The Gaming Den

What is the probability then?

Because frankly, if people who are supposed to know the answer (whether or not they can calculate it) get it wrong more than half the time when it is phrased in what is apparently the best way, making sense of any of this in a way that can be translated is exceedingly difficult.

Out of 10,000 women, 1030 get positive results.

Of those 1030, 80 actually have cancer.

So the probability is 7.8%.

That's not too bad.

AW you read the question wrong. it was not "how many of all 10000 women have cancer?"(1%), but "how many who test positive actually have cancer?", for which IGTN's calculation looks right by my guestimation.

But the difficulty here is the wording rather than the math. The math is still real easy once you see what calculations must be done.

Sure, but most people have problems with understanding how the conditionals work, as illustrated by those results.

And its the problem that we've got here.

Yeah but I don't think E is not questioning the wording he's questioning the mathclear explained and laid out for him which crystal fucking clear examples and he's still not getting it/willfully ignoring. He's indefensible.

No, I'm questioning how much those examples actually neatly apply in play once people start making their actual decisions instead of hypothetical ones.

For drinking poisoned wine? Either your cup is posioned or it isn't (decided however), you notice the poison in time or you don't, and you do or don't save vs. the poison.


A fight? Much more complicated. If I win Initiative and hit someone, assuming hitting them causes a penalty to their to hit, their -actual- threat just dropped. Even though mathematically they had an equal chance to hit me beforehand.

Your opponent could have just as easily won initiative and hit you, lowering your threat. Even though mathematically you had an equal chance to hit them beforehand.

You're not changing any probability here.

My point is, one of those is actually going to happen, and that is going to influence whether or not you actually win and/or survive the encounter.

Since it is extremely unlikely (as in, if you can think of a case of it, I can't) that you'll run into someone with perfectly identical stats, you're likely to have some advantage (or disadvantage) and so will your opponent.

It may balance out overall, but in the immediate fight, it probably won't be perfectly even.

So having an even chance in a fight in theory and having something you could settle in a coin clip are two different things in play.

Elennsar wrote: Since it is extremely unlikely (as in, if you can think of a case of it, I can't) that you'll run into someone with perfectly identical stats, you're likely to have some advantage (or disadvantage) and so will your opponent.

In the real world, yes. You are unlikely to encounter someone perfectly matched to your abilities. In a game, it's a lot more likely. The DM, either through accident or intent, will probably wind up copying one of the PCs stats at some point. If for no other reason than to make a tough guy on the fly.

Regarding things hapening that influence the ultimate outcome, no one is disputing that. What you're doing is just weighting individual components of the fight differently. And that's something that can be accounted for. If going first is so important, then whatever percentage chance you have of going first weights more heavily on your overall chance of winning the fight than does your ability to make armor saves, for example. Get it?

In the real world, yes. You are unlikely to encounter someone perfectly matched to your abilities. In a game, it's a lot more likely. The DM, either through accident or intent, will probably wind up copying one of the PCs stats at some point. If for no other reason than to make a tough guy on the fly.

Since I've never experienced it or seen much sign of it - I presume that this is either from personal experience or a sign its much more common in some (many?) groups.

Regarding things hapening that influence the ultimate outcome, no one is disputing that. What you're doing is just weighting individual components of the fight differently. And that's something that can be accounted for. If going first is so important, then whatever percentage chance you have of going first weights more heavily on your overall chance of winning the fight than does your ability to make armor saves, for example. Get it?

The point is, you can have an even chance overall of winning and have whatever your advantage is wind up winning - for instance:

Axes attack twice as slowly as swords.

They do 1.5 times as much damage.

Assuming that's balanced (I'm not saying it is...would appreciate someone checking, I'm using this as an example) - if you win initiative, and hit someone with an axe, and that amount of damage shoves them into a Bad Position, then your odds of winning the actual fight just shot up.

That sort of thing will happen in play, that sort of thing is still "equal" in the abstract.

Note: Same principle applies for the axe guy if he simply is the first one to hit (which does not require winning Initative).

E, my question regarding how often someone should survive combat was to you. Please give us specifics on how often you would like cahracters to survive.

"Axes attack twice as slowly as swords. They do 1.5 times as much damage."

In 3 sword attacks you have 3 sword damage and 2 axe attacks for 2 axe damage (1.5*2 is 3 sword damage). On the surface this looks balanced, right? In the long run, these do exactly the same damage. What is not taken into account is that the sword-wielder gets 3 data points (hp/ac) to the axe-wielders two. You will see the sword-wielder killing more low-hp monsters than the axe-wielder, and killing large-hp monsters at close to the same rate (the last attack is more likely to be a sword attack).

The above analysis gets shifted if you have anything else. An axe-wielder is better against a monster than has DR, while a sword-wielder is drastically better if there is any kind of bonus damage per attack (SA, flaming sword). If we are playing with PA/CE, then the sword wielder is getting 3 data points to the axe-wielders 2, and can PA/CE significantly more effectively. If we are playing something where the axe-wielder is likely to force a save (massive damage, for instance), then the axe-wielder has an advantage. If we are playing a Wound System where a sword attack does a Light Wound and 2 Light Wounds have a 50% chance of becoming a Moderate Wound, while an axe-wielder is consistently doing Moderate Wounds, then the axe-wielder is favored. If you play with all of the above, it becomes tricky and highly situational.

Given:
1% tested are positive.
80% of positive, test positive.
9.6% of negative, test positive.
Subject tests positive.
--- Inferrred ---
There is a 100-9.6-80 = 10.4% chance of the test failing.
Subject is in the "is positive and tested positive" (80%) category, the "is negative and tested positive" (9.6%), or the "test failed" (10.4%) category. We can simplify this to "with a positive result, she can either have cancer (80%) or something else could happen (20%)".

What is the chance that she has cancer?
80%
What is the chance that she does not have cancer?
9.6%
What is the chance that she tested positive and we don't know why?
10.4%

80% of women that get positive tests have breast cancer. She tested positive.

Elennsar wrote: Personally, I stand by the fact that 50-50 is pretty good for something meant to be a very close call judging by how the survival chances break down.

No, it's really not. Based on how the percentages go, you're very likely to lose half your group or more. And if that happens, it's basically a TPK.

"Close calls" should be set up so that on average they end up being close calls. That is, nobody dies but you're pretty weak. If you've lost half your PCs, that's no longer a close call, it's a bloodbath.

I mean, what else would you call a battle in which half of the main characters in any Star trek show died. If Picard, Data and Troi get offed in a single battle, that's not a close call, it's basically the end of the series.

And you want to set that up as the most likely result?!

SunTzuWarmaster wrote:Given:
1% tested are positive.
80% of positive, test positive.
9.6% of negative, test positive.
Subject tests positive.
--- Inferrred ---
There is a 100-9.6-80 = 10.4% chance of the test failing.

You can't assume the cahnce of the test failing is the same for both those with and without cancer.

(1% of women at age forty who participate in routine screening have breast cancer)
=> 99% of women at age forty who participate in routine screening do not have breast cancer (=100%-99%)

(1% of women at age forty who participate in routine screening have breast cancer) and (80% of women with breast cancer will get positive mammographies.)
=> 0.8% will get true positive results (=1%x80%)

(1% of women at age forty who participate in routine screening have breast cancer) and (0.8% will get true positive results)
=> 0.2% will get false negative results (=1%-0.8%)

(99% of women at age forty who participate in routine screening do not have breast cancer) and (9.6% of women without breast cancer will also get positive mammographies)
=> ~9.5% will get false positve results (=99%x9.6%)

(99% of women at age forty who participate in routine screening do not have breast cancer) and (~9.5% will get false positve results)
=> ~89.5% will get true negative results (=99%-~9.5%)

So, "A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?"

(0.8% will get true positive results) and (~9.5% will get false positve results)
=> ~10.3% will get positive results (=~9.5%+0.8%)

(0.8% will get true positive results) and (~10.3% will get positive results)
=> ~7.8% of positive results will be true positive results (=0.8%/~10.3%)

Therefore, she has a ~7.8% chance of actually having breast cancer.

oh god oh god oh god why is this still going please no more math

Psychic Robot wrote:oh god oh god oh god why is this still going please no more math

It hurts. Oh yes, I went there.

Great game series, but it kind of went FUBAR in terms of plot at the end.

Psychic Robot wrote:Great game series, but it kind of went FUBAR in terms of plot at the end.

Indeed. Also, UMBRELLA!

...Yes, this is more productive than wrestling with Elennsar. Don't complain.

Its important to demonstrate that people do not understand probabilities.

cthulhu wrote:Its important to demonstrate that people do not understand probabilities.

I believe that this thread is sufficient proof.

Clearly, but I'd venture that a number of participants in this thread just answered a probability question incorrectly.

Anyway, until Elessnar articulates a vision, he's not going to be worth engaging with at this point.

IGTN wrote:Out of 10,000 women, 1030 get positive results.

Of those 1030, 80 actually have cancer.

So the probability is 7.8%.

Yep it is. I just spotted my error. I figured all the stuff about the percentages of women with or without breast cancer was just a bunch of red herrings, since it didn't directly tell you the odds that a woman who tested positively actually had cancer. It didn't occur to me to use that information to figure out the missing probabilities. Once you do that, you end up with a probability of about 7.8%.

But I still think getting this particular problem wrong is more about the ability to get the relevant information out of word problems than about probability. I massively failed to figure out how to get the probabilities out of that paragraph, but knew how to use the probabilities once I dug them out. I imagine that's the doctors' problem too. I will agree with you that most U.S. adults don't understand probability, but I don't think this particular study illustrates that point.

And the problems we're arguing with Elennsar about don't involve these kinds of manipulations. They're straightforward applications of basic probability. And Elennsar has the benefit of lots of people repeatedly taking the time to explain the principles to him.

Wait, SunTzuWarmaster, I think you are wrong with your answer to Elennsar.

SunTzuWarMaster wrote:
"Axes attack twice as slowly as swords. They do 1.5 times as much damage."

In 3 sword attacks you have 3 sword damage and 2 axe attacks for 2 axe damage (1.5*2 is 3 sword damage). On the surface this looks balanced, right? In the long run, these do exactly the same damage.

If axes attack twice as slowly as swords, then in three sword attacks you only have one axe attack.

Assuming 50% probability to do damage, then in four sword attacks there are two sword hits and one axe hit. The sword does 2xSword damage and the axe does 1.5xSword damage.

The sword is much better, doing 33% more damage than the axe. In the long run, the sword does a whole lot more damage.

Roy wrote:

Psychic Robot wrote:Great game series, but it kind of went FUBAR in terms of plot at the end.

Indeed. Also, UMBRELLA!

...Yes, this is more productive than wrestling with Elennsar. Don't complain.

If we starting debating the heroism of the protagonist in 7 Days A Skeptic, we'll suddenly be on topic. I think the revelation at the end was really interesting, since it dramatically changed the way I viewed the game the second time through.

There's actually some pretty interesting connections to the varying heroism definitions used here now that I begin to look back. The fact that to defeat the antagonist, you have to use ambush tactics and trickery actually increased the heroism in the game in my opinion.

Blech, somehow I read that, and even quoted it as "Swords attack 1.5 times faster than axes".

Yea, I'm not sure how either.