assumed that the work which you outlined in your last paragraph:

... how to use the known SD values to determine the range of results for a sample of N spins and how large sample (variable N) is needed so that the resulting distribution is close enough to normal distribution, so that such determination is mathematically valid?

would be long and tedious otherwise. Being long and tedious you would thus be disinclined to pursue it. I then assumed that the availability of your sim would make this work much easier, to the extent that generating statistical results which I agree would be very interesting would be "fun". Thus - "having fun with that sim". That's all I meant by that.

BTW, Eliot is in Cambodia right now, attending/speaking at a conference on Casino security.

Again, I apologize for making you so angry, or feeling so insulted.

Chris

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