Summoner Wars » Strategy » Basic Summoner Math: 1-2 = 11%

Author: Jexik
Now, to many of you, none of this will come as a big surprise. When it comes to rolling the dice in Summoner Wars, most of the results could be calculated by someone between 7th and 9th grade without too much difficulty.

One thing I've found though... when some people complain about their luck, in lots of games, they don't actually know what the probability of a given event occurring is! They complain that their dice are poor, but don't know what the average result should be, or even how bad they need to be rolling for their luck to be unusual. I'm not going to go into hypothesis testing or showing that someone 'just has bad luck' today, but I'll give a basic run-down of what to expect from the most frequent kinds of attacks.

For each kind of attack, I'll list at least four pieces of information: the expected value, or mean number of Wounds caused, which is what people normally think about when they say 'average,' but isn't as informative in Summoner Wars unless attacking Champions, Summoners or Walls; the mode, which is the result(s) that has the highest probability of occurring in the distribution; the median, which is the 'balancing point' of the distribution; and the chance to hit, which is the probability that you'll score at least one wound (important when hitting single-life commons).

Let's start with the easiest one:

Attacking with a Guardian (or SotP-enhanced Archer):

Expected Wounds: 1
Mode: 1
Median: 1
Chance to hit: 1

Duh! One important thing to note... they can't do more than one damage. Again, this is super obvious, but can be useful for comparison.

Attacking with 1 die: (Defender, Archer, CG Fighter, non-adjacent Spearman, etc).

Expected Wounds: 2/3
Mode: 1
Median: 1
Chance to hit: 2/3

Attacking with 1 Reckless die: (Cave Goblin Slinger).

Expected Wounds: 1/2
Mode: 0, 1
Median: .5 (or would it be undefined?)
Chance to hit: 1/2

Attacking the same card twice with a CG Slinger thanks to Goblin Rage:
Expected Wounds: 1
Mode: 1 (50% of the time)
Median: 1
Chance to hit: 3/4
Chance to hit 2 cards (if the second is within range): 1/4

Attacking with 2 dice:
Expected Wounds: 4/3 (~1.33)
Mode: 1, 2 [This distribution is bimodal: There is a ~44.4% chance of scoring exactly 1 wound, and a 44.4% chance of scoring 2]
Median: 1
Chance to hit: 8/9 [Put another way, you have a 1/9 chance of scoring 0 wounds]
Chance to hit two 1-life cards with an enraged CG Fighter: 4/9

Attacking with 2 dice (with a Shaman and/or against Baldar, where you must hit on all dice):
Expected Wounds: 8/9
Mode: 0 (happens 55.6% of the time)
Median: 0
Chance to hit: 4/9

Take home lesson: Shaman do more damage (on average) than non-precise 1-attack cards against Champions, Summoners, and Walls, and don't care about Baldar's ability. Their expected damage against cards with 2 or more life is equal to the chance to hit (and expected useful damage) of other 2-Attack cards against single-lifers.

Fire Blast (or SotP enhanced Kaeseeall/Warrior)
Expected Wounds: 2
Mode: 2
Median: 2
Chance to hit: 1 (100%)

Attack of 3 (Krung, Fire Drake, Thorkur, Prince Elien at range)
Expected Wounds: 2
Mode: 2 (12/27 ~44.4% of the time. Note that the odds of 2 or greater [2 or 3 wounds] is 20/27 ~74%)
Median: 2
Chance to hit: 26/27 ~96%
Chance to hit Baldar: 8/27 ~29.6%
Expected Wounds to Baldar: 8/9, or ~.889 [There's that Shaman number again]

Don't use Prince Elien's attack unless you're hoping for 3 damage, or you need the extra range. I find that the range is often the best reason.

Attack of 4 (Grognack):
Expected Wounds: 8/3 ~ 2.67
Mode: 3 (32/81 ~39.5% of the time)
Median: 3
Chance to hit: 80/81
Chance to hit (kill) Baldar (or a full life Prince Elien): 16/81 ~ 19.8%
Chance to 1-shot a 2-life card: 64/81 ~80%
Chance to 1-shot a 3-life card: 48/81 ~60%
Chance to 1-shot a Smasher: 1

Attack of 2 + Burning Blade (Maelena):
Expected Wounds: 7/3 (~2.33)
Mode: 2, 3 [This distribution is bimodal: There is a ~44.4% chance of scoring exactly 2 wounds, and a 44.4% chance of scoring 3]
Median: 2
Chance to hit: 100%
Chance to kill a 2-life card: 88.9%

Attack of 5 Reckless dice (Blagog):
Expected Wounds: 2.5
Mode: 2, 3 (Each have a 10/32 chance: ~31%)
Median: 2.5
Chance to hit a 1-life card: 31/32
Chance to hit Baldar: 1/32
Chance to 1-shot a 2-life card: 81.25%
Chance to 1-shot a 3-life card: 50%
Chance to 1-shot Prince Elien: 18.75% Unintuitively (to me at least), this is actually slightly lower than Grognack's chance to do the same.

These numbers all become more interesting once you start thinking about conditional probability. But I think I might wait for another day to get into that. Another very simple lesson would be to think about the chance to hit when attacking single-life commons, and the expected wounds when attacking multi-life targets.

Also, I didn't delve into Mook or many other Cave Goblin-y tricks, or the Fury ability. Those might need threads all to themselves. This is part of the reason that I think it takes a little while to get used to the CG's, and that some people find the PE's strongest early. It's a lot easier to do their math.
Mon Mar 15, 2010 5:02 pm