Yes, about 9%. It will slowly decrease over time, but it is a negligible amount for the purposes of the game.

Single Attack with Twin Attack: 9.75%
Double Attack with Twin Attack: 18.5494%
Triple Attack with Twin Attack: 26.4908%
Quadruple Attack with Twin Attack: 33.658%
Quintuple Attack with Twin Attack: 40.1263%
Sextuple Attack with Twin Attack: 45.964%

I doubt we will ever see that many attacks, though.
__________________________________________________________________________

I added in the chances for pulling missing pieces out of your second case and your chances to pull the entire set with various numbers of cases in my second post on the front page.

That is a difficult one. The chances are dependant upon your opponents roll also. You could theoretically re-roll initiative checks indefinitely, so it is not as simple as a 95% success rate.

A 1 is an automatic fail (5%)
The chances of a tie is 1/20 (5%)

So, that is a 90% chance of success on your first roll with a 5% chance of rolling again. If you roll again, it is the same chances as before. This means that you could go on forever finding the chances.

1. Fail: .05
2. Reroll, Fail: .05^2
3. RRF: .05^3
4. RRRF: .05^4
5. RRRRF: .05^5
6. RRRRRF: .05^6
7. RRRRRRF: .05^7
8. RRRRRRRF: .05^8
9. RRRRRRRRF: .05^9
10. RRRRRRRRRF: .05^10

This is just an approxamation, it goes on forever. This is one of those things where math becomes illogical. At some point, you could eventually reach 100%. That is obviously erroneous. Anyway, with those ten scenarios, these are my findings:

Success Rate: 94.73684211%
Failure Rate: 5.26315789%

Looks good I got 94.95 but I stop sooner than you did so its all G.

im afraid, but willing. maybe my fear will induce some dark side D20 trickery....

You're dividing by 0. :P

Good stuff though. It's nice to have a refresher on how the statistics work for figuring out things like saves and stuff.

The stuff about getting a full set from multiple cases is cool too. Though if we were talking the Clone Wars set it would go from 1.5% chance with two cases, to a 50% chance. :P Darn clustering.

You win.

Yeah, I intentionally avoided clustering in my figures.

The overall point of the problem is illogical.
9/9=1 and 9/9=.99999..., so .99999...=1
But, 1-.99999...=.00000...1
That means that you have an infinite number of 0s with a one on the end. That would be considered equivilent to 0. This also means that 1 and .99999.... are not the same number since there is a difference between them, you simply never reach it. But since there is a difference, you can average them, it would be .99999...05. You end up with weird stuff no matter if you say they are equal or are not equal. If they are equal then two technically different numbers equal each other, but if they are not equal then a number divided by itself is not 1. The problem lies in infinite numbers. I should have clarified. .999999...=1 is not illogical, but infinite numbers can be seen as illogical. If I had to make a choice, I would say they are equal, it results in less problems. There are still issues with that, though.

True, but for the purposes of the game it is illogical. Thrawn will not win 100% of the time.

There are 3 possible outcomes for an initiative roll:

There's a tie. [20/20^2)] = 5%
Thrawn loses (rolled a 1 and opponent did not). [19/20^2] = 4.75%
Thrawn wins (no tie and Thrawn did not roll a 1). [ (20^2 - 19 - 20) / 20^2 ] = 90.25%

However, whenever there is a tie, it will be rerolled until there is no tie, so we only need to concern ourselves with initiative rolls where no tie exists (and all of these are equally likely).

There are a total of (20^2)-20 possible initiative rolls where there is no tie. Of those, Master Tactician wins all except 19 (the 19 where Master Tactician rolled a 1 but the opponent did not).

The probability of Master Tactician failing is 19/(20^2 - 20) = 5%
The probability of Master Tactician succeeding is 1 - [19/(20^2 - 20)] = 95%

In the other calculations for this, the answer was approaching what I have above and if the limit of the summation is taken it would be the same.




I apologize. I misread the summation. I thought you included the success as part of the summation. The sum of the probability of a success and the probability of a failure must be 100% (obviously).

The limit of the summation for failures is 5%. The summation above will not come up to 5%, though, because you took the probability of a Thrawn failure on the first roll to be 5% instead of 4.75%. Thrawn has a 5% chance of rolling a 1, but if the opponent also rolls a one then that counts as a tie instead of a Thrawn failure.

I need a drink after all this ...it must be almost 5:00 somewhere!

The sigma notation would look like this:

∞
∑ .0475(.0475)^(x-1)
x=1

Well, that makes it 95% and 5%. I need to get more sleep, I am making too many stupid mistakes.

On Topic: Does anybody want me to go further for the cases?