Discussing Probability & Odds: Does Flipping More Cards Increase Chances?

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Discussion Overview

The discussion revolves around the concepts of probability and odds as they relate to the game "Deal or No Deal." Participants explore whether the odds of winning improve as cases are removed from the game, with a focus on the implications of revealing information through card or case flipping.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant argues that the odds of winning remain at 1/26 until the player has the opportunity to "reguess," at which point the odds become 1/2 if only two cases remain.
  • Another participant contends that revealing a case that does not contain the million dollars improves the odds of the remaining cases, suggesting that the odds of having a specific case increase as options are eliminated.
  • A different viewpoint emphasizes that regardless of how information is revealed (either by checking the chosen case or deducing from other cases), the initial odds remain unchanged at 1/26 until a decision point is reached.
  • One participant draws a parallel to the Monty Hall problem, noting that the randomness of the game differs from scenarios where the host knows where the prize is located, suggesting that this affects the probability dynamics.
  • Another participant references external sources to assert that the probability of holding the million dollar case remains at 1/26 until the player is given the option to switch, at which point it becomes 50/50.

Areas of Agreement / Disagreement

Participants express differing views on whether the odds improve as cases are removed, with no consensus reached. Some argue that the odds remain static until a decision point, while others believe that revealing information alters the probabilities.

Contextual Notes

Participants reference specific scenarios and examples, but the discussion remains focused on the theoretical implications of probability without resolving the underlying assumptions or definitions of odds in this context.

  • #31
caprirs302, you are again glossing over points made and questions asked. Are you the least bit interested in having your point of view changed or do you just not want to admit your wrong and have this score settled you mentioned in the OP?

At least answer to post # 24.


caprirs302 said:
Again, you are excluding the other 499,999 time that this scenario wouldn't happen.
That's right. Because they didn't happen!

Of course I would not sell you my lottery ticket, but that doesn't change the fact that I stil only have a 1/1,000,000 chance of having that winning ticket. By asking to sell you are giving me a new choice based on new information, I would be a fool to part with it.
Yes, new information changes probability- not a new choice! How does a new choice change probability? You believe you only have a 1/1,000,000 chance of having the winning ticket, yet as soon as someone asks you to sell it, you have a lot to be excited about because your probability of winning is now 1/2? Explain.

I agree with whatever123 that at the end each card (or ticket) has equal odds of being the ace or a winner, but I am asking for my odds of winning, which cannot change from what they were when the final decision was made, or when the lottery ticket was sold.

Now, there may be some mathematical convention on odds calculating that you know of and I don't, but aside from that I cannot agree with you.
You don't need to know a lot about probability to figure this out. Simply try the experiment with three cards that I mentioned. You'll see that new information changes probability.
 
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  • #32
caprirs302 said:
Of course I would not sell you my lottery ticket, but that doesn't change the fact that I stil only have a 1/1,000,000 chance of having that winning ticket. By asking to sell you are giving me a new choice based on new information, I would be a fool to part with it.
Go over this a few times and see if it still makes sense to you. You're saying you'd be a fool to part with a lottery ticket that only has a 1/1,000,000 chance of being a winner.
 
  • #33
caprirs302 said:
Again, you are excluding the other 499,999 time that this scenario wouldn't happen.

Of course I would not sell you my lottery ticket, but that doesn't change the fact that I stil only have a 1/1,000,000 chance of having that winning ticket. By asking to sell you are giving me a new choice based on new information, I would be a fool to part with it.

I agree with whatever123 that at the end each card (or ticket) has equal odds of being the ace or a winner, but I am asking for my odds of winning, which cannot change from what they were when the final decision was made, or when the lottery ticket was sold.

Now, there may be some mathematical convention on odds calculating that you know of and I don't, but aside from that I cannot agree with you.

Thank Goodness .. at least we are getting somewhere ..

So you have agreed that at the end each card (or ticket) has equal odds of being the ace or a winner.
Now let us see where that leads us ..
There are 2 cards - each has equal odds .. what does that mean --- each of these cards has a 1/2 a chance that it is the right card. So now what are your odds ? --- 1/2 !
 
  • #34
caprirs302 said:
Of course I would not sell you my lottery ticket, but that doesn't change the fact that I stil only have a 1/1,000,000 chance of having that winning ticket. By asking to sell you are giving me a new choice based on new information, I would be a fool to part with it.

"Making a new choice" doesn't have to play in here. Forget I offered to buy it. Wouldn't you feel good -- VERY good -- about your chances of winning at that point?

Back to Deal or No Deal, we'd all agree that the OVERALL odds of winning one million dollars is 1/26: before the show begins and after it ends; regardless of whether the million dollar case is exposed first, last or at any other time; regardless of the show's outcome. But we are analyzing individual instances of a show.

So which of these questions are you asking?

1) What are the odds of winning 1 million on Deal or No Deal? (Answer: 1/26)
2) What are the odds of winning 1 million on Deal or No Deal after 24 cases are exposed and 1 million isn't one of them? (Answer: 1/2)

You seem to be confusing the two.
 
  • #35
caprirs, it's called conditional probability

You ask: What's the probability that event X occurs assuming that event Y has occurred

Can you see how that question allows you to ignore what the probability that event X occurs when Y doesn't?
 

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