Calculating Probability: Did I get something wrong?

[Boci]

So a while ago I made the following claim on another thread:

You beat him on initiative 60% of the time. You get 3d6 iaijutsu damage 50% of the time. You hit his flat footed AC 60%. The chances of every single one working out is 18%.

My maths was 0.6 x 0.6 x 0.5 = 0.18. I was told I was wrong, and I went over everything and I cannot see how else to the chance could work out. Am I missing anything?

[kamikasei]

The quote in your OP seems to link to a different thread/post than the one where this discussion actually took place. Can you give more context?

From what you've said, your calculation appears to be correct.

[Boci]

The quote in your OP seems to link to a different thread/post than the one where this discussion actually took place. Can you give more context?

From what you've said, your calculation appears to be correct.

I didn't think any more context was neccissary. The discussion was one of my all nighter arguments, this time reguarding the CR of Ekolids, here: http://www.giantitp.com/forums/showthread.php?t=151854

My origional claim is at the bottom of post 27.

[Jayabalard]

So a while ago I made the following claim on another thread:



My maths was 0.6 x 0.6 x 0.5 = 0.18. I was told I was wrong, and I went over everything and I cannot see how else to the chance could work out. Am I missing anything?

THe only part that initially looks suspect to me is "You beat him on initiative 60% of the time. "

[Boci]

THe only part that initially looks suspect to me is "You beat him on initiative 60% of the time. "

In what way?

[kamikasei]

I didn't think any more context was neccissary.

Whereas the obvious course of action to my eyes is to ask the guy who told you you were wrong why he thinks so. I thought you might have done so there and so I could take a look at his reasoning and see if I was missing something, but the point doesn't seem to have been followed up at all.

Perhaps he's referring to your wording, saying "you do X Y% of the time" instead of "you have a Y% probability of doing X". They're not the same thing, though the distinction isn't really important in this case.

But ultimately, we can't read Greenish's mind for you. If you want to know his reasoning, you'll have to ask him.

Incidentally, I think your math for the initiative is wrong. My calculation:

Spoiler

Show

His modifier is +3, yours is +6. You win ties. Look at all the results he can get on a roll of 1-20. For each one, work out how many possible results on your own roll will equal or beat his. Add them up and convert to a total probability.
So if he rolls 20 for a result of 23, you can beat that with a result of 17+, which means 4 out of 20 results. If he rolls 19 you beat it on 5 results, and so on down to his rolling a 4 for a 7 which you automatically beat 20 out of 20 results; same for 3, 2, and 1. So if he has 20 different rolls and you have 20 possible results against each of them, that's 400 total rolls in which you succeed 20+20+20+20+19+18...+5+4 times. Comes out to 264 results in your favour, or 66% of the total.

[Boci]

Whereas the obvious course of action to my eyes is to ask the guy who told you you were wrong why he thinks so. I thought you might have done so there and so I could take a look at his reasoning and see if I was missing something, but the point doesn't seem to have been followed up at all.

At first I just assumed I was wrong since maths never was my strong point, then after going over it several times and googling statistical probability I ask him in the last post to explain why I was wrong, but by then the discussion had died out.
Since I felt the issue was more about me than the origional discussion, I felt I should start a new thread rather than bumping that one, especially since it would require me to double post.

Perhaps he's referring to your wording, saying "you do X Y% of the time" instead of "you have a Y% probability of doing X". They're not the same thing, though the distinction isn't really important in this case.

I guess it was my wording. Either that or they got confused with the common mistake of thinking that having gotten 2 heads in a row the probability of getting a third one is 1/8, when it is actually 1/2, and thought I was using the same flawed logic in my calculations.

[kamikasei]

At first I just assumed I was wrong since maths never was my strong point, then after going over it several times and googling statistical probability I ask him in the last post to explain why I was wrong, but by then the discussion had died out.

Ah, I missed that part of the last post, sorry.

[Kylas]

I guess it was my wording. Either that or they got confused with the common mistake of thinking that having gotten 2 heads in a row the probability of getting a third one is 1/8, when it is actually 1/2, and thought I was using the same flawed logic in my calculations.

Just to make sure in this case the chance of getting 3 heads IN A ROW would be 1/8th right?

[Boci]

Just to make sure in this case the chance of getting 3 heads IN A ROW would be 1/8th right?

Yes, but if it has already been established that you have gotten 2 heads, then the chances of getting a third head is just 1/2. At least I think.

[kamikasei]

Just to make sure in this case the chance of getting 3 heads IN A ROW would be 1/8th right?

If you want to predict three heads in a row, before any coins have been flipped, the probability is 1/8th (and the same for any other specific combination, for that matter). But once you've started flipping coins, the probability of each individual one coming up one way or another is unaffected by the flips that have come before. Getting "heads, heads, tails" is just as probable as getting "heads, heads, heads", after all.

(Or in other words: yes, right.)

[Kylarra]

Yes, that's the gambler's fallacy.
http://en.wikipedia.org/wiki/Gambler%27s_fallacy

[Greenish]

Perhaps he's referring to your wording, saying "you do X Y% of the time" instead of "you have a Y% probability of doing X". They're not the same thing, though the distinction isn't really important in this case.

Nah, it was just plain ol' fail at statistics on my part (I was pulling an allnighter too, and in the spirit of one-upsmanship I was also having a beer or two).

[Saeveo]

I'm curious: how did you calculate the probability of winning initiative to be 0.6?

[Kylarra]

Nah, it was just plain ol' fail at statistics on my part (I was pulling an allnighter too, and in the spirit of one-upsmanship I was also having a beer or two).

HEY DON'T KILL MY MORNING WITH YOUR TROPES

[Boci]

I'm curious: how did you calculate the probability of winning initiative to be 0.6?

Initiative modifier was 2 points higher.

[kamikasei]

Initiative modifier was 2 points higher.

+3 dex versus +2 dex and +4 int is a two-point difference? :P

(Also, that'd work out to 61.75% if my earlier math was correct.)

[Jayabalard]

I'm curious: how did you calculate the probability of winning initiative to be 0.6?

That was my question; assuming that you and someone else each roll d20, and you have some bonus advantage, you'll never have a 60% (exactly) chance of beating them.

Initiative modifier was 2 points higher.

I'm pretty sure that's not how it works.

If you look at all the possible combinations of rolls for various bonus advantages:

• p1 bonus advantage= 0, p1 beats p2 190 times, p2 beats p1 190 times, tie 20 times, P1 wins 47.50% of the time, ties 5% of the time
• p1 bonus advantage = 1, p1 beats p2 210 times, p2 beats p1 171 times, tie 19 times, P1 wins 52.50% of the time, ties 4.75% of the time
• p1 bonus advantage = 2, p1 beats p2 229 times, p2 beats p1 153 times, tie 18 times, P1 wins 57.25% of the time, ties 4.55% of the time
• p1 bonus advantage = 3, p1 beats p2 247 times, p2 beats p1 136 times, tie 17 times, P1 wins 61.75% of the time, ties 4.25% of the time
• p1 bonus advantage = 4, p1 beats p2 264 times, p2 beats p1 120 times, tie 16 times, P1 wins 66% of the time, ties 4% of the time

[Saeveo]

Would it not be 0.66? (I'm assuming the +6 modifier trumps the +3 if they tie.)

Edit: Oh, you actually simulated it. Nice.

[kamikasei]

Would it not be 0.66? (I'm assuming the +6 modifier trumps the +3 if they tie.)

It'd be 0.66 with the given figures. 0.6175 was for Boci's mistaken assumption of a 2-point difference. (Or maybe he was right on that and made a typo in the figures.)

[Saeveo]

It'd be 0.66 with the given figures. 0.6175 was for Boci's mistaken assumption of a 2-point difference. (Or maybe he was right on that and made a typo in the figures.)

Agh, I didn't see the edit with your calcs. Could have saved myself the bother of working it out.

[Greenish]

The 18% figure is pretty irrelevant though, since if you win initiative and manage to hit (about 40% chance to do both), you'll get IF damage, so the last roll merely determines the amount.

If someone better versed on statistics than me wants to calculate it, I'd be happy to know the average damage of IF with +11 modifier.

For reference:

{TABLE]score | bonus
10-14:| +1d6
15-19:| +2d6
20-24:| +3d6
25-29:| +4d6
30-34:| +5d6[/TABLE]

[OldTrees]

1d20+11 IF
skill checks do not auto fail

1-3+11->12-14->+1d6
4-8+11->15-19->+2d6
9-13+11->20-24->+3d6
14-18+11->25-29->+4d6
19-20+11->30-34->+5d6

(3/20)x(1d6)->3d6/20
(5/20)x(2d6)->10d6/20
(5/20)x(3d6)->15d6/20
(5/20)x(4d6)->20d6/20
(2/20)x(5d6)->10d6/20

(3+10+15+20+10)(d6)(1/20)
(58/20)d6
2.9d6

or 2.9X3.5 average damage
10.15~10 damage

[gallagher]

If you win initiative, don't you catch them flatfooted in the first round? That would explain why both are 60%. therefore, it is. 30% chance, unless my orginal statement is wrong

[Greenish]

or 2.9X3.5 average damage
10.15~10 damage

So it works out to be about same as 3d6 (which would be average 10.5 damage). Thanks.

If you win initiative, don't you catch them flatfooted in the first round? That would explain why both are 60%. therefore, it is. 30% chance, unless my orginal statement is wrong

I'm not sure I follow what you're saying.