Yep, I was wondering on both.  I'm actually suprised it's only a 58% chance on 1 roll...would have thought it would be north of 60%.

There is a 20% chance of losing 3 in a row at 6v4.

OK, I think I may have figured this out using a binomial distribution calculator

With a 58.3% probability of success of a single trial, and given 14 trials and only 5 successes:

Binomial Probability: P(X = 5)       0.051
Cumulative Probability: P(X < 5)   0.024
Cumulative Probability: P(X < 5)   0.0755

So probability of this happening is 5.1% and the probability of this happening OR worse is 7.6%.  This assumes of course that your opponent had more than 5 to lose.  If he had exactly 5, I'm pretty sure the probability of this happening would be even less likely because all outcomes where he loses the 5th unit on any but the last roll would not count, so for that to happen I get: 

Binomial Probability: P(X = 4)*0.4166 = 0.017

That's my final answer and I'm sticking with it until I change my mind or somebody says I'm wrong. 

Lol, you're blowing my mind M.  

I just did some quick calcs , hope they are right.  There is a good site 'anydice.com' that can give you outcome distributions which you can modify for your specific situation.

M, I agree that the odds of precisely 5 hits out of 14 is 5.1%, but it might be more helpful to say that out of 14 rolls there is a 92.5% chance of 6 or more hits and, therefore a 7.5% chance of 5 or less hits.  For me, I think it is best to say the chances of getting X 'or more hits' since we often don't care about getting an exact number of hits just more or less than our target.  In this case, shown below, saying that there is a 21% chance to getting exactly 8 hits is not usually helpful to formulating a plan.  Instead, if we want to kill 8 armies, we would want to say there is a 65% chance to get 8 or more hits, therefore there is a 65% chance to win the battle.

Just lost 21 units and only took 5. 6v6 dice.

Lol, that's not a bad beat. That's a typical Thingol offensive round. 

Korrun wrote:

Just lost 21 units and only took 5. 6v6 dice.

 I just ran about 100,000 simulations of that and it looks like it's in the 1 in 5000 range.  Pretty pathetic - I'm impressed.

M57 wrote:

Korrun wrote:

Just lost 21 units and only took 5. 6v6 dice.

 I just ran about 100,000 simulations of that and it looks like it's in the 1 in 5000 range.  Pretty pathetic - I'm impressed.

Also have to consider how many games/rolls you play.  What I mean is - (warning - wild assumptions inbound) assume you play 20 rounds a day.  Each round you roll 5 attacks.  So 100 a day.  You'd expect to get that bad of a beat every 50 days, or more than once every other month.  To qualify as a truly bad beat, I think it would happen less than once a year, or basically only a one in ~350,000 chance.

This opens up a can.....I've only been focusing on singleton losses.......calculating.........

I was just running the simulations for a specific case. Even if you play a lot, cases like that, where you attack a stack of 5 with 20-25 happen maybe a dozen times a year. With only a 1:5000 chance of failure, you could play your whole life and it's unlikely to happen.  If we expand the parameters to include any consecutive attacks, even on different borders, then we're talking about 10's of thousands of opportunities, in which case, then yes, it's not so unlikely.