Alex G

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Assumption: losing to a general in combat is a massive setback; turns were spent collecting those cards, and you take severe penalties when you lose -- if you lose to a general, you very likely lose the game (at least the way we play). So it's a good idea to ONLY go into a fight (unless the general is about to walk into Monarch City) with a good chance of winning.

Some Monte Carlo generated statistics (10000 runs) on odds of killing each base game general, with N dice, assuming:

1) No "Battle Luck" or rerolls used
2) No character combat abilities
3) No 2-dice cards with Balazarg

Incorporates Balazarg's card-canceling ability and Gorgutt's parry.

First up, we have Gorgutt. I'll give the numbers between a 20% chance and 90% chance for each general.

DICE: 8 KILL %: 26.47
DICE: 9 KILL %: 34.81
DICE: 10 KILL %: 43.91
DICE: 11 KILL %: 52.03
DICE: 12 KILL %: 59.93
DICE: 13 KILL %: 65.76
DICE: 14 KILL %: 69.56
DICE: 15 KILL %: 76.82
DICE: 16 KILL %: 79.2
DICE: 17 KILL %: 82.79
DICE: 18 KILL %: 86.8
DICE: 19 KILL %: 88.41
DICE: 20 KILL %: 90.17

Gorgutt is pretty easy in some ways, but you do still need 15 dice to have what I would consider an acceptable chance of taking him out, if you have no reroll.

Next up, Sapphire. Surprisingly (to me) even a little easier, though consequences of a loss are considerably worse since you can't quickly regroup and kill her:

DICE: 8 KILL %: 25.5
DICE: 9 KILL %: 35.18
DICE: 10 KILL %: 44.01
DICE: 11 KILL %: 52.5
DICE: 12 KILL %: 60.33
DICE: 13 KILL %: 67.4
DICE: 14 KILL %: 73.4
DICE: 15 KILL %: 78.99
DICE: 16 KILL %: 83.89
DICE: 17 KILL %: 86.95
DICE: 18 KILL %: 90.2

How about Varkolak?

No way to really improve these much, but the numbers aren't bad.

DICE: 7 KILL %: 22.88
DICE: 8 KILL %: 35.32
DICE: 9 KILL %: 50.1
DICE: 10 KILL %: 61.76
DICE: 11 KILL %: 72.55
DICE: 12 KILL %: 80.09
DICE: 13 KILL %: 86.29
DICE: 14 KILL %: 90.78

Who is the most deadly general? Balazarg. Consider:

DICE: 11 KILL %: 27.88
DICE: 12 KILL %: 37.86
DICE: 13 KILL %: 47.17
DICE: 14 KILL %: 56.3
DICE: 15 KILL %: 64.83
DICE: 16 KILL %: 72.08
DICE: 17 KILL %: 77.82
DICE: 18 KILL %: 83.08
DICE: 19 KILL %: 87.02
DICE: 20 KILL %: 90.15

How does all this change if you have a single Battle Luck or one other "reroll all missed dice" available? I'm going to assume 2p here to simplify things, and that only the first half (+1 to account for the fact that you'd probably reroll the person with the most dice to roll) of dice rolled can be re-rolled. I won't redo Varkolak, since he cancels re-roll abilities under normal circumstances (unless you have one quest done). These numbers aren't, therefore, very useful if 1) you tend to go for solo kills of generals (rerolls will be much more powerful there, but your dice cap will be low), or if you send three people to kill a general (where each person will tend to have fewer dice).

Gorgutt:

DICE: 6 KILL %: 37.74
DICE: 7 KILL %: 44.1
DICE: 8 KILL %: 66.48
DICE: 9 KILL %: 72.49
DICE: 10 KILL %: 83.99
DICE: 11 KILL %: 87.31
DICE: 12 KILL %: 92.5

Sapphire:

DICE: 6 KILL %: 37.48
DICE: 7 KILL %: 48.51
DICE: 8 KILL %: 64.14
DICE: 9 KILL %: 71.35
DICE: 10 KILL %: 81.17
DICE: 11 KILL %: 85.76
DICE: 12 KILL %: 91.15

Balazarg:

DICE: 9 KILL %: 37.17
DICE: 10 KILL %: 53.31
DICE: 11 KILL %: 64.01
DICE: 12 KILL %: 76.05
DICE: 13 KILL %: 81.59
DICE: 14 KILL %: 89.29
DICE: 15 KILL %: 91.98


Notice that even with a reroll you need 15 dice to have a 90% shot at killing Balazarg.


Another point: if you want to make it so that you don't lose any general battles, how risk averse do you need to be? Well, if you go in with a 75% chance each fight, your odds of not losing once are bad: 32%.

Going in with an 85% chance gives you a 52% chance of winning all fights. I think we can see that getting our hands on Battle Luck is critical. You need a LOT of dice to have an 85% chance without Battle Luck. You need a reasonable number of dice with it. If you can have more dice early on, you have more chance of escaping the fight without spending your Battle Luck, which means you can keep the game going. It's a good thing Varkolak is made of tissue paper.

So the Inn does several things: it gets you a card of the color you want, with 1/4 or so chance (so two visits gets you on average a bit more than 1 dice). It puts cards for generals you aren't currently focusing on into the discard, so you don't draw them end of turn, and -- this is the big one, possibly -- it gets you to Battle Luck and other critical specials (like the ones that can push back or stop a general) much earlier.
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Runcible Spoon
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Re: Killing the Generals, Monte Carlo style
Thanks for a great analysis, I have always wanted to see something like this so have a thumbsup and a as a token of thanks
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Jeremy Lennert
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So...considering the 10-card hand limit, this seems to imply that a one-hero game would be pretty much unplayable, and even 2 heroes would likely be at a very noticeable disadvantage compared to 3 or 4. That sound about right?
 
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Roger McKay
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Interesting article. I have only played a few times (one win), but have seriously considered basing the Rogue at an inn to get maximum potential out of her rumours ability.

Any ideas about the ORDER in which the generals ought to be killed? Obviously one who is adjacent to Monarch City needs to go first.
 
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Jeremy Lennert
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I generally base it on whatever color I happen to draw the most of, though that may not work as well if you're doing heavy rumor-collecting and therefore need to decide early which color to aim for.

All else being equal, you probably want to aim for the hardest generals first, since if you're going to spend extra time saving up cards, it's better to do that in the early war than in the late war (so you draw fewer total "darkness spreads" cards).

Another consideration I can think of is whose minions you're most worried about, since killing a general earns one hero a "slayer" title that helps against those minions, and prevents the general from spawning extra minions as part of an advance. I can see reasonable arguments to be most worried about dragonkin (hardest to kill), orcs (most numerous), or demons (rapid taint). I think all my losses so far have come from taints, so I guess I'd lean towards doing Balazarg early and Varkolak late.
 
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Joe M
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alexd wrote:

First up, we have Gorgutt. I'll give the numbers between a 20% chance and 90% chance for each general.

DICE: 8 KILL %: 26.47
DICE: 9 KILL %: 34.81
DICE: 10 KILL %: 43.91
DICE: 11 KILL %: 52.03
DICE: 12 KILL %: 59.93
DICE: 13 KILL %: 65.76
DICE: 14 KILL %: 69.56
DICE: 15 KILL %: 76.82
DICE: 16 KILL %: 79.2
DICE: 17 KILL %: 82.79
DICE: 18 KILL %: 86.8
DICE: 19 KILL %: 88.41
DICE: 20 KILL %: 90.17


Quick question for you. I just ran the pure statistical probabilities on your analysis and everything checks out within a reasonable realm of error except for Gorgutt. I'm guessing that it is an error in the success probability? What are you using as a successful attack percentage? I'm using 50% based on 4/6 chance for success on attack, minus 1/6 chance of a parry.

Here is what I am coming up with for percentages:

DICE: 8 KILL %: 14.45
DICE: 9 KILL %: 25.39
DICE: 10 KILL %: 37.70
DICE: 11 KILL %: 50.00
DICE: 12 KILL %: 61.28
DICE: 13 KILL %: 70.94
DICE: 14 KILL %: 78.80
DICE: 15 KILL %: 84.91
DICE: 16 KILL %: 89.49
DICE: 17 KILL %: 92.83
DICE: 18 KILL %: 95.18
DICE: 19 KILL %: 96.82
DICE: 20 KILL %: 97.93

If you happen to stumble back upon this ancient post, please let me know what you find. I've attached a graph of my data.

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Jeremy Lennert
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jdjmad wrote:
What are you using as a successful attack percentage? I'm using 50% based on 4/6 chance for success on attack, minus 1/6 chance of a parry.

A 4/6 chance of +1 and a 1/6 chance of -1 does not give the same distribution as a 3/6 chance of +1 and 0 chance of -1. (The average result is the same, but if that were all that mattered then you could assume a 100% chance of +0.5, and that clearly gives results different from yours.)

Trivial example: suppose we're rolling 1 die and we need 1 hit to kill the general. Under your approximation, our odds of success are 3/6. Under the rules, our odds of success are 4/6. This counter-example shows that the two are not equivalent in the general case.

I haven't personally verified any of the numbers in the original post, but if you tried to simplify the parry ability by instead raising the target number for a successful hit, that could definitely explain a discrepancy.
 
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Joe M
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That will probably do it. I'll re-run my numbers and let you know how they come out.
 
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Joe M
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All fixed. Here is the updated graph.
 
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