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How I Learned to Stop Worrying and Love the Fluke

 
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NMcCoy
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Joined: 20 Jun 2011
Posts: 147
Location: Portland, OR

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PostPosted: Mon Mar 26, 2012 2:58 am GMT    Post subject: How I Learned to Stop Worrying and Love the Fluke Reply with quote

So, after winning several recent tournaments, I found myself giving some thought to why the strategies I use work as well as they do. It fundamentally boils down to making use of a few basic facts about the game:

1. Dragon Diceâ„¢ is a positive-feedback system, in the control-theory sense. Minor advantages, by their nature, tend to increase themselves. Consider an army where each unit will on average generate one save per health. If the army has 18 health, I deal 18 damage to it, and it generates 18 saves, nothing happens. But, if I deal 20 damage to it, it loses 2 health. If i deal the same 20 damage again, it loses 4 health because now it only makes 16 saves; if I deal the 20 again, it loses 8 health... And from this you can also see the next trait of the game:

2. Big advantages are disproportionately better than smaller ones. Let's look at that 18-saves-vs-20-damage again. Suppose I swap my units for ones that generate 20% more damage results - heavy melee instead of cavalry, say. That gets me 24 damage instead of 20; not a huge gain, right? Look again, though - I've just tripled the losses my opponent took from that one attack! Six health instead of two killed. And the next round? Enough damage to wipe out the army. This is why putting your entire army at one terrain is valuable - a 36-point army is far more than twice as effective as an 18-point one. So, the lesson to learn - when you have the advantage, push it as hard as you can; when you're at a disadvantage, focus on recovering if at all possible.

3. Spikes will happen. Simply a trait of rolling a lot of dice - it's a bell curve, and bell curves are pointy at the ends. This is probably not news to you. However, it offers a valuable insight in conjunction with point 2 - you should make the spikes in your favor as strong as possible, because the returns on that investment will pay back far better than the cost would suggest. Likewise, take measures to blunt your opponent's spikes - if they get their lucky fantastic missile roll for 30 damage, and you've dropped a Dancing Lights on them, well, so much for that luck, huh? This is not to say that you shouldn't work on keeping your averages and consistency high, too, but if you can make your spikes bigger, they can turn from an advantage to winning the game - and if you can make them happen twice as often, you will get game-winning events twice as often.

Next up: Some specific advice on how to make use of these traits!
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pattison
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Joined: 04 Mar 2015
Posts: 3

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PostPosted: Thu Mar 26, 2015 1:14 pm GMT    Post subject: Reply with quote

I like this, more please! Rolling Eyes
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Warboss Walton
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Joined: 08 Jun 2013
Posts: 12
Location: Richmond, Va

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PostPosted: Fri Apr 03, 2015 2:13 pm GMT    Post subject: Reply with quote

Very nice discussion. It's an interesting thing to consider that you make sure that your 18-health army generates on average 18 saves and attacks. Would you actually run a statistical analysis to determine this, or more of just go on a "gut feel"?

All of this is long-run probability though, so you'd have to also watch how low or high your army's variance is. You might be able to pull off that 20 damage 18-health army, but if it's bell curve is significantly wider than that 18-damage army, I'll stick with the 18.
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cliffwiggs
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SDA - Rules NitPicker



Joined: 25 Jan 2005
Posts: 10746
Location: Cumming, GA - USA

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PostPosted: Fri Apr 03, 2015 4:45 pm GMT    Post subject: Reply with quote

http://www.sfr-inc.com/armyanalyzer.php

this link will calculate the average and variance of any army.
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