Scattered Odds

[vinylweatherman]

I like to take 5 scatter

Yet again on a very low bet - conspiracy theorists - please form an orderly queue

[Zoozie]

I made the 'number of spins before hitting scatter' plot for ThunderStruck.

For Thunderstruck the probablity for hitting the feature each spin is p=0.007013636363636363

It is a Geometric_distribution which means that hitting the freespins on excactly spin #n (and not before!) is given by:

p(n)=p*(1-p)^(n-1) for n=1,2,3,........

You can add these numbers and thus getting the probability for hitting the
freespins before a given number of spins. This gives cdf(n)=1-(1-p)^n and this I have plotted (I just plotted the continious function, but it is actually only defined for the integer values on the x-axis).

Since it is hard to read the y-values for high values of x, here are some important numbers:

cdf(328)~0.900 (so 10% of the times you will have more than 328 spins before hitting the feature)
cdf(426 ) ~0.950
cdf(655) ~0.990 (so 1% of the times you will have more than 655 spins before hitting the feature)
cdf (982) ~0.9990
cdf(1309)~0.999900
cdf (1636)~0.999990

So if you did not hit the freespins in 982 spins it was about a 1/1000.

Still bad luck, but not that rare.

Edit:data file(txt) included

Zoozie

[Rettahs]

cdf(655) ~0.990 (so 1% of the times you will have more than 655 spins before hitting the feature)

Zoozie

I think I am 99% of that 1% across all thunderstruck play :-). Thank you for taking the time to calculate the odds.

[vinylweatherman]

Munchkins today, after a break of a fortnight.

During a free spin round, again super micro betting 15p a spin, the Munchkins got to chow down on 5 scatters. This pays a mere 120x bet in this case, not as good as getting them on Thunderstruck.

[gerilege]

I made the 'number of spins before hitting scatter' plot for ThunderStruck.

For Thunderstruck the probablity for hitting the feature each spin is p=0.007013636363636363

It is a Geometric_distribution which means that hitting the freespins on excactly spin #n (and not before!) is given by:

p(n)=p*(1-p)^(n-1) for n=1,2,3,........

You can add these numbers and thus getting the probability for hitting the
freespins before a given number of spins. This gives cdf(n)=1-(1-p)^n and this I have plotted (I just plotted the continious function, but it is actually only defined for the integer values on the x-axis).

Since it is hard to read the y-values for high values of x, here are some important numbers:

cdf(328)~0.900 (so 10% of the times you will have more than 328 spins before hitting the feature)
cdf(426 ) ~0.950
cdf(655) ~0.990 (so 1% of the times you will have more than 655 spins before hitting the feature)
cdf (982) ~0.9990
cdf(1309)~0.999900
cdf (1636)~0.999990

So if you did not hit the freespins in 982 spins it was about a 1/1000.

Still bad luck, but not that rare.

Edit:data file(txt) included

Zoozie

I learned that many people use variable bet size for slots. They play some rounds betting their base bet, then they continuously increase the number of coins if they don't hit the feature. Given that, if I take a look on your chart, the followings makes me wonder:

The derivative becomes less than 0.5 somewhere around 250. That means that the chance of hitting the feature within x spins increases more than linear by increasing the number of spins until that point, but after that the chance increases only slightly, less than linear. Of course the probability of hitting is the same on each independent spin, but it might mean that the progressive betting makes less sense after reaching that point where the derivative becomes less than 0.5.

I'm a bit tired yet, so probably I misunderstood something, but still, what do you think?

[Zoozie]

The derivative becomes less than 0.5 somewhere around 250. That means that the chance of hitting the feature within x spins increases more than linear by increasing the number of spins until that point, but after that the chance increases only slightly, less than linear. Of course the probability of hitting is the same on each independent spin, but it might mean that the progressive betting makes less sense after reaching that point where the derivative becomes less than 0.5.

Absolutely not.

Increasing bet-size as you describe is just the Martingale-system for slot. Most of the time it works and you win a little, but sometimes you lose a gigantic amount and if you add what you win and what you lose. And the average lose is larger because of the larger bet. A horrible solution, especially on slots.

There is no memory in the spins. The geometric distributions tell what the probability is that you will not hit the feature in the NEXT 250 spins etc. So if you are not hitting it in 250 freespins, you then start from scratch again and it is the same probability not hitting them the next 250 spins again.

Zoozie

[Slotster!]

Absolutely not.

There is no memory in the spins. The geometric distributions tell what the probability is that you will not hit the feature in the NEXT 250 spins etc. So if you are not hitting it in 250 freespins, you then start from scratch again and it is the same probability not hitting them the next 250 spins again.

Zoozie

This is, of course, mathematically and statistically correct. In reality however, you just generally do - eventually. By gradually increasing your bet, you stand a better chance of recouping previous losses.

Like you intimate though, I've lost a shit load before now when it just never ever hits...

[gerilege]

Absolutely not.

Increasing bet-size as you describe is just the Martingale-system for slot. Most of the time it works and you win a little, but sometimes you lose a gigantic amount and if you add what you win and what you lose. And the average lose is larger because of the larger bet. A horrible solution, especially on slots.

There is no memory in the spins. The geometric distributions tell what the probability is that you will not hit the feature in the NEXT 250 spins etc. So if you are not hitting it in 250 freespins, you then start from scratch again and it is the same probability not hitting them the next 250 spins again.

Zoozie

I didn't want to suggest that progressive betting does any good. Slots take your money, whatever you do, that's no question.

Progressive betting was just a realistic example, although it is not necessary. Each session has always a first spin, so let's stop before that first spin, and just take a look on that geometric distribution before you indeed make the first spin. You know that you have
-~40% percent that you don't hit the feature within 140 spins
-~15% chance that you don't hit the feature within 250 spins
-~5% that you don't hit within 426 spins.

Again, you have not yet started to do the first spin, you just would like to plan how much to spin if you don't hit. Your strategy would be to hit the feature if possible, or quit after a fixed number of spins. I know that the most +EV would be not to play slots at all, but in a realistic situation I guess this is how most people play slots. They don't really mind how much did they put in, and they can't do nothing with the feature payout, they just want the feature. You see that planning to make 250 spins instead of 140 if you don't hit decrease the chance that you do not hit at all by 25 percent. But planning 426 spins instead of 250 decrease the chance only by 10 percent. So before the first spin planning 110 more (250 instead of 140) spins decrease the chance of not hitting by 25 percent, while planning 176 more (426 instead of 250) spins spins decrease the chance of not hitting at all only by 10 percent.

So if someone regularly play slots in a way I described, from the bankroll and strategy management view, by fixing the first spin there should be a planned threshold somewhere (OK I know zero spin is the threshold), where it makes less sense to play on any more on the long run, and book the losses, and this is what I wanted to mention with the derivative, but I'm really tired, and I still can be completely wrong.

[Zoozie]

Again, you have not yet started to do the first spin, you just would like to plan how much to spin if you don't hit. Your strategy would be to hit the feature if possible, or quit after a fixed number of spins. I know that the most +EV would be not to play slots at all, but in a realistic situation I guess this is how most people play slots. They don't really mind how much did they put in, and they can't do nothing with the feature payout, they just want the feature. You see that planning to make 250 spins instead of 140 if you don't hit decrease the chance that you do not hit at all by 25 percent. But planning 426 spins instead of 250 decrease the chance only by 10 percent. So before the first spin planning 110 more (250 instead of 140) spins decrease the chance of not hitting by 25 percent, while planning 176 more (426 instead of 250) spins spins decrease the chance of not hitting at all only by 10 percent.

Okie, I believe I understand what you are talking about now. Still it is just
a Martingale system, but using the chart to construct a betting system for slots. And using the chart you can construct a betting system with this property:

Following the betting system you will win 99% of the times statistically over 1000 spins. (if you are ahead at some time, then stop)
However the last 1% of the times you will lose your house, wife,dog, liver and whatever can be sold etc.

But also remember that that even hitting the feature only gives 35*(bet-size) in average wins for Thunderstruck, so a betting system to do what described above still has to be 'aggressive'.

Zoozie

[gerilege]

Okie, I believe I understand what you are talking about now. Still it is just
a Martingale system, but using the chart to construct a betting system for slots. And using the chart you can construct a betting system with this property:

Following the betting system you will win 99% of the times statistically over 1000 spins. (if you are ahead at some time, then stop)
However the last 1% of the times you will lose your house, wife,dog, liver and whatever can be sold etc.

But also remember that that even hitting the feature only gives 35*(bet-size) in average wins for Thunderstruck, so a betting system to do what described above still has to be 'aggressive'.

Zoozie

No, no betting system, nothing. First of all let's forget the progressive betting completely, and stick to flat betting, it doesn't really matter. I understand that no system could produce winnings. No winnings, it's all about minimizing losses with the typical human style for playing slots, which is -EV.

The question is only whether a point or an interval exists besides zero which if you fix before beginning to play, and stick to it, and you don't get the feature, then it is relatively significantly better to stop there than in any other interval later (absolute case is obvious, sooner is better).

With other words, if you don't get the feature:
Stopping after 0 spins is the best, and it is infinitely better than stopping after 1 spins.
Stopping after 1 spins is the second best, and it is x times better than stopping after 2 spins.
Stopping after 2 spins is the third best, and it is y times better than stopping after 3 spins.
And so on. (and that can be extended more generally, like stopping after 42 spins is the forty-third best, and z times better than stopping after 987654321 spins.) These x,y, etc. values should be on a curve.

Please note that it is always assumed that you don't get the feature and you will stop after the planned spins, and you go for the feature by all means. It's obvious that the more you spin, the more you lose. But adding another spin to the planned stop point might have different effect in different intervals.

For instance planning 4 spins instead of 2 might be a relatively better (or worse) decision than planning 22 spins instead of 20, although it costs the same. The question is whether such difference might exist or not.