Slot Mechanics (Was: Fruit Frenzy Game glitch or frenzy?)

[DogBoy001]

He also states that previous results are never taken into account for the RNG engine when balancing occures. Well - to me this is a contradiction, since a balance algorythm has to use some sort of data. If previous data is not use what do we then use? Future data? And if the goal is 95% payout, which the system will balance somewhere to fullfill, what perspective are we talking here? Is this based on a player session, in $10.000 worth of spins, coin sizes of 10 million spins? It sure seems I meet 95% payout quite quickly when flatbetting any MG casino at $9, do not need 10 million spins to acomplish this.

RTG slots, as with the vast majority of random bricks-and-mortar slots, have RTPs that are the return to player you would receive from the game if every combination in the total cycle of the game hit once and once only, and if every feature probability table hit exactly in line with listed probability (e.g.: If a random pick feature has a 25% chance of awarding 5 free games, 50% of awarding 10 free games and 25% of awarding 15 free games and over the life of the game cycle each hit exactly to those settings).

However, since these are random games you will always get variation from the expected RTP.
Say the top symbol only occurs once on each reel, with each reel being say 30 long, the combinational calculations that the 95% is based on would expect that over the cycle of 24.3M possible combinations this would only hit once.
However it's entirely possible to hit this in consecutive spins, since at no time is there a track of previous results or current RTP from the game that would influence the result of any spin.

We use 95% confidence tables (1.96 standard deviations either side of mean) to determine expected RTP, which on a 95% game can range hugely in small numbers of games and operators know that they stand the chance to be substantially negative on a game (so RTP over 100%).
Over the long term, with large numbers of spins (e.g.: 50 million spins), we'd expect to see the game be pretty close to the 95% RTP.

Individual results over several thousand spins will vary enormously.
For example, Goldbeard might have a table looking like this:

95% Confidence for single credit bet
Games played Range +/- Max Min
1,000 +/-58.528 153.634 36.578
5,000 +/-26.174 121.281 68.932
50,000 +/-8.277 103.383 86.829
1,000,000 +/-1.851 96.957 93.255
50,000,000 +/-0.262 95.368 94.845

That's the way random games work...they're volatile has hell in RTP in small bursts of games...people who believe that playing a couple of thousand spins is going to yield something around 95% every time are gravely mistaken.

The odds are in the house's favour, but by the same token, it means that players can win.

Wooof

 

[RobWin]

Symbols are in a set, static order, with every stop on the reel strip having an equal probability of being hit on any given spin.

Wooof

I call Bulls**t on that statement, if that were truly the case then you would see a hell of a lot more top pay wins than what we now see !!

 

[steinhaug]

By the way, thanks for responding here, I appretiate it!

95% Confidence for single credit bet
Games played Range +/- Max Min
1,000 +/-58.528 153.634 36.578
5,000 +/-26.174 121.281 68.932
50,000 +/-8.277 103.383 86.829
1,000,000 +/-1.851 96.957 93.255
50,000,000 +/-0.262 95.368 94.845

Just a quick question here, since I am a little new to statistical calulations.

Would this: 1,000 +/-58.528 153.634 36.578

Sum up to:
Doing 1000 spins on $1 wager, giving $1000 wagered total. Wining above $1536 is considered impossible statistically?

 

[steinhaug]

I love being mis-quoted, but I did clear up in this thread what I mean by reel strip changes, having misunderstood the discussion of "dynamic", so please don't take isolated quotes and ignore the rest of the information.

Symbols are in a set, static order, with every stop on the reel strip having an equal probability of being hit on any given spin.
Win evaluation is subsequent to the reel stop locations being randomly determined.

I was reading this thread and wasn't quoting anything however my perception after reading was that you may alllow for certain symbols to be altered on the fly to fit a certain win, twisting the entire slot logic, since the illusion is that the reels determine the win - however in this case the win determins the reels. Needless to say, two entirely different approaches to reaching the expected RTP.

So to correct this what you are saying is this, and we are talking theory:
When the game session starts, the casino software may alter the reels (switching symbols) to balance something. The changes will never happen in-game - but can only change at session start. However - this is only practised by the operator and can only be set once a month due to restrictions in the software itself.

(At MG for instance, when you boot up a particular game engine the reels are served to the visualization-engine, so your point that the game doesn't need to update itself is correct. The flash games do not store the reels, only the symbols, the reels are buildt on the fly all the time. Luckily I have programming experience in game design myself so this part is the easy one,

 

[DogBoy001]

By the way, thanks for responding here, I appretiate it!



Just a quick question here, since I am a little new to statistical calulations.

Would this: 1,000 +/-58.528 153.634 36.578

Sum up to:
Doing 1000 spins on $1 wager, giving $1000 wagered total. Wining above $1536 is considered impossible statistically?

Heya,

No, the data above covers 95% of the distribution curve, extremes to both ends are entirely possible.
This means that, statistically, 95% of results for groups of 1000 spins will result in a return ranging from 36.578% RTP to 153.634% RTP, for the 95% RTP version that this is based on.

If you were to look at 90% confidence (covering 90% of results statistically), the calculation would change slightly, and would yield a range of +/-49.122%, so an expected min/max of 45.985% and 144.228%. However, 10% of results will be outside these expected values, and some will be on the extreme of either end.

Wooof

 

[DogBoy001]

I call Bulls**t on that statement, if that were truly the case then you would see a hell of a lot more top pay wins than what we now see !!

Heya,

I'm not saying every symbol has the same change of hitting, I'm saying every stop has the same chance of hitting.

If you have a reel that looks like this...

Symbol: Reel 1
Goldbeard 3
Coin 1
Galleon 2
Parrot 2
Cannon 3
Treasure Chest 3
A 5
K 7
Q 6
J 6
10 6
9 6
Total: 50

...then you're obviously going to have 50 stops and some symbols will appear more than others.

How do you equate this to achieving more top pays?
If there's one of each top symbol as in my example, how can you possibly say that the odds are greater than 1 in 24.3M?

Wooof

 

[DogBoy001]

I was reading this thread and wasn't quoting anything however my perception after reading was that you may alllow for certain symbols to be altered on the fly to fit a certain win, twisting the entire slot logic, since the illusion is that the reels determine the win - however in this case the win determins the reels. Needless to say, two entirely different approaches to reaching the expected RTP.

I've iterated and reiterated that the RTG system is a truly random one, with reel stops determined and then win evaluation, not the other way around.

There are some systems that use the functionality of "determine win and then display appropriate combination", but RTG is not one of them.
There is only one major class that I can think of that falls into this category, and it's land-based and used as a means to have slot display of what is essentially a bingo back end.

So to correct this what you are saying is this, and we are talking theory:
When the game session starts, the casino software may alter the reels (switching symbols) to balance something. The changes will never happen in-game - but can only change at session start. However - this is only practised by the operator and can only be set once a month due to restrictions in the software itself.

The only alterations that can be made are the decision between the different RTP options that are available, all of which are located within a small RTP range of each other.

These can be changed periodically, but yes, it's not something that be done on a day by day or even week by week basis.

(At MG for instance, when you boot up a particular game engine the reels are served to the visualization-engine, so your point that the game doesn't need to update itself is correct. The flash games do not store the reels, only the symbols, the reels are buildt on the fly all the time. Luckily I have programming experience in game design myself so this part is the easy one,

On RTG games all reels have a set, static order, for example (I don't usually use specific maths examples but I will do so in the hope that it clarifies things):

Pos.: Reel 1
1 A
2 10
3 Cannon
4 Q
5 Goldbeard
6 Goldbeard
7 Goldbeard
8 J
9 Coin
10 9
11 K
12 Q
13 Galleon
14 K
15 A
16 J
17 Treasure Chest
18 10
19 A
20 Q
21 Galleon
22 K
23 9
24 Q
25 K
26 J
27 Parrot
28 10
29 J
30 Treasure Chest
31 Q
32 9
33 Cannon
34 K
35 10
36 A
37 9
38 Treasure Chest
39 J
40 K
41 10
42 A
43 9
44 Cannon
45 Q
46 10
47 K
48 J
49 9
50 Parrot

The stop position on each reel is independently determined by the RNG, with the spin then showing a sequence above the last stop position before cutting to the reel section leading up to the stop position that the RNG has now determined.
In the example above there are 50 stop positions on reel one, each of which has the same chance of being hit as any other (the stop position then becomes the position on the centre row of the display).
So if the RNG says stop 47 it will animate and spin to stop on

10
K
J

If the RNG says stop 5 then it would stop on

Q
Goldbeard
Goldbeard

Wooof

 

[RobWin]

Heya,

I'm not saying every symbol has the same change of hitting, I'm saying every stop has the same chance of hitting.

If you have a reel that looks like this...

Symbol: Reel 1
Goldbeard 3
Coin 1
Galleon 2
Parrot 2
Cannon 3
Treasure Chest 3
A 5
K 7
Q 6
J 6
10 6
9 6
Total: 50

...then you're obviously going to have 50 stops and some symbols will appear more than others.

How do you equate this to achieving more top pays?
If there's one of each top symbol as in my example, how can you possibly say that the odds are greater than 1 in 24.3M?

Wooof

Well you said that: "symbols are in a set, static order, with every stop on the reel strip having an equal probability of being hit on any given spin."

So if that is the case and say there is only one top pay symbol per reel for argument sake and every stop on the reel strip has an equal probability of being hit on any given spin then it only makes sense that the top pay could be hit just as often as any other random hit...based on your previous statement there...

Remember you did say "with every stop on the reel strip having an equal probability"

 

[DogBoy001]

Well you said that: "symbols are in a set, static order, with every stop on the reel strip having an equal probability of being hit on any given spin."

So if that is the case and say there is only one top pay symbol per reel for argument sake and every stop on the reel strip has an equal probability of being hit on any given spin then it only makes sense that the top pay could be hit just as often as any other random hit...based on your previous statement there...

Remember you did say "with every stop on the reel strip having an equal probability"

Heya,

Yes, and if you had 13 symbols and had only 13 stop positions then your argument would be valid.

If you have 13 symbols and varying numbers of those symbols, then symbols that are less likely to occur will occur less often.
If there are 50 total stop positions and each has a 1 in 50 chance, but 3 might have a K for example and only 1 a Substitute, then the K is 3 times more likely to come up.

Seems pretty straight forward to me.

Wooof

 

[RobWin]

If there are 50 total stop positions and each has a 1 in 50 chance, but 3 might have a K for example and only 1 a Substitute, then the K is 3 times more likely to come up.
Wooof

Not if each stop truly has a one in fifty chance, it wouldn't matter if there were 49 kings and only 1 top pay symbol if each one of the fifty stops has a one in fifty chance of coming up...or a 2% chance overall

Whereas in your analogy the king should have a 3 in 50 chance of coming up if it is three times more likely to come up...or rather a 6% chance...or further still a 200% greater chance of coming up than the other that is only 1 in 50..

 

[KasinoKing]

Not if each stop truly has a one in fifty chance, it wouldn't matter if there were 49 kings and only 1 top pay symbol if each one of the fifty stops has a one in fifty chance of coming up...or a 2% chance overall

Whereas in your analogy the king should have a 3 in 50 chance of coming up if it is three times more likely to come up...or rather a 6% chance...or further still a 200% greater chance of coming up than the other that is only 1 in 50..

Rob I think you need to forget your argument for a few hours then come back & read it again.
Sorry mate, but your talking nonsense.

KK

 

[RobWin]

Rob I think you need to forget your argument for a few hours then come back & read it again.
Sorry mate, but your talking nonsense.

KK

You probably right KK...I'm kinda in a fog right now...LOL

 

[DogBoy001]

Not if each stop truly has a one in fifty chance, it wouldn't matter if there were 49 kings and only 1 top pay symbol if each one of the fifty stops has a one in fifty chance of coming up...or a 2% chance overall

Whereas in your analogy the king should have a 3 in 50 chance of coming up if it is three times more likely to come up...or rather a 6% chance...or further still a 200% greater chance of coming up than the other that is only 1 in 50..

Heya,

I think you're misunderstanding probability, if you think that 49 K in spearate positions on a 50 long strip does not equate to a 49 in 50 chance of a K occurring in a random system.

On a non-random system it would not matter how the reels were laid out, or what the distribution was, because in a non-random system you would simply display whatever suited.

In the above example there are 7 separate instances where the random determination of stop position between stop 1 and stop 50 will yield a K on the centre row.
There are less instances of some other symbols.
These symbols will occur, in all probability, less than the K will.
That is how random systems with differing reel strip distribution function.

I'm still trying to grasp how you see the above example being anything other than this.

Woooof

 

[RobWin]

Heya,

I think you're misunderstanding probability, if you think that 49 K in spearate positions on a 50 long strip does not equate to a 49 in 50 chance of a K occurring in a random system.
On a non-random system it would not matter how the reels were laid out, or what the distribution was, because in a non-random system you would simply display whatever suited.

In the above example there are 7 separate instances where the random determination of stop position between stop 1 and stop 50 will yield a K on the centre row.
There are less instances of some other symbols.
These symbols will occur, in all probability, less than the K will.
That is how random systems with differing reel strip distribution function.

I'm still trying to grasp how you see the above example being anything other than this.

Woooof

Thanks for all the replies Dogboy, I actually do think that 49 K's would have a 49 in 50 chance of coming up but I guess what I'm getting at based on the last few posts from both you and I is the stops actually don't have a 1 in 50 chance of hitting on any given spin since you originally said "every stop on the reel strip has an equal probability of being hit on any given spin" so based on the number of random symbols per reel strip and each one of those symbols representing so many stops per each 50 then the 1 in 50 probability does not seem attainable.......

49 Kings would represent 49 stops out of 50 possible stops total, so how does that equate into a 1 in 50 probability of being hit on any given spin ??

 

[DogBoy001]

Thanks for all the replies Dogboy, I actually do think that 49 K's would have a 49 in 50 chance of coming up but I guess what I'm getting at based on the last few posts from both you and I is the stops actually don't have a 1 in 50 chance of hitting on any given spin since you originally said "every stop on the reel strip has an equal probability of being hit on any given spin" so based on the number of random symbols per reel strip and each one of those symbols representing so many stops per each 50 then the 1 in 50 probability does not seem attainable.......

49 Kings would represent 49 stops out of 50 possible stops total, so how does that equate into a 1 in 50 probability of being hit on any given spin ??

Heya

It wouldn't...it would be 49 in 50.

I think we agree that if it's a random system then that's the way it works. I think the disagreement is that I'm saying it is a random system, but you're not (?).
So I'm saying that if a reel had 49 out of 50 K, it would be a 49 in 50 chance to have a K hit on the centre reel position, whereas you're saying it wouldn't because you think it's non-random?

Either way it's enough to confuse my brain to the point where sleep is certainly required.

Even the example I've posted with respect to Goldbeard should be enough to show how the system functions (which is a truly random one).
Go have a play (in free or real mode it makes no difference), and check reel 1 stops against the 50.

Play enough and you should be able to compile statistics that indicate each stop is hitting as much as any other (bearing in mind that statistically you will get variance in any given period of play and some will hit more than others, particularly over shorter groupings of gameplay. In the long run, as with any random game, it is highly likely that stops will have been hit a similar number of times)

Wooof

 

[steinhaug]

On RTG games all reels have a set, static order, for example (I don't usually use specific maths examples but I will do so in the hope that it clarifies things):

This is the same as with MG, as I noted. The reel strips are served the visualization engine (read: flash part) on startup - and the reel stips are buildt on the fly. Since they do not change the order from time to time, this means they are in static order... However, they could in theory and real world change in a split second and you do not need to update anything to do so. The player would never see the difference, unless reading the network traffix and comparing present reelstrip configuration with previous configurations.

As an example, say you have this reel strip:
Reel 1:
Symbol 1: 8
Symbol 2: 9
Symbol 3: 10
Symbol 4: 11
Symbol 5: J

Or in shorter terms: 8,9,10,11,J

Instead of compiling this into the game, all you need to do is serve the visualization engine theese numbers and let it visually buildt the reel. The visualization engine has no interest or knowledge what a win is, it spins when it's told do and it blinks when it's told to. However you already know this. I do not believe that your system should be that different from MG, if not you should loke into MG system since it's kinda brilliantly made!

Anyway, my point was, that when the game boots up the strip sequence could change right there. It can even change in-game, looking at how the visualization engine work. To clearly see how this is possible you will have to look at the data feed between the casino and the visualization engine.

On the other hand, this is a side note and has only to do with the game mechanics which I do not have interest in - I am interested in the RNG engine.

The argument is that it is always flawless and fair - it has not been tampered with - we are just experiencing chaos theory we are told.

 

[DogBoy001]

This is the same as with MG, as I noted. The reel strips are served the visualization engine (read: flash part) on startup - and the reel stips are buildt on the fly. Since they do not change the order from time to time, this means they are in static order... However, they could in theory and real world change in a split second and you do not need to update anything to do so. The player would never see the difference, unless reading the network traffix and comparing present reelstrip configuration with previous configurations.

As an example, say you have this reel strip:
Reel 1:
Symbol 1: 8
Symbol 2: 9
Symbol 3: 10
Symbol 4: 11
Symbol 5: J

Or in shorter terms: 8,9,10,11,J

Instead of compiling this into the game, all you need to do is serve the visualization engine theese numbers and let it visually buildt the reel. The visualization engine has no interest or knowledge what a win is, it spins when it's told do and it blinks when it's told to. However you already know this. I do not believe that your system should be that different from MG, if not you should loke into MG system since it's kinda brilliantly made!

Anyway, my point was, that when the game boots up the strip sequence could change right there. It can even change in-game, looking at how the visualization engine work. To clearly see how this is possible you will have to look at the data feed between the casino and the visualization engine.

On the other hand, this is a side note and has only to do with the game mechanics which I do not have interest in - I am interested in the RNG engine.

The argument is that it is always flawless and fair - it has not been tampered with - we are just experiencing chaos theory we are told.

Heya,

I've experienced systems that build on the fly (3 symbols are randomly selected via a probability schedule for each reel for each spin).

Personally I've always found that this method is vastly inferior to static reel strip layout.
As I player I like to know that there's a set order to the reel, as in most regular land-based machines.
Building via a schedule also creates issues in calculating return and testing on multi-line games. In a fixed order you have the ability to accurately simulate all possible combinations (full cycle test), and the RTP over the cycle should match theoretical calculations exactly.
Building on the fly you have to test (n) spins and it will be roughly within a range, but will not be precise, since it introduces variance into the reel composition itself.
In some B&M jurisdictions this is specifically excluded by regulators.

Building on the fly also allows software providers to make changes to the probability schedule that will not be immediately obvious to the players.
In a static reel strip order it's usually apparent if a change to the order is made.

RNGs are a little out of my field of expertise.
Expected return over short periods of game play (which can include as per the above example quite substantial numbers of spins) is always going to be volatile, so in my opinion wild fluctuations in RTP (to both extremes) are not entirely unexpected.

Woooof

 

[quber]

Kimms: Dogboy already confirms this, he already states that a system with a low payout will balance this out with tweaking the symbols to present higher wins than possible to achieve a higher payout to balance out. This would explain the obvious win cycles...

Kimms, This bit that you quote from dogboy001 was his reference to UK AWP machines which we all know are not random.

And Robwin, I think you were just getting confused between symbol and stop positions, on the goldbeard example given each stop position had a 1 in 50 chance of hitting however this would result in the K symbol showing 7 times to every 1 coin symbol as the K has 7 different stop positions

 

[Fleur-De-Lis]

It is an amazing thread, way more profound and important than OP that triggered it. Anyway, I just thought I'll post an update, since my loooong issue with KS seems finally resolved: I got a letter (only few months later ) confirming that the glitch I reported is indeed discovered and by now taken care of.

I am sorry for the late reply but our technicians just got back to us.
You were right, there was a glitch on the game.
This didn't affect the players, as the payout ratio was not affected.
The technicians from our software have now fixed the problem.

 

[gerilege]

Scatters and feature event probabilities

Dogboy, could you please do me a favor and answer a specific and a general question?
The specific one. A few weeks ago I got 5 archery boards on Prince of Sherwood. In the first round I got 2xbet for the opponent, 5xbet for my player, and I got 15 or 20 spins at 3x. Does the hidden 'picking' probabilities change in this game when you trigger the feature by more than 3 boards? If yes, I believe it should be included in the help section. If not, then I think it's a design flow as why the boards are on the last two reels? I'm asking because most of the time I get 2x and 5x in the first round when I get 3 boards, and now I got 5 boards, but the award was the same. The only difference was that I was awarded more free spins.
The general one. Is there any other games when the number of feature trigger symbols might implicitely relate to the feature awards, I mean Warlock's Spell could be an example.

 

[DogBoy001]

Dogboy, could you please do me a favor and answer a specific and a general question?
The specific one. A few weeks ago I got 5 archery boards on Prince of Sherwood. In the first round I got 2xbet for the opponent, 5xbet for my player, and I got 15 or 20 spins at 3x. Does the hidden 'picking' probabilities change in this game when you trigger the feature by more than 3 boards? If yes, I believe it should be included in the help section. If not, then I think it's a design flow as why the boards are on the last two reels? I'm asking because most of the time I get 2x and 5x in the first round when I get 3 boards, and now I got 5 boards, but the award was the same. The only difference was that I was awarded more free spins.
The general one. Is there any other games when the number of feature trigger symbols might implicitely relate to the feature awards, I mean Warlock's Spell could be an example.

Heya,

Yep, the probability schedules that are used to determine what the selected and opposing archers, as well as any subsequent shots in rounds 2 and 3, are different based on the number of scatters triggering the feature.

On a 5 scatter trigger, for instance, there is almost no chance of not progressing and the average number of free games awarded is over 17, with an average multiplier of over 4.
This gives additional impact for 4 or 5 scatter triggers, but rather than advertise items such as this within the pay table we tend to leave these as "nice surprises" that players find.

As for other games that have higher non-advertised bonuses for 4 or 5 scatter triggers, there aren't that many, as the norm is to have the higher scatter prize which gives an apropriate reward in lieu of changing probabilities inside the feature itself (I say non-advertised because some games in the suite award an indicated higher number of free games for 4 or 5 scatters, while others like the White Diamond pick feature in Diamond Dozen or the extra picks in Aladdin's Treasure, Sunken Treasure or Mister Money are obvious benefits).

In fact I think Green Light may be the only similar one. This one doesn't change the race probabilities, but the chance of Lights turning Green and triggering is increased greatly when 4 or 5 Lights appear.

Something to look for in coming months though


Woooof

 

[gerilege]

This gives additional impact for 4 or 5 scatter triggers, but rather than advertise items such as this within the pay table we tend to leave these as "nice surprises" that players find.

Thanks for the clarification. I could accept your argument in case it would be guaranteed that a higher number of triggering symbols results in a "better" feature each and every time.
I understand that as long as getting the absolute top award on a 3 scatter trigger has non-zero probability, it can't work that way. But still I feel that the fact that you have a chance to hit a "poorer" feature on a higher number of scatters than one that you might get on 3 scatters is a bit counterintuitive.
I know no other example at other sw providers where you could get less with 4 scatters than with 3 scatters. I - don't know about other slot players - would rather prefer straightforward intervals, even if I would completely lose the chance to hit top award on 3 scatters. With the archery board example, for instance on the free spin shot, I would prefer to have for instance something like a board of 5,7,10,12,13,15,17,19,23,25, and 3 scatters would shot to 5-12, 4 scatters to 12-17 and 5 scatters to 17-25.

Green light is slightly different and ok, as it is understandable that a light is not always a feature trigger, it has to be green to become that. The increased "turning green" probability is only an extra, as having more lights (= more chance to turn to green) is already an incentive for more scatters in itself, just like in case of the lamps in Aladdin.

 

[DogBoy001]

But still I feel that the fact that you have a chance to hit a "poorer" feature on a higher number of scatters than one that you might get on 3 scatters is a bit counterintuitive.
I know no other example at other sw providers where you could get less with 4 scatters than with 3 scatters. I - don't know about other slot players - would rather prefer straightforward intervals, even if I would completely lose the chance to hit top award on 3 scatters.

Heya,

Looking back on it we might have done better to still have the chance to hit the top award on a 3 scatter trigger, but introduce nil chance of not progressing to round 2 and 3 for 4/5 scatters, and again have a nil chance of the minimum number of games and multiplier for higher trigger events.

The overall RTP consumption probably wouldn't have been that high, so you're right in pointing out that the design probably wasn't 100% as good as it could have been.

Certainly something we'll bear in mind with future feature design.

Wooof

 

[Rusty]

Question for DogBoy;

How many symbols are there on the first reel in Diamond dozen?

 

[DogBoy001]

Question for DogBoy;

How many symbols are there on the first reel in Diamond dozen?

Heya,

30:

Symbol: Reel 1
White Diamond 1
Blue Diamond 2
Man 2
Woman 2
Ring 3
Rose 2
Purse 2
A 2
K 3
Q 2
J 3
10 3
9 3
Total: 30


Wooof