Triplanes ?

[Adjuvant]

Yes, and two independent events at 50% would have a 25% chance to get tails+tails.

I understand the academic point, but it's meaningless as there can be no proof. Turned back on itself, even with 10 million "tries", the likelihood of "netting 25%" is "even" to the likelihood of 23%, 21% or 19% as possible outcomes.

edit : If, for the next 3 days, no triplane in any game intercepted, you can call it a statistical anomaly, but it doesn't change the 100% fact this is what occurred. Further, the following 3 day's results have no obligation to "lean" the composite statistical result toward 25%... there "could" be another 3 days of complete misses.

 

[Biologist]

The larger the statistical sample, the more likely outcomes are to reflect probabilities based upon possible outcomes. This is why larger sample sizes are better than small ones for making accurate statements based on statistical data.

If you have a deck of cards, and you need to draw two kings in a row without replacing cards, then you have to draw a king for your first card. The probability of doing this is 4/52. If you fail to do this, the probability of two kings in a row becomes 0. If you succeed in doing this, the probability becomes 3/51. The overall probability of drawing 2 kings in a row is (4/52) * (3/51).

With triplanes, the planes are each considered separately. The success of the first plane does not affect the success of the second plane, but it must succeed in order for the second plane to matter (if you are going for two successes out of two attempts). The probability of the first plane succeeding is 1/2. If this happens, the probability of the second plane succeeding is still 1/2. The probability of the first plane succeeding and the second plane succeeding is (1/2) * (1/2) = 1/4.

Algebraically, for dependent events (cards): P(A and B) = P(A) + P(B given A succeeds).

Independent events (triplanes): P(A and B) = P(A) * P(B).

 

[Magma_Dragoon]

I understand the academic point, but it's meaningless as there can be no proof. Turned back on itself, even with 10 million "tries", the likelihood of "netting 25%" is "even" to the likelihood of 23%, 21% or 19% as possible outcomes.

edit : If, for the next 3 days, no triplane in any game intercepted, you can call it a statistical anomaly, but it doesn't change the 100% fact this is what occurred. Further, the following 3 day's results have no obligation to "lean" the composite statistical result toward 25%... there "could" be another 3 days of complete misses.

What the hell are you talking about? If the triplane has a 50% intercept chance and there are two triplanes in the city, there is a 25% probability of the observed outcome, no interception.

 

[kaspergm]

What the hell are you talking about? If the triplane has a 50% intercept chance and there are two triplanes in the city, there is a 25% probability of the observed outcome, no interception.

Not if there is only one bomber attacking. If only one bomber attacks, only one of the triplanes get a shot at intercepting, which means 50 % chance of no interception happening.

I do hope you guys are aware that all this statistical discussion was spawned by a misreading (and possibly a vague sentencing) of my post earlier. What I referred to with my 25 % was the case with multiple bombers attacking.

 

[Biologist]

Yeah. I think Adjuvant and Magma Dragoon are talking about two different things. Adjuvant seems to be talking about obtaining a 25% overall success rate for intercepting bombers over multiple trials. OP and Magma are talking about the chance of a specific sequence of events occurring: 1 success followed by 1 success (or 1 failure followed by 1 failure, those scenarios are equivalent in this case).

If you run "10 million" trials of a procedure with a 50% probability of success, your overall success rate should closely approach 50%. If you only run 10 trials, random chance means you might get a 10% success rate because you don't have a statistically significant sample size.

Regardless of how many trials you run, the probability of the specific outcome of "1 success followed by 1 success" is (1/2) * (1/2) = (1/4) for any one trial of the triplane scenario.

I'm assuming in my posts that we're discussing a situation in which there are enough triplanes to defend the incoming bombers. If you only have 1 triplane against 2 bombers, obviously your probability of two successes on the same turn is 0.

 

[GhostSalsa]

Jeez i had no idea GW fighters only intercepted half the time. I always thought it was just a bug or cheating haha. Kudos for the knowledge..

In my last game my AI opponent seemed to 'adapt' after I had knocked out their bombers and started taking cities, it actually built fighters instead and used them on intercept. Probably an AI decision fluke but maybe it (eventually) knows when it's on defense, not offense.

 

[Barghaest]

Jeez i had no idea GW fighters only intercepted half the time. I always thought it was just a bug or cheating haha. Kudos for the knowledge..

In my last game my AI opponent seemed to 'adapt' after I had knocked out their bombers and started taking cities, it actually built fighters instead and used them on intercept. Probably an AI decision fluke but maybe it (eventually) knows when it's on defense, not offense.

Not a fluke. I've seen the AI switch to parking planes on intercept where I'm doing air strikes while maintaining offensive posture elsewhere where my planes are absent. The AI reacts to what's happening a bit - sometimes a little late or poorly.