Chance (quick question)

Dottie · Post by **Dottie** » Wed Oct 28, 2009 2:13 pm

fable wrote:Something's wrong, there. You don't get 40 wins out of 100 rolls. You're assuming that this isn't a matter of random rolls, but of a fixed rate of success. It isn't, it's a 40% chance of success on each successive roll: less than half likely, on every roll. On the other hand, you have 1 roll at a 60% rate of success, more than half a chance at winning.

The reason to explain it in terms of rate of sucess is that it's otherwise difficult to account for the double award and still get a number that is easily comparable with the 60% chance of a single award. However, it really doesn't make any difference in this case.

Tricky · Post by **Tricky** » Wed Oct 28, 2009 2:21 pm

... I was beginning to think Dottie was your wife, Fable.

I'm starting to see the marvel of this advertisement. People score lottery tickets while buying products at rates they think are higher than they really are. Most of them do, anyway. Expensive products get the 60% turnout rate tickets, cheap ones get the 40% rate trick. I wonder if a fixed lottery kind of thing like this is even legal in the Dutchlands.

fable · Post by **fable** » Wed Oct 28, 2009 2:25 pm

Tricky wrote:... I was beginning to think Dottie was your wife, Fable.

No, Dottie's a guy, and my wife's a woman named Janet.

I'm starting to see the marvel of this advertisement. People score lottery tickets while buying products at rates they think are higher than they really are. Most of them do, anyway. Expensive products get the 60% turnout rate tickets, cheap ones get the 40% rate trick. I wonder if a fixed lottery kind of thing like this is even legal in the Dutchlands.

I'm still no closer to understanding how 2 40% chances are better than a single 60% one, but I'm beginning to feel as if I'm incredibly stupid--rather like Chico Marx arguing "Okay, I know why-a-dis, why-a-dat, but I no understand vy-a-duck, vy-a-no-chicken?"

Tricky · Post by **Tricky** » Wed Oct 28, 2009 2:27 pm

It's okay Fable. It's kind of neat to have finally figured out your weakness.

Dottie · Post by **Dottie** » Wed Oct 28, 2009 2:34 pm

fable wrote:I'm still no closer to understanding how 2 40% chances are better than a single 60% one, but I'm beginning to feel as if I'm incredibly stupid--rather like Chico Marx arguing "Okay, I know why-a-dis, why-a-dat, but I no understand vy-a-duck, vy-a-no-chicken?"

Ok, what part is it that you have objections agains? Is it that two chances of some value can be represented as one chance of some other value, or is it the specific value for this case seem to high?

Tricky wrote:... I was beginning to think Dottie was your wife, Fable.

I have asked him, but he told me to bugger off.

fable · Post by **fable** » Wed Oct 28, 2009 2:52 pm

Dottie wrote:Ok, what part is it that you have objections agains? Is it that two chances of some value can be represented as one chance of some other value, or is it the specific value for this case seem to high?

The latter. Each of the two chances is still less than 50%. The likelihood of losing is better than average in both instances. Admittedly, the more shots you have at it, the more likely you are to beat the odds--but at 2-to-1 chances, 40% vs 60%, I'm afraid I still don't understand it.

I have asked him, but he told me to bugger off.

Too much Swedish around the house. I'm learning Hungarian.

Become Hungarian, change your sex, and find a hot cuisine to cook, and we'll talk.

Dottie · Post by **Dottie** » Wed Oct 28, 2009 3:15 pm

fable wrote:The latter. Each of the two chances is still less than 50%. The likelihood of losing is better than average in both instances. Admittedly, the more shots you have at it, the more likely you are to beat the odds--but at 2-to-1 chances, 40% vs 60%, I'm afraid I still don't understand it.

The way to calculate the chance of succeding at two or more consecutive rolls is to simply multiply the chances together. So for example if you roll a d10 and succed on all results but one your chances is 90%, or 0.9. If you need to succed twice your chance is 0.9*0.9 or 0.81. if you need to succed three times your chance is 0.792. etc.

What we are interested in is not that, because we win if either of the rolls turn out a success, so we look at the risk of loosing instead. The risk of loosing is 60% or 0.6 for both rolls, and we need to fail both if we are going to loose so we multiply the chances together like above. 0.6*0.6 = 0.36 or 36% of loosing wich is the same as 64% of winning something.

In addition we have a chance to win a double. it's already included in the figure above, so we wont have a larger chance to win than 64% but there is a 16% chance (0.4*0.4) that we win two times.

Too much Swedish around the house. I'm learning Hungarian.

Become Hungarian, change your sex, and find a hot cuisine to cook, and we'll talk.

Adding large amounts of garlic to everything i cook won't do then?

fable · Post by **fable** » Wed Oct 28, 2009 3:24 pm

Dottie wrote:What we are interested in is not that, because we win if either of the rolls turn out a success, so we look at the risk of loosing instead. The risk of loosing is 60% or 0.6 for both rolls, and we need to fail both if we are going to loose so we multiply the chances together like above. 0.6*0.6 = 0.36 or 36% of loosing wich is the same as 64% of winning something.

Eh? So if you had only one roll with a 60% of losing, that's a 40% of winning, but if you have two rolls with a 60% of losing, that's a 64% of winning? I'm pretty sure something's wrong, there. That formula isn't correct.

I'm going to send this off to someone else to look at.

Adding large amounts of garlic to everything i cook won't do then?

I'm afraid not. But, as a consolation prize, we could help you set up a Southern Italian restaurant in Cleveland, if you'd like.

Dottie · Post by **Dottie** » Wed Oct 28, 2009 3:53 pm

fable wrote:Eh? So if you had only one roll with a 60% of losing, that's a 40% of winning, but if you have two rolls with a 60% of losing, that's a 64% of winning?

Yes, because in the second case both rolls have to be failed for you to lose.

Vicsun · Post by **Vicsun** » Wed Oct 28, 2009 6:39 pm

fable]Eh? So if you had only one roll with a 60% of losing wrote: When you phrase it like that it sounds like either one of the 60% rolls can make you lose (which would invert the question and make your chances of losing 84%). However, you need to lose both 60% rolls to really and truly lose. The chances of losing both at the same time are lower than the chances of losing a single one.

fable]The latter. Each of the two chances is still less than 50%. The likelihood of losing is better than average in both instances. Admittedly wrote: Everything so far is absolutely correct...
--but at 2-to-1 chances, 40% vs 60%, I'm afraid I still don't understand it.

..and here is when I feel like you lost me.

I'm incredibly curious exactly where the misunderstanding is in this, so I'd like to ask: would you concede that if you have 40% chance of winning, but you play ten times, you have better-than-even chance of winning at least once? How about if you play five times? How about three? How about two?

fable · Post by **fable** » Wed Oct 28, 2009 7:32 pm

Vicsun wrote:I'm incredibly curious exactly where the misunderstanding is in this, so I'd like to ask: would you concede that if you have 40% chance of winning, but you play ten times, you have better-than-even chance of winning at least once? How about if you play five times? How about three? How about two?

Oh, yes: if you play 10 times, I'd say you have a much better chance with 40% on each try than once, with 60%. I'm sorry I can't refine this further, but I have asked someone else for assistance, and I'm hoping to get some answers--to satisfy myself, if no one else.

I'll post what I find out, no matter which way it goes. I'm really curious how this one turns out, now.

Xandax · Post by **Xandax** » Thu Oct 29, 2009 12:57 am

Dottie wrote:Yes, because in the second case both rolls have to be failed for you to lose.

The key - I think - is this statement here, and perhaps it is what's missing from the understanding?

To loose with two rolls, you need to loose both rolls, not just one of them.
And then Dottie/Vicsun can do the math they do because the events are independent of each other and the events must both happen.
It doesn't matter you loose the first roll, if you win the second roll.
So to truly loose we have to hit the 60% outcome twice in a row, meaning the 0.6 x 0.6 = 0.36 chance we loose over two throws.

Dottie and Vicsun are indeed correct.

Fljotsdale · Post by **Fljotsdale** » Thu Oct 29, 2009 9:17 am

Bleah....

my brain hurts... I could never understand people actually LIKING figuring numbers...

I can measure a room for carpets and wallpaper and if the furniture/curtains will fit; I can measure a body for if the clothes will fit; I can figure up how what I have in the bank tallies with what I want to spend; anything else is beyond me... and, frankly, I want it to stay that way! :laugh: I'm not one of the clever buggers!

Xandax · Post by **Xandax** » Thu Oct 29, 2009 10:00 am

Fljotsdale wrote:Bleah.... my brain hurts... I could never understand people actually LIKING figuring numbers...

I can measure a room for carpets and wallpaper and if the furniture/curtains will fit; I can measure a body for if the clothes will fit; I can figure up how what I have in the bank tallies with what I want to spend; anything else is beyond me... and, frankly, I want it to stay way! :laugh: I'm not one of the clever buggers!

If there's 40% chance your shirt with fit and 40% your trousers ... what's the probability that either your shirt or trousers will fit ?

Loki[D.d.G] · Post by **Loki[D.d.G]** » Thu Oct 29, 2009 12:36 pm

Xandax wrote:If there's 40% chance your shirt with fit and 40% your trousers ... what's the probability that either your shirt or trousers will fit ?

I know this! Uhh, three? Yes, that's right... three is my answer!

So, what do I win?

Bloodstalker · Post by **Bloodstalker** » Thu Oct 29, 2009 1:37 pm

Always buck the odds that are most stacked against you. If you win, you win big. If you lose, people still talk about you in hushed whispers for taking the big risk. Either way, you wind up a legend.

No one respects a gambler who hedges his bets.

Fljotsdale · Post by **Fljotsdale** » Thu Oct 29, 2009 2:35 pm

Xandax wrote:If there's 40% chance your shirt with fit and 40% your trousers ... what's the probability that either your shirt or trousers will fit ?

Um... er... 40%? I dunno!

Me, I'd just look at the size on the label!

If there wasn't a size (and what sort of clothes shop doesn't give the sizes!?), then just looking would give a pretty fair idea if either garment would fit. Then I'd try it on to sure. :laugh: I wouldn't stand there figuring the odds!

fable · Post by **fable** » Thu Oct 29, 2009 3:09 pm

Xandax wrote:If there's 40% chance your shirt with fit and 40% your trousers ... what's the probability that either your shirt or trousers will fit ?

Silk, or cotton blend?

BlueSky · Post by **BlueSky** » Thu Oct 29, 2009 4:48 pm

fable wrote:Silk, or cotton blend?

Need to take into account...where and who's its made by....

gaminging · Post by **gaminging** » Thu Oct 29, 2009 11:25 pm

one change at 60%.