Couple of casino odds queries
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12-02-2011, 01:57 PM (This post was last modified: 12-02-2011 02:02 PM by Buddy Christ.)
Couple of casino odds queries
This is mostly a science-y crowd, so I'm assuming the bulk of you are mathematically proficient as well. My brain has trouble grasping 2 concepts.

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.


Next Scenario

This one was featured on the movie "21" and is a favorite of math professors everywhere. I also get this one, but only when drawn out a specific way. Here's the scenario:

A gameshow host informs you there is a car behind 1 of the 3 doors. (33% chance of winning) He knows which door is the winner. You pick a door and he opens one of the remaining doors that doesn't have the car behind it. Then he asks if you would like to stay with your original pick or choose the other remaining door. You say "yes I would like to change my pick and thank you for the additional 33% (Now you have a 66% chance of winning).

Here's the movie clip for a better explanation.
http://www.youtube.com/watch?v=cXqDIFUB7YU

To everyone who first hears this, they go "huh? you're still just choosing between 2 doors so it's only 50%, right?"

I've heard the mathematical explanation, but the only way I can grasp it is if I spell it out like this:

Possibilities:
W L1 L2
-you chose W (winner) door first, and after he removes one L, you then switch to L
-you chose L1 (loser1) door first, and after he removes L2, you switch to W
-you chose L2 door first, and he removes L1, you switch to W

66% chance of winning after switching ...and yet, all I can think of is: you're down to 2 doors... you can choose either door... should be 50/50

(head explodes)

"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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12-02-2011, 02:16 PM (This post was last modified: 12-02-2011 02:31 PM by Kikko.)
RE: Couple of casino odds queries
Ahh... I used to love gambling odds.
Quote: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.
There's an incredible amount of different possible combinations of heads and tails. If you choose to flip untill you get 20 heads in a row, your probability of getting it is the same as if you'd be waiting for THTTHTHHHTTTHTHTHTTH (or any other outcome you choose). You'll see both outcomes as ''often''.
Quote:66% chance of winning after switching
No, it's 50%. Your possibility of winning the car is always 50%, because one of the loser doors will always be selected out.
_____________________________________________

Now that gambling odds are the topic, I'd like to ask: does this* winning strategy sound good (with a large enough bankroll of course)?

* You are flipping a coin against the house. Pick the right side of the coin and double your money (no casino would actually be so stupid to play this game with 50/50 odds).
You bet 10 for a head and lose.
Then you bet 20 for head and lose again.
Then you bet 40 for head and lose again.
Then you bet 80 for head and lose again.
Then you bet 160 for head and win.
Outcome: You bet 310 and won 320 = 10 profit. As long as you always double your bet after losing, you'll eventually win 10 when you choose the right one. Then you start again from 10 and repeat and repeat and repeat. Even if the odds are not exactly 50/50 (like in roulette 'cause there's a zero) you'll eventually end up choosing the right outcome and you'll win the amount of money that you started the betting with (in this case 10).

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12-02-2011, 03:26 PM
RE: Couple of casino odds queries
Well first, your question is what I mentioned: it's called the Martingale system, and it's flawed. You would have to have an unlimited bankroll for it to work 100% of the time. All it takes is 10 consecutive Blacks or Heads(coin) and you're betting 10,230 dollars to win 10 bucks. And I've seen red/black hit 18 straight times before. And if you have the 500,000 to cover all that, there are better ways to make 10 bucks... like bank interest.

I tried all kinds of different Martingale strategies when I was a young lass. I would play online casinos and spin the roulette wheel until red or black hit 10 times in a row, then I would start my first bet.. giving me about 6-7 more bets to work with. All it took was Red 18 times in a row and I was bankrupt. So I tried it with red/black alternating 10 times or no Low numbers hitting, then doubling up on Low numbers. None of it works. Which is why I stick to poker now.. something I can control.

And back to the "50% chance" ...look at my W L L example again. It IS 66% to win by switching choices. But I think I figured it out.

I was looking at the immediate choice offered to me, which was choosing 1 of 2 doors, one winner and one loser and thinking 50%. But it's more accurate to consider that there's still 3 doors, only you've been given a free pick. So now you're technically choosing 2 of 3 doors... wait... that doesn't work either or else it would still be 66% chance to win without switching your choice. And my example shows that that isn't true. Dammit.

"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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12-02-2011, 03:32 PM
RE: Couple of casino odds queries
(12-02-2011 01:57 PM)Buddy Christ Wrote:  A gameshow host informs you there is a car behind 1 of the 3 doors. (33% chance of winning) He knows which door is the winner. You pick a door and he opens one of the remaining doors that doesn't have the car behind it. Then he asks if you would like to stay with your original pick or choose the other remaining door. You say "yes I would like to change my pick and thank you for the additional 33% (Now you have a 66% chance of winning).
This is called, the Monty Hall problem.
I found a simulation here but it does not run on my computer. (gotta update and stuff)

Observer

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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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12-02-2011, 03:42 PM (This post was last modified: 12-02-2011 03:53 PM by Kikko.)
RE: Couple of casino odds queries
Oh, so that's the Martingale system. Yep, flawed.
Quote:And back to the "50% chance" ...look at my W L L example again. It IS 66% to win by switching choices. But I think I figured it out.

I was looking at the immediate choice offered to me, which was choosing 1 of 2 doors, one winner and one loser and thinking 50%. But it's more accurate to consider that there's still 3 doors, only you've been given a free pick. So now you're technically choosing 2 of 3 doors... wait... that doesn't work either or else it would still be 66% chance to win without switching your choice. And my example shows that that isn't true. Dammit.
If you could choose 2 of the doors, then you would have 66% chanche of winning. But because the final decision is made after one of the wrong doors is selected out, you have a 50% chance of winning.
Quote:Which is why I stick to poker now.. something I can control.
I tried internet poker (illigally in my dad's name) when other people lost their interest in the game, but it sucked. I get my kicks from playing in person (4 or 5 card omaha if possible). Even when I grow up I don't think I'll start playing online or in the only casino of Finland (high rake and far away).

Correct me when I'm wrong.
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12-02-2011, 03:51 PM
RE: Couple of casino odds queries
But you don't. That's the mind blowing part. Go to the site observer posted or just look again.

The only possibilities:

W L1 L2

You originally chose W, host removes an L, you switch and choose other L (You Lose)
You originally chose L1, host removes L2, you switch and chose W (You Win)
You originally chose L2, host removes L1, you switch and chose W (You Win)
-you win 66% of the time by changing your pick after host removes L

or

You chose W, host removes L, you stay with pick W (You win)
You chose L1, host removes L2, you stay with pick L1 (You lose)
You chose L2, host removes L1, you stay with pick L2 (You lose)
-you win 33% of the time if you stay with pick

So it's not 50/50, but because it seems that way, people become baffled (including me).

People just focus on: choice of 2 doors, can choose either door so 50%... but that's mathematically incorrect. I'll see if I can get my Math major buddy to explain it to me.

"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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12-02-2011, 04:06 PM (This post was last modified: 12-02-2011 04:28 PM by Kikko.)
RE: Couple of casino odds queries
Quote:W L1 L2

You originally chose W, host removes an L, you switch and choose other L (You Lose)
You originally chose L1, host removes L2, you switch and chose W (You Win)
You originally chose L2, host removes L1, you switch and chose W (You Win)
-you win 66% of the time by changing your pick after host removes L

or

You chose W, host removes L, you stay with pick W (You win)
You chose L1, host removes L2, you stay with pick L1 (You lose)
You chose L2, host removes L1, you stay with pick L2 (You lose)
-you win 33% of the time if you stay with pick
Well fuck me. Sorry that it took so much effort to make me ''understand'' it, but how the hell? It seems so illogical and logical at the same time. You have just destroyed my chances of catching sleep tonight.

Btw, The Observer's simulator doesn't work on my browser.
_______________________________________________

But why can't we ignore the first picking of a door and the removal of one loser door, since what ever you pick first doesn't matter because you'll still get to pick from the two remaining doors, since one loser door will be removed, leaving one winner and one loser?

Correct me when I'm wrong.
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12-02-2011, 04:25 PM
RE: Couple of casino odds queries
Yeah it didn't work with my Firefox, but it works with IE. It just lets you run the "change your door" and "keep your original door" outcomes hundreds of times so you can see it levels out at 33% for keep and 66% for change.

"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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12-02-2011, 05:49 PM
RE: Couple of casino odds queries
Buddy Christ, what are the chances that someone could have their head explode, twice, and still be alive to communicate? Tongue

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, 07:28 PM
RE: Couple of casino odds queries
(12-02-2011 05:49 PM)No J. Wrote:  Buddy Christ, what are the chances that someone could have their head explode, twice, and still be alive to communicate? Tongue

66%

"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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