@FinneousPJ. Apparently, the probability of critting at least once in a round with SW Style is close to 30%, but it is really 27.1%. The formula that I used of (9/10)^x for the probability of x consecutive non critical swings actually proves it.
@Cardinal_Thor. On tossing a coin, the probability of throwing tails twice in a row is (1/2)^2 = 25%, so the probability of tossing heads at least once in two tosses is 75%.
On tossing a coin, the probability of throwing tails twice in a row is (1/2)^2 = 25%, so the probability of tossing heads at least once in two tosses is 75%.
Granted; keeping in mind that the specific probability of tossing heads on either roll, individually, is still 50%.
-CT
Edit: This is reminding me of Rosencrantz and Guildenstern...
Anyway, the more attacks you throw, the better your chance of getting your results. This is because, if the system is unbiased, with a large enough sample, everything will come out even. If you roll a d20 20,000,000 times you're probably going to see an almost equal distribution of every number.
You could still end up with20.000.000 20's. the chance is not big, but it is bigger than 0 .
Chance and probability was one of the best Uni courses I ever took. The professor was a little bit like Sheldon Cooper...numbers and equations to justify every/any thing.
You've all been very crafty in some of your ideas in this thread. Im very thankful and its come to be that I have a different idea for a critical hit thief char. I originally thought of single weapon for crit bonus, then twohanded for crit bonus and dam bonus. Now I concede and go with the fact that a thief's biggest weapon in a game where fighters dominate melee, is a ranged weapon (preferably a bow). The reason why is that if you have 2 attacks or more, that's extra chances of rolling a critical. Compare that to a single weapon or twohanded weapon focus char. Although they get more chance, they get less attacks. Which would make a better critical hit chance for a thief archer, a short bow (2 attack) or a dart thrower (3 attack) ?
Hrm~ there are a lack of dart throwers in the game. And Rate of Fire is important. You could dual class a fighter to a thief. That would let you max out dart throwing (or shortbows for that matter) then switch to thief. If all you care about is crits as a thief, you could go swashbuckler and put two points into ranged weapons.
The Assassin is a decent kit around level 16 or so when the higher backstab multiplier comes into play, until then its not really all that amazing. The 15 skill points per level is a tough pill to swallow for poisoned weapon and a +1 to hit and damage in my opinion. Also, if you plan on using ranged attack (therefore forgoing backstabbing) Assassin really isn't that great of a choice but if your heart is set I'd suggest using Darts for the higher number of attacks per round and therefore better chance to spread your poison around since it works on ranged attacks.
A Fighter > Thief dual class or Fighter/Thief multiclass will be better at ranged fighting (well any fighting really) since they get greater Thac0 progression, at least weapon specialization and more attacks per round. If you're only going to play BG:EE I'd suggest the multiclass so you wont be stuck for a good portion of the game without your fighter abilities. If you want to carry the character over to BG2:EE Fighter til level 7 then dual class to Thief will be pretty strong and will still let you use your thief abilities in the first game.
The Assassin is a decent kit around level 16 or so when the higher backstab multiplier comes into play, until then its not really all that amazing. The 15 skill points per level is a tough pill to swallow for poisoned weapon and a +1 to hit and damage in my opinion. Also, if you plan on using ranged attack (therefore forgoing backstabbing) Assassin really isn't that great of a choice but if your heart is set I'd suggest using Darts for the higher number of attacks per round and therefore better chance to spread your poison around since it works on ranged attacks.
A Fighter > Thief dual class or Fighter/Thief multiclass will be better at ranged fighting (well any fighting really) since they get greater Thac0 progression, at least weapon specialization and more attacks per round. If you're only going to play BG:EE I'd suggest the multiclass so you wont be stuck for a good portion of the game without your fighter abilities. If you want to carry the character over to BG2:EE Fighter til level 7 then dual class to Thief will be pretty strong and will still let you use your thief abilities in the first game.
I agree that dualclass is more powerful. However, I find that dualclassing characters is the most overpowered thing in the game series. I find it is a uber player's paradise and with my experience in the game, it makes soloing the party without armor all too easy. The reason I usually used solo classes is that they have visible weaknesses. Dualclassing while strong, has no weaknesses. My fighter/thief I used to solo bg2 and tob was a god who could not be destroyed and had no weakness. When solo-dual class. When party-single class. That's just how I play although I appreciate the idea
Since there seem to be some misconceptions about the way critical hit chances are calculated, I want to clarify this.
Critical hits occur when if you roll a natural 20 on your attack roll and a natural 20 would be enough to hit your target (except for two handed weapons if you put two points into two-handed weapon style). The easiest way to explain the probabilites is by examples.
Example 1: Charname THAC0 18, Enemy AC 0. Natural roll needed to hit: 18. Hit Chance: 15%. Critical hit chance per attack: 5%. Critical hit chance per hit: 33%.
Example 2: Charname THAC0 18, Enemy AC -1. Natural roll needed to hit: 19. Hit Chance: 10%. Critical hit chance per attack: 5%. Critical hit chance per hit: 50%.
Example 3: Charname THAC0 18, Enemy AC -2. Natural roll needed to hit: 20. Hit Chance: 5%. Critical hit chance per attack: 5%. Critical hit chance per hit: 100%.
Example 4: Charname THAC0 18, Enemy AC -3. Natural roll needed to hit: 20. Hit Chance: 5%. Critical hit chance per attack: 0%. Critical hit chance per hit: 0%.
I hope this helps.
i think the last is wrong because critical hit = always hit
I'm faily sure that is correct. If you couldn't hit your target even on a 20 roll (disregarding special rules), then rolling a 20 will be a hit, but not a crit. If you could hit your target, it will be a crit (and, of course, a hit).
This rarely matters in practice, as there are few instances where your THAC0 is terrible while enemy AC is amazing AND they aren't immune to crits anyway.
With all the stats flying around, I'm surprised no one's mentioned expected value. It seems pretty relevant here. The probabilities that have been thrown around so far are the chance of getting at least one crit in x attacks. Expected value is how many crits you can expect to get in x attacks, on average. These are not the same thing (unless x = 0 or 1), and since we care about every single crit we get, expected value seems like the more relevant thing to calculate. It's also really, really easy.
To get the expected value, simply add up the probabilities. So if we have a 5% (.05) chance to hit with each attack, and we attack three times, we get .05 * 3 = .15 critical hits on average. This works because, unlike "at least"-style probabilities, expected value cares if you score more than one critical hit ("at least" considers 1 crit, 2 crits, and 3 crits to be the same thing). Since we also care about that, expected value probably makes more sense here than the probability of scoring at least one crit. Also, note that while expected value is derived from probabilities, it is not a probability itself. It's just an average.
The reason why people don't delve deeper into the details is that they are fairly irrelevant; itemization is very limited, and so is choice of the factors involved in critical hits. It's not like can "gear for crit" the way you can in other games - criticals just happen, and that's nice, but it's largely out of your control. The only thing that influences criticals in an active way is the Critical Strike HLA, and that just gives a flat 100% so it's not exactly very hard to calculate.
The only time critical hits would be even remotely relevant is with 1h/2h specialization. But given the absurd power of APR in this game, 1h almost always falls short due to dual-wield; and 2h is, once again, a no-choice scenario since it's the only available option anyway.
So I suppose you could use EV numbers to calculate 1h-spec vs. dual-wield without an APR OH. That could be interesting, but most likely it's another no-brainer due to the fact that the available non-APR OHs still confer significant other bonuses (like, say, Crom Faeyr).
Since we are discussing percentage chances and whatnot, I'd like to take this time to point out the interesting "gambler's fallacy" that Franco seemed to be making in the posts on the previous page, namely along the lines that if you have a chance of something happening (say a 10% chance), it adds up the more attempts you have (so in 9 attempts you would have a 90% chance). It's better to think of it as having a 10% chance every fresh roll than to add them together with the last roll. History doesn't influence future odds.
from "gambler's fallacy" link: The most famous example of the gambler’s fallacy occurred in a game of roulette at the Monte Carlo Casino on August 18, 1913, when the ball fell in black 26 times in a row. This was an extremely uncommon occurrence, although no more nor less common than any of the other 67,108,863 sequences of 26 red or black. Gamblers lost millions of francs betting against black, reasoning incorrectly that the streak was causing an "imbalance" in the randomness of the wheel, and that it had to be followed by a long streak of red.
The reason why people don't delve deeper into the details is that they are fairly irrelevant; itemization is very limited, and so is choice of the factors involved in critical hits. It's not like can "gear for crit" the way you can in other games - criticals just happen, and that's nice, but it's largely out of your control. The only thing that influences criticals in an active way is the Critical Strike HLA, and that just gives a flat 100% so it's not exactly very hard to calculate.
The only time critical hits would be even remotely relevant is with 1h/2h specialization. But given the absurd power of APR in this game, 1h almost always falls short due to dual-wield; and 2h is, once again, a no-choice scenario since it's the only available option anyway.
So I suppose you could use EV numbers to calculate 1h-spec vs. dual-wield without an APR OH. That could be interesting, but most likely it's another no-brainer due to the fact that the available non-APR OHs still confer significant other bonuses (like, say, Crom Faeyr).
This is both correct and crucially important. Especially given that immunity to crits is fairly common, and increases to crit chance are virtually nonexistent, critical hits just aren't very important in Baldur's Gate. Are they nice? Sure. Are they occasionally life-saving? Occasionally, yes, depending on good you are at the game. Do they impact the strategies in a significant way? Absolutely not. That extra 5% crit chance from one-weapon and two-handed styles will be as good as a single extra attack only once we already have 20 attacks per round (which is, to my knowledge, impossible). Also our target has to not be wearing a helmet. Since two-weapon fighting is generally going to give two extra attacks (one at a penalty, but still), we'd basically always be happier dual-wielding. I suppose the AC bonus helps even that out slightly, but only very, very slightly (the precise math depends on incoming attacks per round, but it tends to be fairly low).
Since we are discussing percentage chances and whatnot, I'd like to take this time to point out the interesting "gambler's fallacy" that Franco seemed to be making in the posts on the previous page, namely along the lines that if you have a chance of something happening (say a 10% chance), it adds up the more attempts you have (so in 9 attempts you would have a 90% chance). It's better to think of it as having a 10% chance every fresh roll than to add them together with the last roll. History doesn't influence future odds.
from "gambler's fallacy" link: The most famous example of the gambler’s fallacy occurred in a game of roulette at the Monte Carlo Casino on August 18, 1913, when the ball fell in black 26 times in a row. This was an extremely uncommon occurrence, although no more nor less common than any of the other 67,108,863 sequences of 26 red or black. Gamblers lost millions of francs betting against black, reasoning incorrectly that the streak was causing an "imbalance" in the randomness of the wheel, and that it had to be followed by a long streak of red.
but they are idtiots roulette doesn't have a memory
it is like with this question when you flip a coin 5 times and it is 5 times tail what is the probability of getting tails for the 6th time? it is 50% like always
but they are idtiots roulette doesn't have a memory
it is like with this question when you flip a coin 5 times and it is 5 times tail what is the probability of getting tails for the 6th time? it is 50% like always
People think that to get the 50% chance of heads or tails, if you flip 5 heads in a row, you have to have 5 tails in a row. 50% heads, 50% tails. So if you get 26 black in roulette, you must get 26 reds - but -
each time a coin is flipped (or roulette ball rolls) there is a fresh 50% chance.
It's not hard, that's right. However, most people in the US (and throughout the world, as well as I can tell) receive little-to-no statistics education. They know that if you flip a coin 6 times, you can expect 3 heads and 3 tails on average. No one's bothered to actually teach them that the average can change dramatically if you already know the outcome of the first 3 coin flips. It's not their fault. It's the fault of whoever decided that the average person needed trigonometry more than they needed statistics.
Comments
@Cardinal_Thor. On tossing a coin, the probability of throwing tails twice in a row is (1/2)^2 = 25%, so the probability of tossing heads at least once in two tosses is 75%.
-CT
Edit: This is reminding me of Rosencrantz and Guildenstern...
Chance and probability was one of the best Uni courses I ever took. The professor was a little bit like Sheldon Cooper...numbers and equations to justify every/any thing.
A Fighter > Thief dual class or Fighter/Thief multiclass will be better at ranged fighting (well any fighting really) since they get greater Thac0 progression, at least weapon specialization and more attacks per round. If you're only going to play BG:EE I'd suggest the multiclass so you wont be stuck for a good portion of the game without your fighter abilities. If you want to carry the character over to BG2:EE Fighter til level 7 then dual class to Thief will be pretty strong and will still let you use your thief abilities in the first game.
for example long sword +1 or better long sword+1+1cold damage
is it (str+proficiency+sword dmg+sword magic+sword elemental dmg)*2=critical hit?
or is it only sword dmg*2+ the rest?
i would go only for 19 str orc thiefes!
This rarely matters in practice, as there are few instances where your THAC0 is terrible while enemy AC is amazing AND they aren't immune to crits anyway.
To get the expected value, simply add up the probabilities. So if we have a 5% (.05) chance to hit with each attack, and we attack three times, we get .05 * 3 = .15 critical hits on average. This works because, unlike "at least"-style probabilities, expected value cares if you score more than one critical hit ("at least" considers 1 crit, 2 crits, and 3 crits to be the same thing). Since we also care about that, expected value probably makes more sense here than the probability of scoring at least one crit. Also, note that while expected value is derived from probabilities, it is not a probability itself. It's just an average.
The only time critical hits would be even remotely relevant is with 1h/2h specialization. But given the absurd power of APR in this game, 1h almost always falls short due to dual-wield; and 2h is, once again, a no-choice scenario since it's the only available option anyway.
So I suppose you could use EV numbers to calculate 1h-spec vs. dual-wield without an APR OH. That could be interesting, but most likely it's another no-brainer due to the fact that the available non-APR OHs still confer significant other bonuses (like, say, Crom Faeyr).
from "gambler's fallacy" link:
The most famous example of the gambler’s fallacy occurred in a game of roulette at the Monte Carlo Casino on August 18, 1913, when the ball fell in black 26 times in a row. This was an extremely uncommon occurrence, although no more nor less common than any of the other 67,108,863 sequences of 26 red or black. Gamblers lost millions of francs betting against black, reasoning incorrectly that the streak was causing an "imbalance" in the randomness of the wheel, and that it had to be followed by a long streak of red.
roulette doesn't have a memory
it is like with this question when you flip a coin 5 times and it is 5 times tail
what is the probability of getting tails for the 6th time? it is 50% like always
each time a coin is flipped (or roulette ball rolls) there is a fresh 50% chance.
no memory = fresh 50% chance
i don't get it how can someone think different
it is not hard nor high level or quantum physics
If you flip a coin 10 times and it somehow turns up heads every time, what are the odds the next flip you will get tails?