Probability and % chance

[Simpo Two]

I'm having a discussion with an online game's tech support department.

One action has a declared '20% chance' of happening, yet it seemed to be occurring much more for the computer's side than for my side.
So I contacted them to see what they said...

'I've now fought many battles where 'keen eye' units are involved, and whilst I haven't collected the data, I'm fairly certain that enemies get a lot more than 20% and I get a lot less. For example I've just been hit by 3 in a row - that's a 0.008% probability. And frequently it's two in a row, which doesn't make statistical sense. Is there any way the 20% can be influenced?'

They replied: 'While statistically it might be correct, yet this is a 20/80% chance. That means each single hit you have the same 20/80 chance and again and again. Like throwing a coin. it means you have more or less luck each time.'

I replied: ''more or less luck each time". Not quite, the amount of 'luck' (ie probability) remains the same each time. My observation over several weeks is that the probability is skewed to the opponent.'

They replied: 'As i said probability and statistics do not really work with a percentage chance. but thank you very much for your feedback.'



I can't see how a 20% chance is any different from a 0.2 probability. Are they pulling the wool over my eyes or is their maths more advanced than mine?

[Isotopologue]

Maybe it is the same underlying statistics, but there is a sampling problem.

If I toss a fair coin 100 times I expect 50 heads and 50 tails. Say I really did get that result of 50-50, it doesn't follow that any pair of coin tosses within that hundred will have exactly one head and exactly one tail and therefore reflect that 50-50 result exactly. There might be quite long runs of the same result - getting several heads in a row isn't unexpected even for a fair coin.

Your in-game experiences are an incomplete sample - but I don't think that's necessarily evidence (especially as you said you had no real data) that the underlying distribution is wrong.

(I seem to remember a Derren Brown clip which showed him getting 10 heads in a row when tossing a coin into a bowl - a seemingly amazing task - they then showed that this was simply a subset of all the other attempts where he didn't get ten in a row - he did actually get ten in a row, he just needed quite a lot more than ten attempts to have it captured on video. If you only look at a subset of a population things can be unexpected.)

[QuartzDad]

If losing a 20/80 three times in a row is a problem please don't take up online poker...

You probably are winning at the correct rate, confirmation bias is real. As above, play for long enough and you'll both win and lose ten times in a row.

[Simpo Two]

Thanks - I appreciate there's no actual sampling so I can't prove any bias, but I was more interested to know what the difference was, if any, between '20% chance' and '0.2% probability'. I think they're the same, but tech support says 'Probability and statistics don't really work with a percentage chance'. That had my bullst meter twitching.

So on the basis that every day is a school day etc, and that maybe there's a difference, I asked if they could explain. They just said 'I've already explained'. It didn't seem much of an explanation to me!

[Shaoxter]

Simpo Two said:

'I've now fought many battles where 'keen eye' units are involved, and whilst I haven't collected the data, I'm fairly certain that enemies get a lot more than 20% and I get a lot less. For example I've just been hit by 3 in a row - that's a 0.008% probability. And frequently it's two in a row, which doesn't make statistical sense. Is there any way the 20% can be influenced?'

0.2*0.2*0.2 = 0.008, or 0.8%, or 1 in every 125 times.

[jeremyc]

Probability is expressed as a ratio. A percentage is also just a ratio (it just happens to be expressed as a proportion of 100).

So a probability of 1 in 5 = 1/5 = 0.2 = 2/10 = 20/100 = 20%.

I think your customer service droid doesn't have a full grasp of mathematics.

[Jakg]

Simpo Two said:

Thanks - I appreciate there's no actual sampling so I can't prove any bias, but I was more interested to know what the difference was, if any, between '20% chance' and '0.2% probability'. I think they're the same, but tech support says 'Probability and statistics don't really work with a percentage chance'. That had my bullst meter twitching.

What scale are we talking here - is this a small game or a big one? Is there money involved?

It's likely that the maths of how it works will be sound, but the understanding of probability buy the customer services team, less so.

[Hoofy]

Keeping it simple, if you flip a coin 100 times, you might still get 80 heads. Try flipping it 100,000,000 times and it's more likely to skew towards 50:50 BUT it might still be slightly biased towards one or the other.

So for your specific example, how many times have you flipped that 80% coin?

[Simpo Two]

jeremyc said:

Probability is expressed as a ratio. A percentage is also just a ratio (it just happens to be expressed as a proportion of 100).

So a probability of 1 in 5 = 1/5 = 0.2 = 2/10 = 20/100 = 20%.

I think your customer service droid doesn't have a full grasp of mathematics.

Well that was my immediate thought, and the 'explanation' about luck was what you might tell a 5-year old. I just had to be careful in case they were a maths geek and knew some subtlety I didn't.

Jakg said:

What scale are we talking here - is this a small game or a big one? Is there money involved? It's likely that the maths of how it works will be sound, but the understanding of probability buy the customer services team, less so.

The only money involved is optional and leaving rather than arriving... Forge of Empires, which I stumbled into last year and can't quite give up

[Simpo Two]

Hoofy said:

So for your specific example, how many times have you flipped that 80% coin?

I know I should record it all until I have significant results, but frankly CBA - it is after all only a game

[Hoofy]

Simpo Two said:

Hoofy said:

So for your specific example, how many times have you flipped that 80% coin?

I know I should record it all until I have significant results, but frankly CBA - it is after all only a game

I'm sensing a lack of commitment! Get that spreadsheet loaded pronto!

[andy_s]

Hoofy said:

Simpo Two said:

Hoofy said:

So for your specific example, how many times have you flipped that 80% coin?

I know I should record it all until I have significant results, but frankly CBA - it is after all only a game

I'm sensing a lack of commitment! Get that spreadsheet loaded pronto!

Beaten to it - https://arxiv.org/abs/2310.04153

"Our data therefore provide strong evidence that when some (but not all) people flip a fair coin, it tends to land on the same side it started."

[Simpo Two]

andy_s said:

Hoofy said:

Simpo Two said:

Hoofy said:

So for your specific example, how many times have you flipped that 80% coin?

I know I should record it all until I have significant results, but frankly CBA - it is after all only a game

I'm sensing a lack of commitment! Get that spreadsheet loaded pronto!

Beaten to it - https://arxiv.org/abs/2310.04153

"Our data therefore provide strong evidence that when some (but not all) people flip a fair coin, it tends to land on the same side it started."

I think the data should include the number of spins the coin makes in the air. The fewer the number, the easier it is to replicate.

I've also heard that results can be biased towards heads because that side of the coin has more metal on it. All I know is that the suspension on my car is so hard that if I drive over a coin I can tell which way up it is

[gangzoom]

Simpo Two said:

I can't see how a 20% chance is any different from a 0.2 probability. Are they pulling the wool over my eyes or is their maths more advanced than mine?

In some situations you will be right, where prior knowledge may help you determine a true probability. However in a pure random situation Bayes theorem wouldn’t apply.

https://en.m.wikipedia.org/wiki/Bayes%27_theorem

[Hoofy]

andy_s said:

Hoofy said:

Simpo Two said:

Hoofy said:

So for your specific example, how many times have you flipped that 80% coin?

I know I should record it all until I have significant results, but frankly CBA - it is after all only a game

I'm sensing a lack of commitment! Get that spreadsheet loaded pronto!

Beaten to it - https://arxiv.org/abs/2310.04153

"Our data therefore provide strong evidence that when some (but not all) people flip a fair coin, it tends to land on the same side it started."

That's interesting. There's probably something about an average height that people are happy to flip to and how fast a coin can rotate based on how hard most people flip a coin? I mean, there's probably some maniac who flips a coin 4 metres into the air with a powerful thumb flick but that will most likely result in the coin landing several feet away so to be able to catch it without having to run after it, there's probably a limit as to how much you can flick it with a sense of purpose.