One of the reasons the casualties were so low in the Battle of Ostwald was quite simply the "god awful die rolls". In one series of melees there were 3 Battalions of 7 elements on each side, both sides throw the die requiring a 6 to cause a "hit", out of 21 die per side both got 1x 6. So in in the case of a draw both sides withdraw in disorder. Yet when they go back in again the result is the same, statistically it shouldn't have happened, but according the die rollers lore it was bound to happen.

In fact this was the first game I have played where we had so many drawn melees, it was only with the Cavalry where the dies were better and inflicted decisive results (unfortunately for Rechburg).

Sometimes it seems there is no figuring the dice gods.

Yes, rolling 1 '6' in 21 dice is out of left field, but the probability is not insignificant. Doing it twice, as it were in a row, is getting moderately weird.

ReplyDeleteThe mathematician in me isn't going to let this one go. The 'expected' number of 6s rolled with 21 dice is 3.5 (mathematically speaking). The possible scores up to 3 are 0,1,2,3,; over 3 are 4,5,6,...,21. So many more possibilities 4 or more than 3 or less. What that means is that you are marginally more likely to roll 3 or less than 4 or more.

The chances of rolling no 6's is very small - about 2.2%. The chances of rolling exactly one 6 is 4.2 times as great - a little over 9%. So the overall chances of rolling zero or 1 '6' is roughly 11.3%. Doing it twice in a row is a bit over 1 in 100.

Bear in mind that these probabilities begin with the premise that we don't know ahead of time what the result of this or that roll will be. In a series of die rolling events, any possible result will come up. Wait long enough, and someone will roll 21 6's! Taking the first roll you are talking about for that particular roll the chances of 0 or 1 '6' was 11%.

These kinds of results, by the way, is one of the reasons I'm not all that keen on this kind of combat resolution: the variances are too high. I much prefer if possible to make all possible scores count for something, or if not all, most. And if I can 'dampen' the variances even more, then fine.

Having said that, though, I do sometimes wonder whether maybe the high variances aren't after all the more realistic.

Cheers,

Ion

I have to say after the last battle as wierd as the results were I tend to agree with you, may need to look at a way of varying greater casualties.

ReplyDeleteI still recall with horror a game with a very well-known rule set that also required 6's to hit. On this occasion, I had 16 dice for 16 stands, split among 3 distinct combats. The enemy had precisely 8 dice for 8 stands again split among 3 combats. Of these, one was an even combat with 2 stands apiece, so the other two would have been 14-6 in my favour. In this rule sets, 'hits' had a more powerful impact than in the 'Vive l'Empereur' rules we have been using.

ReplyDeleteMy 16 dice resulted in 2 hits. Fine. Not great: I could have expected more, but 2 was a fairly high probability result. The enemy rolled. Six 6's! The even combat honours were share 1-all, which meant I was 1-5 down on the other two. Of course I got screwed.

The probability of my scoring less than 3 hits was was quite significant: roughly 48% (E(hits) = 2.67, and recall that the curve is skewed to the left). But the probability of 6 or more hits with 8 dice is less than 3 in 2000! So I was defeated by dumb luck.

5+ hits out of 6 you're looking at odds approaching 1.2 in 10000; 0 or 1 hit in 14, about 18%. Yep, it can happen. It happened to me (and my hard-luck stories are legion). The thing is, we are told that this should even out in the long run. And that would be correct... provided you got a long run. But you don't in wargames - at least, not in a single game. And even if it did, a bizarre low-probability result would at best be cancelled out (bearing in mind you are now behind and so less capable of damaging your opponent), not reversed.

So many times in 'hit or miss' type combat systems, good play to establish odds-on propositions have come unglued for relying upon a single roll (of however many dice) to determine the outcome. Sure I've won more than I've lost of these. But that would be true also if these were broken down more (the fist-full of dice method). This can be achieved in all sorts of ways. Actually, I have few quarrels with VLE in this regard, as it takes 2 hits to remove a stand, and units can usually withstand the loss of a couple of stands at least.

Here is something worth remembering. Suppose by superb tactics you created a situation in which there were two combats to come, and experience told you that in each one you were 2 to 1 favorite to win. What are your chances of winning both? Not that great: 5:4 against. In other words, taken together you are favorite to lose at least one of them.

Is it worth setting up such situations then (supposing you could)? On the whole, yes. Even if you lost one, your winner is twice as big as his winner (supposing the combats were similar in size), so you will be still 2:1 to win the decider. Taken from the top, your overall winning chances fall just a whisker short of 3:1 on (~74%).

What does one get out of this? Not sure. The 'paper battle' if the last couple of paragraphs does show in principle a method of increasing favorable odds to be even more favorable! But it also indicates a possible method of obtaining - by means other than deaf, dumb and blind luck - chances of positive outcomes when the odds are against you. I have it on good authority that Horatio Nelson went through a vaguely similar sort of exercise in planning Trafalgar.

Cheers,

Ion