The Transitive Property of Gaming blog, which I read a lot for warhammer information, had a post a while back about the relative merits of conservative vs. reckless stances in combat. The post compares the success rates of a theoretical attack using the Troll-Feller Strike (a fairly nasty card) in reckless versus conservative stances, and argues based on the results that the reckless stance doesn’t deliver rewards that match the apparent benefits written on the card. I think there might be a few errors in the calculations of average damage for this analysis, and in fact I think the difference between the damage done in the two stances is quite large (see my addendum below). Even with these mistakes though the post seems generally correct – on an analysis of success rates and the differential damage which flows from them, reckless stance is not worth the risk it entails compared to conservative stance. However, I don’t think this is correct because the analysis at Transitive Property of Gaming fails to consider the extreme risk of delay symbols, which only appear on conservative dice.

Delay symbols appear in conjunction with success symbols, and basically give the GM the option of either placing two recharge tokens on one of the player’s cards, or moving that player’s initiative token one step down the initiative ladder. The risk of this is very high as the stance depth increases. I tested the probabilities using 40 dice rolls on this convenient simulator, and found a delay occurred in 48% of all skill checks, with the longest run of checks between delays being 5 checks, and the usual run being just 1 or 2 checks. This is actually a ferociously dangerous result, as I will describe based on last night’s adventure.

Last night the PCs got into a fight with 6 mutants, two of them quite nasty melee combatants, one a vicious ranged attacker, and one a wizard. The entire party went into conservative stance for the fight, and delay symbols were flying about with gleeful abandon. I restricted myself to using delay symbols only on action cards, but this is how I used them:

*Preventing*Magic Dart:*Magic Dart*is petty magic with a recharge of 0 (it can be used every round) and a very low difficulty. It’s the magic missile of WFRP, but it’s deadly – the wizard can usually ignore armour with this attack, and get criticals. The low difficulty makes it ideal for fast casting, so it can be used every round. But with delay symbols appearing willy-nilly, I was able to put recharge tokens on this card, and prevent the wizard from doing devastating attacks every round. The wizard’s other major attack spell is lightning bolt, which is really nasty but has a high power cost and recharge, so can’t be deployed more than once in a decent combat. So by delaying the wizard’s magic dart I get to prevent the wizard from doing anything successful for several rounds.*Interfering with*Execution Strike: The Roadwarden is armed with a pistol and sword, and has a 4-recharge-token action that enables her to fire and melee strike in the same round, with reasonable chance of success. This fight lasted a while and the roadwarden was in a position to use this action maybe 3 times; but because she kept rolling delays on basic melee attacks, I was able to keep stacking recharge tokens on this card so that she actually only used it once in the whole combat. This is the roadwarden’s only high-damage attack, and the delays significantly reduced her ability to do damage*Crippling the Thief:*The thief has the*rapid sho*t card, which enables a second bowshot in conservative stance, or a third in reckless stance, with increased difficulty on each. The thief has a ferocious missile attack dice pool and could easily expect three successful strikes with this – enough to kill all but the toughest mutants – but chose to use the conservative side. The delays that the thief rolled up were then sufficient for me to prevent the reuse of this card for the remainder of the battle. This card is absolutely evil, and has been used by the thief to decimate enemy groups before. Not so with all those delays*Preventing defences:*The recharge tokens can also be used to prevent defence cards from becoming available for reuse. Most PCs only have two defence cards, so if I keep one card recharging they are only able to defend once per round. Given that most PCs were subject to two attacks in this battle, this was a bad outcome for them

The wizard spent a portion of this battle in a very deep conservative stance, which is probably a good plan for a wizard since it reduces the risk of miscast. But it opens the wizard up to all sorts of challenges – as a rule I don’t do this but I could keep the *Channel Power* card on recharge, which would basically prevent the wizard from using any magic for most of the battle.

But worse still, with 4 PCs fighting 6 mutants, I could have moved their initiative cards tokens down the initiative tracker, which by mid-battle would have left the PCs facing 4 unanswered mutant attacks before they could act. This means that the wizard could have unleashed some bad-arsed support spells, rather than having to respond to incoming damage directly.

In short, I think the delay effects on conservative dice are very risky, and you need a good justification for going into a deep conservative stance, especially if your main role is delivering melee damage. With a reasonable toughness you can manage a few fatigues, and you’re much better copping a few fatigue-related penalties on your available actions than not having those actions available at all.

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*Addendum regarding Transitive Property of Gaming’s calculations*

The calculations in the linked post are of average damages, but when I put the given probabilities and damage outcomes into a spreadsheet and run the calculations, I get very different results. Using the same assumed damage (10) and average armour soak (2) I get a post-armour average damage in reckless stance of 11.69, vs. 10.14 in conservative stance (an average difference of 1.55). As armour soak increases the difference increases too – for an armour soak of 4 it becomes 1.79, and at 6 it is 2.03. For these calculations I’m using the standard method for calculating expected costs of an action: Expectation (Damage) = Sum over ( Probability (event)*Value(event) ), where here Value(event) incorporates the damage bonus, +1 for a critical, and the soak effect. I assume this is what was used in the linked post, but I think the calculations are wrong.

It’s important to note though that the issue in combats is not average damage done but survival, which is determined by the probability of a hit and the probability of death on a given hit. Typically a troll-feller strike will kill most opponents in 2 blows, so the best card is the one which delivers those blows as quickly as possible. In fact the conservative and reckless stances deliver the same chance of a hit, so survival is similar in both cases, but the conservative side makes the second – essential – hit much less likely to happen. There’s a 45% chance that the troll-feller will be hit with a delay, meaning that the next troll-feller strike won’t happen for an extra 2 rounds (increasing target survival) or – worse still – the GM will put those recharge tokens on the PCs basic melee strike card, rendering the troll-slayer useless in the following round. Alternatively the GM could put those tokens on a defense card, which will probably render the troll slayer defenseless in the next round.

Conservative stances, then, are particularly good if you have a lot of action cards available to choose from, so you are safe if you get one hit with a delay.

As a further aside, WFRP3 probabilities are fiendishly hard to calculate and fiendishly hard to game. Being a combination of different sets of dice with the same outcomes, an analytic solution to the problem of the probability of any event in a dice pool is theoretically calculable as the convolution of several multinomial probabilities. But there are as many as 5 different multinomial distributions, so this calculation would run over many pages. This means that we need to use simulated empirical estimates of probabilities (as I have done here) for most situations, or we need to use up an entire amazon’s worth of paper on the calculations. It would be much easier for me to write a simulator in R and calculate empirical probability distributions than it would be to actually calculate the analytical probabilities of any given event. How hideous!

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