It is an increasement of ~2% points, but it is an improvement of 33.3%
Yes you are technically correct about the 33% but that isn't how math works. The 33% is still relative to a very small number. It isn't as if you go from a 6% chance to a 39% chance with that 33%. The increment that matters is the one that comes after your 33% are applied to the original odds. For example, if the odds of being struck by lightning during a thunderstorm while you're taking a walk were 0.01 %, and having a Heroic Epic would increase that by 33%, that would still only be an increment of 0.003% to a final chance of 0.013%, and not 33.01%.
If you are attacking and winning with elite units 10 times per turn on average you will receive 12.5 leaders on average in 20 turns without Herioc Epic and 16.67 times with it. So during 20 turns of war you gain 4.17 additional leaders on average
That is correct, yes. Personally, I've never conducted warfare of such large proportions as to make such a large difference. In this case, I do concede that you are correct at such a large scale war, and, in that scenario, a Heroic Epic would indeed be a bit more effective.
I can make a few corrections to your figures. If you have 10 elite units, you will, on average, only be able to attack with them every 3-4 turns. Please keep in mind that unless we are talking about an easy game like Monarch, you're going to be fighting somewhat formidable units.
Let us take the example that you like best: Cavalry. In a decent game, Emperor and above, you are most likely to be encountering Musketmen, fortified in either a Town or City. In a town, not only is there a 25% percent chance your unit will die, but there is an 85% chance that your unit will take damage. If you take that into consideration, only 1-2 of your 10 elite units will be able to attack each time in 20 turns. For the ones that take damage, they will need 1 turn to wait, one turn to heal- 2 turns if they take more than one damage. That means they'll be able to attack 5-7 times in those 20 turns. Not to mention that with every attack it is most likely that you will lose 2-3 Cavalry. However, let's just say that you'll have a few Veterans becoming elites to make up for the losses so we can keep that figure as a constant.
So, 2 of your units will attack 20 times indeed. The other 8 will attack 5-7 times. The new figures are as such: 20*2+ 6*8 = 88 Elite Victories in 20 turns. So really your figure should be 5.5 leaders in 20 turns. (All of this is of course assuming that your logistics are impeccable and youre able to find the 3 units for an army within the exact turn in which your leader is produced). WITH the heroic epic your figure climbs to 7.3 leaders in 20 turns. Indeed you've gotten 2 more leaders in this time, if all circumstances are perfect. This does make the Heroic Epic marginally useful, but still far from overwhelming.[/QUOTE]
'
Only at great expensive of gold maybe better invested in research. Knights become Cavalry and unlike Knights Cavs are a major and cost effective improvement. Knights fail at the later. Still compared to simple horsemen they are much more convenient as they effectively save both war weariness and unit support. It becomes even clearer when those troops need to be shipped, too.
Cavalry? Sure, if you don't care about score that seems like a good enough choice. I guess it depends on the person. At this point in my Civs playing, I've beaten the game at every difficult, and my main objective isn't an easy ride but a fast victory. I mean, by your philosophy you could just as well wait for Modern Armor which is even more effective.
In conclusion: I personally have never conducted warfare on such a massive scale in the MA, but it is not to say that my way is the only way. I am by no means the best player here so I am aware that my personal style of play is not a standard. I will say that I can see that the Heroic Epic is indeed marginally useful if you conduct warfare on such a massive scale in the game.
One final thing to keep in mind is the timeline of events and the propagation of early events. Every city you attain adds to your overall science and shield count. With the 7 aforementioned Knights you coul have captured 3-5 MORE cities than without them in the time it took you to build the Heroic Epic. I guess it depends how important science is to you, or the quest towards more land for your Domination.
) Man-O-War are useful now with Conquests!. Build a couple of them, and watch your Navy grow with the captured Units...
Poor Columbus.
