Couple of casino odds queries
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12-02-2011, 09:44 PM
RE: Couple of casino odds queries
66% in total or 66% each time, or would it be 66% per head?

When I find myself in times of trouble, Richard Dawkins comes to me, speaking words of reason, now I see, now I see.
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12-02-2011, 10:35 PM
RE: Couple of casino odds queries
(12-02-2011 01:57 PM)Buddy Christ Wrote:  The first is the Martingale bettor's nightmare: the ol' roulette strategy of "well there have been 10 reds in a row, I'll bet black because it's due." People say this logic is flawed because every spin is 50/50 (disregarding the zeros for now) and independent of the previous results. This statement makes sense to me and at the same time, it doesn't. To me, there's a separate probability; the probability of hitting a certain combination of that 50/50. To hit red, red, red for instance, to me would be 1/2 * 1/2 * 1/2 ... red hitting 3 times has a 1/8 probability. And I realize that writing out all the possibilities, still proves me wrong.

BBB 1/8
BBR 1/8
BRB 1/8
BRR 1/8
RBB 1/8
RBR 1/8
RRB 1/8
RRR 1/8

Just looking at this shows that a red streak can only go RRB or stay RRR... both same odds (still 1/8 vs 1/8...50/50)... AHHH, but you never see 30 reds in a row in real life! (head explodes)

Following the 50/50 every time logic means that if you flip a coin 20 times, it is just as likely to hit 20 heads in a row as it is to hit any random number of heads and tails. But I guarantee you, you could sit there all day flipping a coin and not hit 20 heads in a row.

It just seems probable to me that if you wait until say 12 reds in a row hit, your chances of hitting black in the next 5 rolls are greatly increased. But of course, every mathematician would tell me I'm wrong.

Well, the Monty Hall problem has already been addressed, so I'll deal with this one.

Here's the thing: RRRRRRRRRR is exactly as probable as RRRRRRRRRB.

For that matter, RRRRRRRRRR is exactly as probable as RBRRBRBRRB.

Here's how it works. The first time that you take a spin on the roulette, the odds are fifty-fifty that it'll land on red. So your two possible results are:

- R (50%)
- B (50%)

Now you take another spin. Your possible chains are:

- RR (25%)
- RB (25%)
- BR (25%)
- BB (25%)

Now follow the RR chain down for eight more spins. Your final probability of getting the chain RRRRRRRRRR is one-half to the tenth power, or .09765625%. But that same probability applies to every other chain. No one chain is any more likely than any other, but ultimately, one of them has to show up.

And there's nothing to say that black is "due". There's no supernatural force which stores the previous chain and says that black is "due" for an appearance.

"Owl," said Rabbit shortly, "you and I have brains. The others have fluff. If there is any thinking to be done in this Forest - and when I say thinking I mean thinking - you and I must do it."
- A. A. Milne, The House at Pooh Corner
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13-02-2011, 07:49 AM
RE: Couple of casino odds queries
(12-02-2011 01:57 PM)Kikko Wrote:  Btw, The Observer's simulator doesn't work on my browser.
(12-02-2011 04:25 PM)Buddy Christ Wrote:  Yeah it didn't work with my Firefox, but it works with IE.

You can install Internet-explorer tab to emulate IE in your Firefox-browser without actually installing it (handy). But that doesn’t run on my Linux-machine. Sorry

Observer

Agnostic atheist
Secular humanist
Emotional rationalist
Disclaimer: Don’t mix the personal opinion above with the absolute and objective truth. Remember to think for yourself. Thank you.
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13-02-2011, 09:32 AM
RE: Couple of casino odds queries
What's funny here (to me) is I understood the roulette one immediately. I don't know if I could have explained it as well as Unbeliever did but as soon as it was posed I understood it.

The Monty Hall one, however, I'm still baffled by. Can someone try that one again? I saw the movie "21" and I did not understand it then, either.

Shackle their minds when they're bent on the cross
When ignorance reigns, life is lost
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13-02-2011, 10:08 AM
RE: Couple of casino odds queries
Well I "understood" the roulette one mathematically, just not practically. The "odds" of getting 20 blacks in a row seems very unlikely to me, even though it's technically the same odds as getting 19 blacks and a red. But that's what keep Vegas rich, false hope and flawed systems.

"Ain't got no last words to say, yellow streak right up my spine. The gun in my mouth was real and the taste blew my mind."

"We see you cry. We turn your head. Then we slap your face. We see you try. We see you fail. Some things never change."
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13-02-2011, 10:41 AM
RE: Couple of casino odds queries
The thing with the roulette example is the odds of hitting anything on each spin are exactly the same, regardless of what happened previously. The odds of any combination of results over time is the same for each combination and it gets worse with each spin. There is no pattern, though, and the past will never predict the future. So, if you see 20 blacks in a row, the odds of #21 being black do not go up or down based on what happened in the past. That I absolutely get.

The door one, though, I'm still struggling with.

Shackle their minds when they're bent on the cross
When ignorance reigns, life is lost
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13-02-2011, 10:59 AM
RE: Couple of casino odds queries
Monty Hall... The friendly yet, baffling gameshow-host Smile
By adding the 2 guesses you made you have 66% of being correct.

Yes, you make 2 guesses! You can picture the door chosen by Monty as a second guess. What baffles you is not your logic but your "first guess emotion". This origins in the "when in doubt, stick with your first guess" way of thinking. This is a good approach on subjects you have data for somewhere in your subconscious. But chance is almost never subject to approachable data.

As for "roulette colours being due"

It’s something I read in "Risk" by Daniel Gardner. I've tried this myself to see how it works.

Modus operandi:
Take a 10 sided dice (I installed an electronic dice on my computer). Create a calculation sheet (exell, openoffice,...) and create a 100 by 100 grid. Now... print that grid 2 times. Take a black marker and start filling in 200 cells on the first grid at random.
Now... Take your dice and roll 400 times. The first roll is your number on de X axis the second roll is your number on Y axis. Mark the cell on the second grid in the same way as you did on the first sheet. compare both sheets and note a striking difference!
I'll build in a pause here so you can stop reading and do this fun experiment non-biased. Smile
*lalala*
...
..
.
*tum-de-dum*
...
..
.
*clips nails*
...
..
.
Ever heard of "grouping phenomenon"? (Not sure if this is the correct English therm)
If you look at the second sheet you will note that most dots group themselves into clusters, while on your manual sheet clusters exist but are scares. This is because the human mind does not really grasps the concept of random and mistakenly takes "spreading-out" for random. This is not how real random processes work. Now, you can be sceptical about your "random computer dice" and try this with real dice. It is something I have yet to try, but I am pretty sure it will give the same result.

look again at that second grid:
Now imagine it is a map of cancer casualties in a neighbourhood and you are a scientist or a politician who has to explain that. If you calculate emotion in these results you can bet on some nasty conclusions. The same counts for winning or losing a lot of money.

Observer

Agnostic atheist
Secular humanist
Emotional rationalist
Disclaimer: Don’t mix the personal opinion above with the absolute and objective truth. Remember to think for yourself. Thank you.
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13-02-2011, 11:09 AM
RE: Couple of casino odds queries
By the way, I wasn't posing the roulette question as another paradox, I just literally can't get my brain to accept it.

Here's something that kind of helps with the doors.

[Image: 197px-Monty_open_door_chances.svg.png]

"By opening his door, Monty is saying to the contestant 'There are two doors you did not choose, and the probability that the prize is behind one of them is 2/3. I'll help you by using my knowledge of where the prize is to open one of those two doors to show you that it does not hide the prize. You can now take advantage of this additional information. Your choice of door A has a chance of 1 in 3 of being the winner. I have not changed that. But by eliminating door C, I have shown you that the probability that door B hides the prize is 2 in 3.'"


The only thing I don't get is why then is choosing the other door + the revealed goat 2/3 and keeping your door + the revealed goat is only 1/3.

In my mind, you can just as easily draw a rectangle around your original door and the goat and label it 2/3.

"Ain't got no last words to say, yellow streak right up my spine. The gun in my mouth was real and the taste blew my mind."

"We see you cry. We turn your head. Then we slap your face. We see you try. We see you fail. Some things never change."
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14-02-2011, 02:25 PM
 
RE: Couple of casino odds queries
The 3-door problem is quite simple, actually.
When you pick a door there's a 2/3 chance it's a wrong door. And a 1/3 chance you pick the right door.
Suppose you picked a wrong door. The other wrong door is then opened. The last remaining door (the one you get by switching doors) will be the right door. The probability you originally picked the wrong door is 2/3.
Suppose you picked the right door in the beginning. One of the wrong doors is then opened. Switching doors will put you on the other wrong door. The probability of this event is 1/3.
So staying with your original choice will keep your odds at winning equal to the starting situation, while switching doors means the odds get reversed.

The error that a lot of people make is that they perceive the switching as a new choice, and that previous events, or obtaining more knowledge has no correlation with the end result. But they do, as I have just demonstrated.
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15-02-2011, 12:31 AM
RE: Couple of casino odds queries
Yes. Take it to its simplist form. The odds of getting it right go up dramatically and the odds of understanding what you just got right will sky-rocket.

When I find myself in times of trouble, Richard Dawkins comes to me, speaking words of reason, now I see, now I see.
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