There's no need to account for this. This is called the Gambler's Fallacy. You would think that rolling the dice over and over, your chances to hit or crit would improve, but they don't. They're exactly the same, every time. You have as much chance to crit on the first attack as the last. More iterations don't increase probability.The more attacks you get, the more chances you have to critically hit your opponent. How would you account for this? Also, if you are limited to only one attack each round and that single attack misses, you don't have more chances to hit that round, how would you account for this?
I'm not discussing the merits, just wondering how to take these things into account.
On any individual roll, your chance to crit is the same (barring a one-time effect to expand your threat range). Just like any individual coin flip has the same probability of being heads. But if a coin came up all heads or all tails in a long run, you'd think it quite improbable, wouldn't you? The individual chances are equally likely or unlikely, but the more times you take the chance, the more opportunities the result you want has to come up.
Just to clarify the TB rules: at level 6 you get 2 attacks if using a 2h weapon at -2 hit, 4 if TWF. When you would normally get extra attacks, your hit penalty goes down instead.
In most situations, they claim up to a 15% dpr increase. On outliers (monsters you need a 3 or less, or an 18 or more, to hit), average dpr goes down.
However, this is not related to crit chance. I believe on the low end this is because of a lack of splash damage, and on the high end because of the small hit chance.
The Gambler's Fallacy is so named because it is a case where conventional wisdom fails. If what you guys are claiming is true, then the more hits you get to make, you would have to use a higher and higher crit multiplier to calculate dpr. This is not the case, you use the same multiplier no matter how many hits you get to make.
One hit:
10 dmg x 1.1 (crit on 19-20) = 11.
4 hits:
40 x 1.1 = 44, or an average of 11 each hit.
But you're missing my point. If I have two-weapon fighting chain and a speed weapon, I have 8 chances to crit every round after level 16. If I only get 1 attack each round then I only have 1 chance to crit each round. If I buy 8 lottery tickets I have 8 chances to win, not 1. My odds of any single ticket winning doesn't change. My odds of at least 1 ticket winning does change.
So how do you account for this if you reduce the number of attacks from 4 to 1? How do you account for the player losing 3 chances of criting with his keen rapier while not changing the marilith's 7 chances of criting each round? I'm sure it can be done. I just don't know how.
Oh, and I'm not going to spend money to read something I'm not going to use. I don't have an issue with high level play slowing down. As the GM I take the time the players are rolling and adding to make sure I'm ready for my next actions and I tell the other players to do the same. High level casters take too long if they wait until their turn to decide what to do.
Usually the single attack has a bonus to hit. This offsets the multiple attack rolls giving a higher chance some damage will go through. It applies the same towards crits.
Multiple lower chances at critting vs one higher chance at critting.
As someone mentioned previously, star wars saga edition only had one attack per round, unless augmented with feats etc. I was a very smooth system and ran much quicker than d+d/pathfinder.
If the way crit worked was, you roll all your hit dice at once, and then the DM rolled a die, and a match meant you crit, then the lottery example would hold true. Buying more tickets does increase your chance in a lottery.
But dice rolls behave like coin tosses, not lotteries.
Each roll is statistically independent of the others, and any combination of crit/non-crit is equally likely.
In a series of rolls, all possible combinations will have probability equal to crit^rolls.
If you have 50% crit and one roll, you will get a crit or a non-crit 0.5^1 times.
If you have 2 rolls, you will get the following combinations, each with 0.5^2 or 25% probability:
Crit/crit
Crit/non
Non/crit
Non/non
In other words, you have a 50% chance to crit one time, a 25% chance to crit twice, and a 25% chance to not crit at all. Your overall chance to crit in the round does not increase with more rolls, and your chance to crit mutiple times goes down with more rolls.
Basically your chance to crit more than once in one round is crit^rolls.
(I am not a mathematician, but I believe this is correct. If there is still contention that doesn't convince me otherwise, I'll pose the question in general.)
If the way crit worked was, you roll all your hit dice at once, and then the DM rolled a die, and a match meant you crit, then the lottery example would hold true. Buying more tickets does increase your chance in a lottery.
But dice rolls behave like coin tosses, not lotteries.
Each roll is statistically independent of the others, and any combination of crit/non-crit is equally likely.
In a series of rolls, all possible combinations will have probability equal to crit^rolls.
If you have 50% crit and one roll, you will get a crit or a non-crit 0.5^1 times.
If you have 2 rolls, you will get the following combinations, each with 0.5^2 or 25% probability:
Crit/crit
Crit/non
Non/crit
Non/nonIn other words, you have a 50% chance to crit one time, a 25% chance to crit twice, and a 25% chance to not crit at all. Your overall chance to crit in the round does not increase with more rolls, and your chance to crit mutiple times goes down with more rolls.
Basically your chance to crit more than once in one round is crit^rolls.
(I am not a mathematician, but I believe this is correct. If there is still contention that doesn't convince me otherwise, I'll pose the question in general.)
Buying multiple tickets does increase your odds of at least one ticket winning. It does not increase your odds of a particular ticket winning. Just like if I have a 1 in 6 chance of rolling a 6 on a d6, the more dice I roll the more chances I have of getting at last one 6. This is where I'm coming from. If the fighter crits on a 20 and rolls 4 times, then his chance of criting at least once increases. If the fighter has a better chance with each roll, then he can crit more often (that's the whole point of keen or improved critical) and you take away his number of attacks, then you reduce his chances of critting.
I don't play SWS. Are there creatures with 2 or more attacks each round? How is this handled? I'm not trying to be difficult. If this isn't accounted for, then non-casters are seriously affected by having only 1 attack each round.
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In other words, you have a 50% chance to crit one time, a 25% chance to crit twice, and a 25% chance to not crit at all. Your overall chance to crit in the round does not increase with more rolls, and your chance to crit mutiple times goes down with more rolls.
If i'm reading you right you're wrong.
He's saying his 1) average number of crits increases with more attacks (which is true) and that 2) His odds of getting one or more crits increases with extra attacks.(also true)
I think you're calculating the odds of a crit on any particular, single die, not for 1 or more crits in the round.
If something crits on a 20 the odds of 1 crit is 1 in 20 or 5%. The chance of not getting a crit is 95%
If you have 8 attacks the chance of not getting ANY crits is.
(.95) ^8 or ~ 66.3% , Meaning you have a 33.7 % chance of getting one or more crits.
Armor class, the confirmation roll, and attack penalties from 2wf will severely mess with those numbers, but he's right in saying that the more he attacks the better chance he has for a crit.
Thank you BigNorseWolf for explaining it better than I did. I wish I could remember all the math I learned to show it like you did.
I see where I missed you, thanks for clarifying.
Yeah, it's a factor of applying towards the "crit triggers an effect", not damage overall.
Overall damage might not be hugely changed, it reacts more like how you put it Hudax (overall crit chance applying towards average damage).
But if you have a vorpal weapon, you are dang well going to want as many attack rolls as possible, because just one single crit means insta-death (or at least a head flying from someone's shoulders, death being dependent on how one reacts to such trauma).
The single attack roll having a higher chance to land and confirm can cover this difference (as I mentioned earlier).
The math gets off on the extreme ends (very high or very low AC), so there isn't a direct way to equate it, but you can keep normal odds within a similar range.
It handles it for SWSaga, and I haven't looked at it in years, but does it deal with the disparity between PCs having only 1 attack and dragons having 6?
I see the problem.
There is no disparity - everything gets one attack per round unless specifically constructed not to.
So, for a Dragon to have 6 attacks per round, there would be multiple feats on the Dragon's behalf involved, full round actions would be taken, and the PC's would have a greater chance on the round in which the Dragon took its multiple, grossly-devastating 6 attacks (at significant penalties, mind you) to do a tremendous amount of damage to said Dragon - thus evening up the fight a lot.
As well, further posts in this thread address the issues of statistics and probability for crits and the like - sadly not the focus of my replies, so I'll stay out of them. Suffice to say, though, my group -has- had success with the one-standard-per-round, as utilized in SWSaga.
Like I said, though, make sure the 1/2-level damage increase gets tacked on, or things get really bad for the PC's, really quickly.
It handles it for SWSaga, and I haven't looked at it in years, but does it deal with the disparity between PCs having only 1 attack and dragons having 6?I see the problem.
There is no disparity - everything gets one attack per round unless specifically constructed not to.
So, for a Dragon to have 6 attacks per round, there would be multiple feats on the Dragon's behalf involved, full round actions would be taken, and the PC's would have a greater chance on the round in which the Dragon took its multiple, grossly-devastating 6 attacks (at significant penalties, mind you) to do a tremendous amount of damage to said Dragon - thus evening up the fight a lot.
As well, further posts in this thread address the issues of statistics and probability for crits and the like - sadly not the focus of my replies, so I'll stay out of them. Suffice to say, though, my group -has- had success with the one-standard-per-round, as utilized in SWSaga.
Like I said, though, make sure the 1/2-level damage increase gets tacked on, or things get really bad for the PC's, really quickly.
Thanks. That's one of the concerns I would have had. Are there enough feats to do this for creatures that should have multiple attacks, like many tentacled creatures? Would a 1 attack per round rule drag a combat out to 3 or 4 times longer in Pathfinder since creatures have tons of hit points? This could make things just as bad as what is trying to be avoided, with bookkeeping on durations being more of a problem. The barbarian rage and the monk's ki will deplete faster since it could be needed longer or more often.
Thanks. That's one of the concerns I would have had. Are there enough feats to do this for creatures that should have multiple attacks, like many tentacled creatures? Would a 1 attack per round rule drag a combat out to 3 or 4 times longer in Pathfinder since creatures have tons of hit points? This could make things just as bad as what is trying to be avoided, with bookkeeping on durations being more of a problem. The barbarian rage and the monk's ki will deplete faster since it could be needed longer or more often.
In this order:
Yes - it's entirely possible to build, say, a Roper, a Marilith, or what-have-you. There are, I believe (I don't have the books in front of me right now) plenty of "this creature has multiple limbs" type feats, enabling you to, within the rules, craft such creatures handily (pardon the pun).
No - Creatures in SWSaga also have tons of hit points. It -may- have been the inclusion of per-encounter powers in SWSaga, but I never found the combats I ran my players through to take any longer than they do in Pathfinder/3.X. In fact, due to the gross lack of iterative attacks, they actually went a bit faster.
Bookkeeping - I didn't find any real issues with this. Your experience may vary.
Rage and Ki - There's not a lot in the SWSaga game that maps to this, except for Wookie Rage. Again, never saw a lot of issues, here.
Trailblazer from Bad Axe games did a simple fix. At level 6 you still get your extra attack as normal, but the penalty is -2 and this applies to all attacks when you full attack. When you would normally get your 3rd attack, the penalty lessens to -1 (you never get more than 2 iterative attacks). When you would get your 4th, the penalty is gone. This only applies to iterative attacks derived from classes, monsters primary and secondary attacks are unaffected.
I'm thinking about using this... ;)
But well, one of my players is a fighter specialized in critics... Ha ask me about the issue of the critics with this rules (which has been discussed at length in this thread ;) ), and with your math I've seen his point... What about a +1 crit range (19-20 if you have a 20 weapon) at the moment of the third iterative ?(where you only have 2 attacks at -1 with this rule) ?
That's only a 5% more crit per rolls, is it too much or is it balanced ?
I think another +1 to crit range at 4th iterative would be too much... What about a crit damage increment ?
In one of my 3.5 Campaigns I used house rules extensively, and one of the rules dealt with iterative attacks. While you still had iterative attacks, the attack and full attack action was merged. The first attack each round was treated as normal, while all other attacks were treated like off-hand attacks regarding damage. If you wanted to you could opt to sacrifice an iterative attack to deal additional damage with your first attack equal to the damage dice of the weapon you used (almost like vital strike now). It seemed to work really well and since you could move between attacks it made combats much more fluid.
Our group has house-ruled vthe vital strike feats so that you do an additional 2d6 damage instead of base weapon damage (making the feat equally good no matter what weapon you use) and you can combine the feat with any maneuver that allows you to make only one attack(like charge, spring attack etc.).
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I've never found multiple attacks slowing my games.
I haven't seen an issue with iterative attacks causing gameplay slowdown.
It's a drop in the bucket compared to the delay added to the game by spellcasters, summoners, or wild shapers, in my experience.
Heck, I'm even a big fan of Rapidstrike and Improved Rapidstrike, which essentially can give creatures iterative attacks (and, alas, do not have Pathfinder versions). It lets creatures that don't wield weapons keep up with the PCs. Nothing like a kraken with the full Rapidstrike/Improved Rapidstrike chain to warm a GM's heart :)
I do agree that damage can be an issue though. These days I often use average damage instead of rolling, say, 3d6+14+2d6 for 18 attacks.
Trailblazer from Bad Axe games did a simple fix. At level 6 you still get your extra attack as normal, but the penalty is -2 and this applies to all attacks when you full attack. When you would normally get your 3rd attack, the penalty lessens to -1 (you never get more than 2 iterative attacks). When you would get your 4th, the penalty is gone. This only applies to iterative attacks derived from classes, monsters primary and secondary attacks are unaffected.This is a great system and I've used it for a few months.
Having only two attacks that roll at the same bonus really speeds up the math. What's more, by very-high-level (16th) when iterative attacks were at their most annoying, the math actually becomes easier because your full attacks all have the same bonus as your standard attack.
On top of all this, the damage output remains pretty close to RAW (except on the extremes).
This has got to be one of the great all-time rule patches. It's a damn shame it's closed content, or I would push hard for inclusion in Pathfinder 2e. Hell, maybe Bad Axe would be nice and share if asked.
I'd love to see this as a PF 2e fix for higher level. I should dust off my TB PDF to see what other gems are lurking there.
This has got to be one of the great all-time rule patches. It's a damn shame it's closed content, or I would push hard for inclusion in Pathfinder 2e. Hell, maybe Bad Axe would be nice and share if asked.
As far as I can tell from its OGL, chapter 1 "contains no open content" but is not listed under their Product Identity, which I think means it can be used under OGL.
Okay, example time.
Kukri Karl, the 17th level fighter wielding paired Kukris, has the two weapon fighting chain, improved critical, critical focus, critical mastery, stunning critical and exhausting critical. If karl gets a critical, his opponent will be both stunned and exhausted. He is fighting Dastardly Dan, and do to various bonuses, needs a 4 to hit, and crits on a 15. Doing damage is nice, but he really wants to get at least one critical to trigger his feats.
His first two attacks, he has a 30% chance for a possible crit, and confirms on a 2. His second two attacks, he has a 30% chance at a possible crit, and confirms on a 5. His third two attacks, he has a 30% chane for a possible crit, and confirms on a 10. His final attack only has a 10% chance for a possible crit, and confirms on a 15.
Since he only cares on getting at least one crit, he wants to know the probability of getting the critical feats to activate. So, the first chance of a crit is 28.5% (.3 * .95), and a 71.5% of not critting. The second chance of a crit is 20.4% chance (.715 (the chance of not critting on the first chance) * .3 * .95). The third chance is 12.3% (.511 * .3 * .8) The fourth chance is 9.3% (.388 * .3 * .8). The fifth chance is 4.9% (.295 * .3 * .55). The sixth chance is 4% (.246 * .3 * .55). The seventh chance is .6%(.206*.1*.3).
So, there is an 80% chance he will get a critical hit against a roll of 4 or higher. If you are only rolling once, to have an equal chance of critting, you pretty much need to crit on a 5.
(I really hope I got the math right...)
...
No - Creatures in SWSaga also have tons of hit points. It -may- have been the inclusion of per-encounter powers in SWSaga, but I never found the combats I ran my players through to take any longer than they do in Pathfinder/3.X. In fact, due to the gross lack of iterative attacks, they actually went a bit faster.
...
I think the amount oh hp on those creatures has a lot to do with weapons that are in use. My lvl 7? soldier specialised on rapid firing heavy assault rifles could do 5d12 damage (due to elite trooper (controlled burst) I could brace the gun, a talent (rapidfire assault?) allowed me to brace even rifles and riflemaster feat increased damage) at full BAB, but that's hardly the heaviest thing you have there, especially if a sith dragon has to deal with speeders, tank or even a fighter under PC's command.
(I really hope I got the math right...)
Isn't it easier to calculate the chances of not critting and multiplying those, then subtracting that from 1? :p P(at least one crit) = 1 - P(no crit at all). The result was extremely close to 0.8 though.
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Vital strike doesn't really come close to what iterative attacks end up doing at higher levels. Your idea might work at lower levels, but at higher levels it would represent a massive drop in damage for martial characters.
It would also drastically shift the power in favor of natural weapons vs iterative attacks with manufactured weapons.
Thankfully paizo has offered a slightly better option in unchained, its much faster then rolling all those attacks, but keeps damage numbers pretty even.
I know as a GM, it can be time consuming in some cases for everyone to be rolling multiple attacks.
I don't buy it. This only takes a meaningful amount of time because someone's being lazy.
Look. Calculate all the bonuses and penalties going on ONCE. You already have to do that for your first attack.
"Wizzy's got bless up, but my Strength is drained 3, and oh, I'm raging..." Figure out the bloody number.
Roll the die. Add the number. The DM resolves it as a hit or a miss.
Roll the die. Add the number. Subtract five.
Rinse, repeat until you're out of attacks.
Unless you've got people who take a million years to add a few damage dice, there isn't a meaningful difference between one attack and six attacks.
If it takes longer than any high-level caster's considerations, someone's seriously got a math impediment.
This thread is just about ready for Kindergarten.
My issue with all of the "remove iterative attacks" plans is that it removes versatility.
This thread is just about ready for Kindergarten.
My issue with all of the "remove iterative attacks" plans is that it removes versatility.
Have you looked at the unchained rules? They actually dont remove a lot of versatility.
While I like 3.5/Pathfinder there are some things that I hate about it. The first and I think most crippling is multiple attacks. At low levels not so bad. BUT hit 10th-16th and the game comes to a crawl. No matter the shortcuts involve(using different color dice, random generators etc)it's still a drag on the game. My question is simple: Would it kill the game if every character had a base of one attack with higher up and maybe certain classes getting maybe one extra attack or something in that ballpark? Alot of people say "well the spellcaster would out do a fighter type in damage. But if the fighter type is doing +16 damage is that still the case?
Multiple attacks were a thing since First Edition.
And usually at high level games, most of the delay is coming from the spellcasters, especially the summoning ones.
Remember that there are a few feats and class features that easily allow characters to completely nullify a single attack... So if that's all everyone gets, these feats and class features should be removed as well.
Wait, black magic?
Necromancy of the threadly variety.
Have you looked at the unchained rules? They actually dont remove a lot of versatility.This thread is just about ready for Kindergarten.
My issue with all of the "remove iterative attacks" plans is that it removes versatility.
I have, and they remove just as much versatility as every other suggestion.
1) Some people might want to use a full attack to hit multiple targets without necessitating cleave or whirlwind attack to do it. Maybe they want to trip multiple people, disarm, sunder, or something.
2) Effects that trigger from critical hits become less useful since you have fewer opportunities to confirm critical hits.
You want to slow down a game? Give PCs pets & minions to control.
You get actions for each additional critter.
You get decision paralysis of what to do.
You get more opportunities for weird rule interactions that must be looked up.
In comparison, an iterative is usually quickly resolved since it is against the same AC with the same weapon at -5/-10/-15. Multiple weapons are a little more complicated, but not too much. Also, the usual attack form is usually stated out on the character's sheet with relevant mods listed.
I once had to play a ship's compliment of NPCs against the DM's monsters. There were multiple classes, many effects in play, and so much to consider, that I forgot to have the cleric cast bless. :-/
/cevah
Having 1 attack would be bad, terribly so, for weapon-based users. I mean they're already significantly nerfed as it is in Pathfinder and this would pretty much bury them altogether. Honestly I think the entire premise that you subtract from the attack roll on your iterative attacks is a pretty terrible one. Getting multiple attacks should be a good class feature, not overly penalized for....I don't really know why? Hell I'd be willing to sacrifice an entire 4th iterative attack if I could keep the same bonus over the course of a 20 level progression. A warrior-type (full BAB) could get a second attack at 6th and a final attack at 12th and be done, all with a total BAB = to level.