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To fudge or not to fudge: that is the question
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<blockquote data-quote="EzekielRaiden" data-source="post: 6786526" data-attributes="member: 6790260"><p>Well, I kinda recognized that the <em>stated</em> case was too extreme, hence why I considered a second case that was much less extreme--merely 4 consecutive crits from the DM, and 8 consecutive misses from the party...exactly like you asked for. I'm not sure how I failed to meet your requirements! In fact, since most combats are longer than 2 rounds, even in 5e, you can instead consider that to be non-consecutive ones in a single combat, of say 3-4 rounds--the statistics shouldn't meaningfully change if all other attacks are "average." That you have, in fact, actually seen <em>any</em> combats that were THAT bad, let alone 2-4 per campaign, is eyebrow-raising--and, again, makes me think there is something <em>else</em> going on besides "100% pure double-distilled luck."</p><p></p><p>I could probably get into some more complex, multi-part binomial statistics, which, sure, would increase the odds (since the DM needs to merely get <em>at least</em> 4 crits in, say, 8 attacks, while the party needs <em>at least</em> 8 misses in 16 attacks). But it's still going to be a hyper-rare event, because of that "lots of DM crits" thing. "At least 4 crits out of 8 DM attacks" has a binomial probability of p[SUB]1[/SUB]=0.00037175, while "at least 8 PC misses out of 16 attacks, 40% miss chance" has only a p[SUB]2[/SUB]=0.28394. The odds of two independent events happening together is the product of their probabilities, so p[SUB]1[/SUB]*p[SUB]2[/SUB] = 0.00037175*0.28394 = 0.00010555, or approximately 1 in 9,474. With weekly sessions for 1.5 years, and an expected value of 3 of these events per campaign, you'd need to have (3*9474)/(1.5*52) = ~364 four-round combats per session to achieve that expected value.</p><p></p><p>But if the game is so fragile that just <em>one round</em> being unusually unlucky is enough to doom the party...well, again, I'd argue that there's something wrong here that fudging doesn't fix. In <em>that</em> case, it would be "the game system isn't designed to handle its own probability distribution," which is (IMO) a serious and condemnable design flaw.</p><p></p><p>[Edit: For fairness, I ran the same numbers, e.g. miss chance of 40% for four PCs vs. two monsters over the course of 4 rounds, but with just "one round's worth" of crits on the DM's side (e.g. 2 crits) and misses on the players' side (4 misses). Probability is approximately 1 in 18.69--slightly more common than rolling any individual crit. Events at least this severe, or worse, would happen approximately (78/18.69) = ~4 times per average 1.5 year campaign, if there's only one combat per session on average. I suspect actual practice is going to be more like 3-4 average combats per session, so an average campaign should have around 15 of these events--roughly one per month. If a game system is so fragile, it causes divergent, party-killing issues once every four sessions or so, <em>that's bad and should be fixed.</em> And if it's <em>not</em> so bad that fudging is required if you want to fix it, I don't see how you can argue that my above, toned-down example is not precisely what is being asked for--and still sufficiently uncommon as to be not particularly worth considering.]</p></blockquote><p></p>
[QUOTE="EzekielRaiden, post: 6786526, member: 6790260"] Well, I kinda recognized that the [I]stated[/I] case was too extreme, hence why I considered a second case that was much less extreme--merely 4 consecutive crits from the DM, and 8 consecutive misses from the party...exactly like you asked for. I'm not sure how I failed to meet your requirements! In fact, since most combats are longer than 2 rounds, even in 5e, you can instead consider that to be non-consecutive ones in a single combat, of say 3-4 rounds--the statistics shouldn't meaningfully change if all other attacks are "average." That you have, in fact, actually seen [I]any[/I] combats that were THAT bad, let alone 2-4 per campaign, is eyebrow-raising--and, again, makes me think there is something [I]else[/I] going on besides "100% pure double-distilled luck." I could probably get into some more complex, multi-part binomial statistics, which, sure, would increase the odds (since the DM needs to merely get [I]at least[/I] 4 crits in, say, 8 attacks, while the party needs [I]at least[/I] 8 misses in 16 attacks). But it's still going to be a hyper-rare event, because of that "lots of DM crits" thing. "At least 4 crits out of 8 DM attacks" has a binomial probability of p[SUB]1[/SUB]=0.00037175, while "at least 8 PC misses out of 16 attacks, 40% miss chance" has only a p[SUB]2[/SUB]=0.28394. The odds of two independent events happening together is the product of their probabilities, so p[SUB]1[/SUB]*p[SUB]2[/SUB] = 0.00037175*0.28394 = 0.00010555, or approximately 1 in 9,474. With weekly sessions for 1.5 years, and an expected value of 3 of these events per campaign, you'd need to have (3*9474)/(1.5*52) = ~364 four-round combats per session to achieve that expected value. But if the game is so fragile that just [I]one round[/I] being unusually unlucky is enough to doom the party...well, again, I'd argue that there's something wrong here that fudging doesn't fix. In [I]that[/I] case, it would be "the game system isn't designed to handle its own probability distribution," which is (IMO) a serious and condemnable design flaw. [Edit: For fairness, I ran the same numbers, e.g. miss chance of 40% for four PCs vs. two monsters over the course of 4 rounds, but with just "one round's worth" of crits on the DM's side (e.g. 2 crits) and misses on the players' side (4 misses). Probability is approximately 1 in 18.69--slightly more common than rolling any individual crit. Events at least this severe, or worse, would happen approximately (78/18.69) = ~4 times per average 1.5 year campaign, if there's only one combat per session on average. I suspect actual practice is going to be more like 3-4 average combats per session, so an average campaign should have around 15 of these events--roughly one per month. If a game system is so fragile, it causes divergent, party-killing issues once every four sessions or so, [I]that's bad and should be fixed.[/I] And if it's [I]not[/I] so bad that fudging is required if you want to fix it, I don't see how you can argue that my above, toned-down example is not precisely what is being asked for--and still sufficiently uncommon as to be not particularly worth considering.] [/QUOTE]
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