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snoopy369

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Of the Peanuts Gallery
Apr 2004 time: 23:33
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Hmm.
They have: 9 Immortals, 4 regular 5 veteran.
We have: 10 swords, 4 spear (all vet).
On average, immortals will lose 5 hp for each 4 hp spearman or sworsdman. They have 4*3+5*4 or 32 HP total; so they will, on average, kill 6.5 units of ours in exchange for their 9 units. (Although we'd actually not lose these units, on average - we'd on average lose almost nothing, because we'd put up a fresh new unit each time we won; my guess is that we'd lose 3 units or so.)
I'm not sure what the 'range' (standard deviation) of civ random numbers is [if it is a standard bell curve or if there is some concentration or dispersal] ... Assuming that civ essentially rolls 1d5 for us and 1d4 for the immortal and compares the values, and the random numbers are normally distributed (and assuming I remember my stat):
Mean score for us: 2.5
Mean score for immortal: 2
SD for us: about 1.2
SD for them: about .95
68% score for us: between 1.3 and 3.7 [68% of our rolls will fall here]
68% score for them: between 1.05 and 2.95
We would probably lose about 70% of the battles if we got the absolute worst reasonable luck - if we consistently rolled near the bottom of the 68% range - but our mean score is near the top of their 68% range, probably about [34%+16%+20%]=70% of their rolls will be below our mean [50%]. (If it's a standard distribution, and not a flat distribution.)
--
If it's a flat distribution (even chance of getting any given roll, from 0.05 to 4.95), then we have a slightly lower chance to win (as Rhoth says, 55% to 44%). That would mean our potential risk is greater, ie we COULD get horrible luck and lose totally - but we probably won't, on balance, and just as likely could win totally and not lose a unit.
As I said tho, it's been a while since stat for me. 
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