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?

[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!

[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

[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