Does Gambler's Fallacy Apply Here?

[randay]

The game here is EVE Online. It is a space game, where PVP involves fighting other ships. A lock must be obtained on the target before you can shoot at it, A lock can be interrupted/prevented by jamming the attacker.

Each ship has a "sensor strength", and each jammer module has a sensor strength also.
Multiple jammer modules can be fitted to a ship.

The jamming formula is as follows.

ship strenght / module strength = jam percentage

The common formula for multiple modules is calculated by taking the percentage to not jam and then calculating it for each module fitted. So say you had a ship strength of 10, and a module strength of 1, with 5 modules fitted. You would end up with a 1 out of 10 chance to jam that ship. each subsequent jammer would have another 1 out of 10 chance to jam it, or 10%. Does each jammer increase your chances of jamming or is the chance always 10%. The common thought in-game is that each jammer increases your chances. So in the example I have given, you would calculate a 59.049 "chance of not jamming"/40.951% success rate. Is this a prime example of gamblers fallacy since each jammer still only has a 10% chance of succeeding?

please excuse me for my horrible math 🙂

 

[blackllotus]

Originally posted by: randay
Is this a prime example of gamblers fallacy since each jammer still only has a 10% chance of succeeding?

Nope because each individual jammer operates independently of the other jammers. Gamblers fallacy would be like assuming that, say, the fifth jammer has a greater than 10% chance of firing because the four ones before it did not fire.

EDIT: I have not checked your calculations, however it is correct to assume that with five jammers, each with a 10% chance of firing, the chance of atleast one out of the five firing is [considerably] greater than 10%.

 

[randay]

So in my example would I be correct in saying that my success rate is 40% even though each individual attempt only has a 10% success rate?

 

[knightwhosaysni]

You need to calculate 1-(the chance of all the jammers failing), which is 1-(0.9)^n giving your 41%.

A fallacious gambler would assume that if each has a 10% chance then after nine failures the tenth *must* work, and proceed to bet his horse on it.

A wise gambler would know that the tenth independent event has the same 10% chance as the others, with the chance of any one of the ten working being 65%.

 

[pcy]

Hi,


Yes, the chance of succesfully jamming your attacker is the chance that at least one jamming device succeeds. The alternative is that all fail - which is why knightwhosaysni's formula is correct.

You get no additional benefit if more than one jammer succeeds.

The average number of successful jaming events is still 0.5 per attack in your example - as you'd expect from five attempts each with a success rate of 10%.

But some of those sucessful jamming events go to waste bwcause there was another sucessful jamming event in the same attack.



Peter