50:50 vs Double Dip: Which would a contestant prefer?
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50:50 vs Double Dip: Which would a contestant prefer?
Ed Toutant pointed out to me that I was too quick to dismiss the 50:50, arguing that the old 50:50 lifeline can actually be preferable to the Double Dip. The more I thought about it, the more complicated the comparison seems to be, but I do think Ed's general impression may be right.
Now, if we imagine a case where a contestant truly has no idea what the answer is -- where it's a blind guess -- then they're equal (both have a 50% chance of being correct).
Let's say a contestant can eliminate one choice. Let's say you know it's not D.
With the 50:50, there's a 33% chance of that known wrong answer remaining ( for example, A D). But then you can be 100% sure of getting the right answer. If the wrong answer is eliminated, well, now you've got a 50:50 chance of getting it right. Thus, overall, if you can eliminate one answer -- and you're going to guess no matter what -- then the 50:50 gives you a 60% chance of getting it right. *
But the real benefit is that you have a 1 in 3 chance of being guaranteed a correct answer.
With the DD, if you can eliminate 1 wrong answer, then you have a flat 67% of getting it right. So, higher odds in general... but, no guarantees!
Let's say you can eliminate 2 choices. Ah, now the tables are turned! The Double Dip guarantees you the correct answer! Woo hoo!
The 50:50 isn't bad... you've got a 67% chance that one of your known wrong choices will show up... but oops, 33% of the time, you'll still be stuck with two possibly correct answers. If you guess, you've got a 50% chance. Overall, assuming you're going to go for the answer no matter what, you've got a 75% chance of getting a correct answer.
SUMMARY
According to these admittedly hurried calculations, I think:
- DD and 50:50 are identical if you can't eliminate anything.
- 50:50 is probably better if you can eliminate 1 choice, since you have a shot at getting a guaranteed correct answer, even though overall the DD gives better odds to guessing.
- DD is definitely better if you can eliminate 2 choices.
So which is better? I guess it depends on how much you know!
* If you can eliminate D, and the answer is A, then the three possible post 50:50 outcomes are A-B, A-C, A-D. You'll never choose D. Therefore, there are 3 out of 5 correct outcomes (the 3 A's).
Now, if we imagine a case where a contestant truly has no idea what the answer is -- where it's a blind guess -- then they're equal (both have a 50% chance of being correct).
Let's say a contestant can eliminate one choice. Let's say you know it's not D.
With the 50:50, there's a 33% chance of that known wrong answer remaining ( for example, A D). But then you can be 100% sure of getting the right answer. If the wrong answer is eliminated, well, now you've got a 50:50 chance of getting it right. Thus, overall, if you can eliminate one answer -- and you're going to guess no matter what -- then the 50:50 gives you a 60% chance of getting it right. *
But the real benefit is that you have a 1 in 3 chance of being guaranteed a correct answer.
With the DD, if you can eliminate 1 wrong answer, then you have a flat 67% of getting it right. So, higher odds in general... but, no guarantees!
Let's say you can eliminate 2 choices. Ah, now the tables are turned! The Double Dip guarantees you the correct answer! Woo hoo!
The 50:50 isn't bad... you've got a 67% chance that one of your known wrong choices will show up... but oops, 33% of the time, you'll still be stuck with two possibly correct answers. If you guess, you've got a 50% chance. Overall, assuming you're going to go for the answer no matter what, you've got a 75% chance of getting a correct answer.
SUMMARY
According to these admittedly hurried calculations, I think:
- DD and 50:50 are identical if you can't eliminate anything.
- 50:50 is probably better if you can eliminate 1 choice, since you have a shot at getting a guaranteed correct answer, even though overall the DD gives better odds to guessing.
- DD is definitely better if you can eliminate 2 choices.
So which is better? I guess it depends on how much you know!
* If you can eliminate D, and the answer is A, then the three possible post 50:50 outcomes are A-B, A-C, A-D. You'll never choose D. Therefore, there are 3 out of 5 correct outcomes (the 3 A's).
- kusch
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Re: 50:50 vs Double Dip: Which would a contestant prefer?
I think I prefer the 50/50, initial reaction anyway. Also, I think it changes as the $$ question increases.LastMinuteRequest wrote:Ed Toutant pointed out to me that I was too quick to dismiss the 50:50, arguing that the old 50:50 lifeline can actually be preferable to the Double Dip. The more I thought about it, the more complicated the comparison seems to be, but I do think Ed's general impression may be right.
Now, if we imagine a case where a contestant truly has no idea what the answer is -- where it's a blind guess -- then they're equal (both have a 50% chance of being correct).
Let's say a contestant can eliminate one choice. Let's say you know it's not D.
With the 50:50, there's a 33% chance of that known wrong answer remaining ( for example, A D). But then you can be 100% sure of getting the right answer. If the wrong answer is eliminated, well, now you've got a 50:50 chance of getting it right. Thus, overall, if you can eliminate one answer -- and you're going to guess no matter what -- then the 50:50 gives you a 60% chance of getting it right. *
But the real benefit is that you have a 1 in 3 chance of being guaranteed a correct answer.
With the DD, if you can eliminate 1 wrong answer, then you have a flat 67% of getting it right. So, higher odds in general... but, no guarantees!
Let's say you can eliminate 2 choices. Ah, now the tables are turned! The Double Dip guarantees you the correct answer! Woo hoo!
The 50:50 isn't bad... you've got a 67% chance that one of your known wrong choices will show up... but oops, 33% of the time, you'll still be stuck with two possibly correct answers. If you guess, you've got a 50% chance. Overall, assuming you're going to go for the answer no matter what, you've got a 75% chance of getting a correct answer.
SUMMARY
According to these admittedly hurried calculations, I think:
- DD and 50:50 are identical if you can't eliminate anything.
- 50:50 is probably better if you can eliminate 1 choice, since you have a shot at getting a guaranteed correct answer, even though overall the DD gives better odds to guessing.
- DD is definitely better if you can eliminate 2 choices.
So which is better? I guess it depends on how much you know!
* If you can eliminate D, and the answer is A, then the three possible post 50:50 outcomes are A-B, A-C, A-D. You'll never choose D. Therefore, there are 3 out of 5 correct outcomes (the 3 A's).
Going for $50,000 (being a free guess and having no idea of the correct answer) and I have 50/50 or Double dip, I would take 50/50 hands down.
One guess with two choices. DD I have to guess 1 of 4 then 1 of 3.
Again initial reaction.
- Here's Fanny!
- Peekaboo!
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Double Dip. Because if I have a 50/50 shot at getting it right, then I have a 90% chance of picking the wrong one.
I know, the mathletes are cringing, but it makes perfect sense to me. Ha!
Plus with the 50/50 I'd be too busy playing mind games about why they took away the two they took away. They can say it's random all day long, I'll still wonder.
I know, the mathletes are cringing, but it makes perfect sense to me. Ha!
Plus with the 50/50 I'd be too busy playing mind games about why they took away the two they took away. They can say it's random all day long, I'll still wonder.
Spoiler
I'm darned good and ready.
- sunflower
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It depends on the question. If I had it down to 2, I'd love the double dip, the 50/50 can let you down if it narrows it down to the same 2 (or it can pay off if it doesn't).
I do NOT like the fact that you have to answer once you invoke the double dip. For that reason, I might even leave it on the table. Unless I could reasonably get an answer down to 2 choices, it wouldn't be worth the risk of using it.
So for that reason, I'd have to say I slightly prefer the 50/50.
I do NOT like the fact that you have to answer once you invoke the double dip. For that reason, I might even leave it on the table. Unless I could reasonably get an answer down to 2 choices, it wouldn't be worth the risk of using it.
So for that reason, I'd have to say I slightly prefer the 50/50.
- peacock2121
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- themanintheseersuckersuit
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Can we talk about the phone game too?
Suitguy is not bitter.
feels he represents the many educated and rational onlookers who believe that the hysterical denouncement of lay scepticism is both unwarranted and counter-productive
The problem, then, is that such calls do not address an opposition audience so much as they signal virtue. They talk past those who need convincing. They ignore actual facts and counterargument. And they are irreparably smug.
feels he represents the many educated and rational onlookers who believe that the hysterical denouncement of lay scepticism is both unwarranted and counter-productive
The problem, then, is that such calls do not address an opposition audience so much as they signal virtue. They talk past those who need convincing. They ignore actual facts and counterargument. And they are irreparably smug.
- 15QuestionsAway
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If a player has no idea what the answer to the question is, they're both useless. The only difference is the player will walk before using Double Dip.
If a player can eliminate 2 answers completely, then obviously he would prefer Double Dip.
If a player can eliminate 1 answer completely, then it depends on a player's risk tolerance and what he thinks of the other 3 answers. If that player has equal feelings about the other 3 answers, then Double Dip gives him a 2/3 chance of getting the question right rather than the 1/3 50:50 would give him. (Ogi's already explained these odds.)
But if our player has no risk tolerance, he'd prefer the 1/3 chance of 50:50 taking him to the next question versus the 2/3 chance of Double Dip. He would rather have the opportunity to walk away after using the 50:50.
So it really depends on the player's assessment of the question and answers and their appetite for risk. For viewers, Double Dip will be more exciting. For players, you'll see some panic when they use Double Dip and their first choice turns out to be incorrect.
If a player can eliminate 2 answers completely, then obviously he would prefer Double Dip.
If a player can eliminate 1 answer completely, then it depends on a player's risk tolerance and what he thinks of the other 3 answers. If that player has equal feelings about the other 3 answers, then Double Dip gives him a 2/3 chance of getting the question right rather than the 1/3 50:50 would give him. (Ogi's already explained these odds.)
But if our player has no risk tolerance, he'd prefer the 1/3 chance of 50:50 taking him to the next question versus the 2/3 chance of Double Dip. He would rather have the opportunity to walk away after using the 50:50.
So it really depends on the player's assessment of the question and answers and their appetite for risk. For viewers, Double Dip will be more exciting. For players, you'll see some panic when they use Double Dip and their first choice turns out to be incorrect.
- smilergrogan
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Re: 50:50 vs Double Dip: Which would a contestant prefer?
LastMinuteRequest wrote:Let's say a contestant can eliminate one choice. Let's say you know it's not D.
With the 50:50, there's a 33% chance of that known wrong answer remaining ( for example, A D). But then you can be 100% sure of getting the right answer. If the wrong answer is eliminated, well, now you've got a 50:50 chance of getting it right. Thus, overall, if you can eliminate one answer -- and you're going to guess no matter what -- then the 50:50 gives you a 60% chance of getting it right. *
No, 67%. (.33 x 1) + (.67 x .5) = .67
LastMinuteRequest wrote:* If you can eliminate D, and the answer is A, then the three possible post 50:50 outcomes are A-B, A-C, A-D. You'll never choose D. Therefore, there are 3 out of 5 correct outcomes (the 3 A's).
But the three A's aren't equivalent, since the first two will be chosen 50% of the time each, and the third 100% of the time. So of the 5 outcomes (A, B, A, C, A), the 5th gets twice as much weight as each of the other four, making the probability 4/6 (or .67) instead of 3/5.
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Re: 50:50 vs Double Dip: Which would a contestant prefer?
I was about to post essentially this reasoning but was beaten to the post. I agree that it's 2/3 here. And that assumes that you have no inkling between A-B or A-C. If you have some reason to lean toward A in either of those situations, you're even better off.smilergrogan wrote:LastMinuteRequest wrote:Let's say a contestant can eliminate one choice. Let's say you know it's not D.
With the 50:50, there's a 33% chance of that known wrong answer remaining ( for example, A D). But then you can be 100% sure of getting the right answer. If the wrong answer is eliminated, well, now you've got a 50:50 chance of getting it right. Thus, overall, if you can eliminate one answer -- and you're going to guess no matter what -- then the 50:50 gives you a 60% chance of getting it right. *
No, 67%. (.33 x 1) + (.67 x .5) = .67
LastMinuteRequest wrote:* If you can eliminate D, and the answer is A, then the three possible post 50:50 outcomes are A-B, A-C, A-D. You'll never choose D. Therefore, there are 3 out of 5 correct outcomes (the 3 A's).
But the three A's aren't equivalent, since the first two will be chosen 50% of the time each, and the third 100% of the time. So of the 5 outcomes (A, B, A, C, A), the 5th gets twice as much weight as each of the other four, making the probability 4/6 (or .67) instead of 3/5.
Of course, if the 50-50 isn't truly random...
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Re: 50:50 vs Double Dip: Which would a contestant prefer?
Not quite. By the same logic as the other situation, your chances are:LastMinuteRequest wrote:
Let's say you can eliminate 2 choices. Ah, now the tables are turned! The Double Dip guarantees you the correct answer! Woo hoo!
The 50:50 isn't bad... you've got a 67% chance that one of your known wrong choices will show up... but oops, 33% of the time, you'll still be stuck with two possibly correct answers. If you guess, you've got a 50% chance. Overall, assuming you're going to go for the answer no matter what, you've got a 75% chance of getting a correct answer.
(2/3)*1 + (1/3)*(1/2) = 5/6 = 83.3%
Last edited by slam on Wed Jul 30, 2008 12:07 pm, edited 1 time in total.
- Bob78164
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Re: 50:50 vs Double Dip: Which would a contestant prefer?
You got the math wrong -- the choices aren't equally likely. Let's assume you play the question six times. Then twice you'll be left with AB, twice with AC, and twice with AD.LastMinuteRequest wrote:Let's say a contestant can eliminate one choice. Let's say you know it's not D.
With the 50:50, there's a 33% chance of that known wrong answer remaining ( for example, A D). But then you can be 100% sure of getting the right answer. If the wrong answer is eliminated, well, now you've got a 50:50 chance of getting it right. Thus, overall, if you can eliminate one answer -- and you're going to guess no matter what -- then the 50:50 gives you a 60% chance of getting it right. *
But the real benefit is that you have a 1 in 3 chance of being guaranteed a correct answer.
With the DD, if you can eliminate 1 wrong answer, then you have a flat 67% of getting it right. So, higher odds in general... but, no guarantees!
* If you can eliminate D, and the answer is A, then the three possible post 50:50 outcomes are A-B, A-C, A-D. You'll never choose D. Therefore, there are 3 out of 5 correct outcomes (the 3 A's).
In the first case, you'll choose A once and B once. In the second case, you'll choose A once and C once. But in the third case, you'll choose A twice. In sum, you'll choose A four times out of six. The 50-50 gives you a 2/3 chance of a correct answer when you can eliminate one choice.
Nevertheless, I still prefer the Double Dip. It's rare that I'm completely clueless on a question, and when I am, 50-50 is the last lifeline that I'd choose. It's not uncommon that at least once a stack, I can narrow the choices to two, and that's the best time to use the Double Dip. So when I will use the lifeline, there's a pretty decent chance that I'll find Double Dip preferable to 50-50.
One other point, though. It now makes much more sense for many contestants to consider using Double Dip earlier in the stack. For example, if you know you'll be happy to walk with $16,000, there's an incentive to use Double Dip at $8,000 or $16,000, since you won't want to risk being forced to answer at $25,000. --Bob
"Question with boldness even the existence of a God; because, if there be one, he must more approve of the homage of reason than that of blindfolded fear." Thomas Jefferson
- silverscreenselect
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On high dollar questions other than the 50K, you won't see players use the double dip as much because they are committed to guessing at what will be at best a 1/3 chance. There won't be a lot of questions for which players can confidently eliminate two answers at this level. Even if you can eliminate one, and the double dip offers you a better chance, most people would rather walk than make a 50/50 guess and would therefore leave the double dip on the table.
- MarleysGh0st
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We hardcore fans can analyze the mathematics, but I think sunflower's opinion will dominate with the typical contestants who are cast for the Hot Seat. How often have we seen contestants who don't have a clue on a question, use the 50/50, and then--still not having a clue--refuse to take a guess on the remaining two answers and walk away? Since using the Double Dip requires an answer, these contestants will leave the lifeline on the table, instead.sunflower wrote:I do NOT like the fact that you have to answer once you invoke the double dip. For that reason, I might even leave it on the table. Unless I could reasonably get an answer down to 2 choices, it wouldn't be worth the risk of using it.
For myself, I'd probably favor the Double Dip, to avoid that situation of the 50/50 leaving the choices I was thinking of.
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Re: 50:50 vs Double Dip: Which would a contestant prefer?
There's a fundamental problem with your analysis in practice in that it doesn't quite model the situation. You're assuming that you either can completely eliminate a possible answer or two and amongst the remaining answers, you have no preference. But that's not how I would approach the situation. I'd be mentally rating the possibility that an answer is the correct one. For example, I might say that A has a 65% chance of being right, B has 20%, C has 15% and D has 0% (corresponding to a situation where I'm able to eliminate one answer definitively). Now, for the DD I'll pick A then B and have an 85% chance of being right. Let's forget about the possibility of any contingent information that A being wrong might give me (though it could be relevant).LastMinuteRequest wrote:Ed Toutant pointed out to me that I was too quick to dismiss the 50:50, arguing that the old 50:50 lifeline can actually be preferable to the Double Dip. The more I thought about it, the more complicated the comparison seems to be, but I do think Ed's general impression may be right.
Now, if we imagine a case where a contestant truly has no idea what the answer is -- where it's a blind guess -- then they're equal (both have a 50% chance of being correct).
Let's say a contestant can eliminate one choice. Let's say you know it's not D.
With the 50:50, there's a 33% chance of that known wrong answer remaining ( for example, A D). But then you can be 100% sure of getting the right answer. If the wrong answer is eliminated, well, now you've got a 50:50 chance of getting it right. Thus, overall, if you can eliminate one answer -- and you're going to guess no matter what -- then the 50:50 gives you a 60% chance of getting it right. *
But the real benefit is that you have a 1 in 3 chance of being guaranteed a correct answer.
With the DD, if you can eliminate 1 wrong answer, then you have a flat 67% of getting it right. So, higher odds in general... but, no guarantees!
Let's say you can eliminate 2 choices. Ah, now the tables are turned! The Double Dip guarantees you the correct answer! Woo hoo!
The 50:50 isn't bad... you've got a 67% chance that one of your known wrong choices will show up... but oops, 33% of the time, you'll still be stuck with two possibly correct answers. If you guess, you've got a 50% chance. Overall, assuming you're going to go for the answer no matter what, you've got a 75% chance of getting a correct answer.
SUMMARY
According to these admittedly hurried calculations, I think:
- DD and 50:50 are identical if you can't eliminate anything.
- 50:50 is probably better if you can eliminate 1 choice, since you have a shot at getting a guaranteed correct answer, even though overall the DD gives better odds to guessing.
- DD is definitely better if you can eliminate 2 choices.
So which is better? I guess it depends on how much you know!
* If you can eliminate D, and the answer is A, then the three possible post 50:50 outcomes are A-B, A-C, A-D. You'll never choose D. Therefore, there are 3 out of 5 correct outcomes (the 3 A's).
What happens if the 50-50 eliminates two of the answers randomly? Well, it gets a bit complicated depending on which answer is actually right.
Let's assume for the moment that I'll always make a guess and I'll always guess the favorite from my initial ordering (I'll always choose A if it's there and I'll choose B over C or D and C over D). Now, my chances of getting this question right are:
When A is correct: .65*(.33*1 + .33*1 + .33*1) = .65 plus
When B is correct: .20*(.33*0 + .33*1 + .33*1) = .133 plus
When C is correct: .15*(.33*0 + .33*0 + .33*1) = .05,
for a total chance of .833, a bit worse than the DD.
But I still have the chance to walk after seeing the 50-50. Let's say I still pick A whenever it shows up and walk whenever B and C are the two choices. Now, my results look like:
Correct: 76.7%
Walk: 11.7%
Wrong: 11.7% (results don't add due to rounding).
Is that a better result than the simple 85% with the Double Dip? It depends on your risk preferences and on the level of the clue. If you are going for $50K, you'll never walk and so DD clearly is better. At other levels, the situation varies.
And, of course, if you use different assumptions for the relevant probabilities, results will be different. I haven't worked out any others yet but I suspect you can jigger the probabilities such that the 50-50 is clearly better than the DD. Maybe I'll do some of that analysis later.
- mikehardware
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I believe there's another problem with the Double Dip.
The 50/50 could be used first, before an ATA or PAF, to narrow down the choices. That could make it easier to get a correct answer.
Now, if you're combining lifelines, the Double Dip must be the last one used.
And how about this scenario. A contestant is at 16K, down to either a Double Dip or 50/50. There's no downside to using the 50/50, so that would be used.
Now, if the person has no clue and is still wanting to gamble, would they be more likely to go for it with only 2 answers showing, or with 4? We know the odds are the same, but the perception of the average player might be different.
The 50/50 could be used first, before an ATA or PAF, to narrow down the choices. That could make it easier to get a correct answer.
Now, if you're combining lifelines, the Double Dip must be the last one used.
And how about this scenario. A contestant is at 16K, down to either a Double Dip or 50/50. There's no downside to using the 50/50, so that would be used.
Now, if the person has no clue and is still wanting to gamble, would they be more likely to go for it with only 2 answers showing, or with 4? We know the odds are the same, but the perception of the average player might be different.
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Re: 50:50 vs Double Dip: Which would a contestant prefer?
You're absolutely right! I botched the math. You nailed it.smilergrogan wrote:LastMinuteRequest wrote:Let's say a contestant can eliminate one choice. Let's say you know it's not D.
With the 50:50, there's a 33% chance of that known wrong answer remaining ( for example, A D). But then you can be 100% sure of getting the right answer. If the wrong answer is eliminated, well, now you've got a 50:50 chance of getting it right. Thus, overall, if you can eliminate one answer -- and you're going to guess no matter what -- then the 50:50 gives you a 60% chance of getting it right. *
No, 67%. (.33 x 1) + (.67 x .5) = .67
LastMinuteRequest wrote:* If you can eliminate D, and the answer is A, then the three possible post 50:50 outcomes are A-B, A-C, A-D. You'll never choose D. Therefore, there are 3 out of 5 correct outcomes (the 3 A's).
But the three A's aren't equivalent, since the first two will be chosen 50% of the time each, and the third 100% of the time. So of the 5 outcomes (A, B, A, C, A), the 5th gets twice as much weight as each of the other four, making the probability 4/6 (or .67) instead of 3/5.
So, since the DD and 50:50 gives the same odds if you can eliminate 1 wrong answer, the 50:50 is DEFINITELY preferable in this case.
SUMMARY
SITUATION .....................PREFERABLE
Can't eliminate anything.....The same.
Eliminate 1 answer.............50:50
Eliminate 2 answers............DD
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Re: 50:50 vs Double Dip: Which would a contestant prefer?
See my lengthy post above for why this conclusion doesn't quite work when you can eliminate 1 answer.LastMinuteRequest wrote: SUMMARY
SITUATION .....................PREFERABLE
Can't eliminate anything.....The same.
Eliminate 1 answer.............50:50
Eliminate 2 answers............DD
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Re: 50:50 vs Double Dip: Which would a contestant prefer?
Yes, when Ed pushed me on the 50:50 vs DD, I started down this track -- which I agree, models the most likely situation, where we have a strong feeling about one answer, and then milder hunches about another -- but then my brain got hot and started to glow and I opted for the easy analysis.slam wrote:There's a fundamental problem with your analysis in practice in that it doesn't quite model the situation. You're assuming that you either can completely eliminate a possible answer or two and amongst the remaining answers, you have no preference. But that's not how I would approach the situation. I'd be mentally rating the possibility that an answer is the correct one. For example, I might say that A has a 65% chance of being right, B has 20%, C has 15% and D has 0% (corresponding to a situation where I'm able to eliminate one answer definitively). Now, for the DD I'll pick A then B and have an 85% chance of being right. Let's forget about the possibility of any contingent information that A being wrong might give me (though it could be relevant).LastMinuteRequest wrote:Ed Toutant pointed out to me that I was too quick to dismiss the 50:50, arguing that the old 50:50 lifeline can actually be preferable to the Double Dip. The more I thought about it, the more complicated the comparison seems to be, but I do think Ed's general impression may be right.
Now, if we imagine a case where a contestant truly has no idea what the answer is -- where it's a blind guess -- then they're equal (both have a 50% chance of being correct).
Let's say a contestant can eliminate one choice. Let's say you know it's not D.
With the 50:50, there's a 33% chance of that known wrong answer remaining ( for example, A D). But then you can be 100% sure of getting the right answer. If the wrong answer is eliminated, well, now you've got a 50:50 chance of getting it right. Thus, overall, if you can eliminate one answer -- and you're going to guess no matter what -- then the 50:50 gives you a 60% chance of getting it right. *
But the real benefit is that you have a 1 in 3 chance of being guaranteed a correct answer.
With the DD, if you can eliminate 1 wrong answer, then you have a flat 67% of getting it right. So, higher odds in general... but, no guarantees!
Let's say you can eliminate 2 choices. Ah, now the tables are turned! The Double Dip guarantees you the correct answer! Woo hoo!
The 50:50 isn't bad... you've got a 67% chance that one of your known wrong choices will show up... but oops, 33% of the time, you'll still be stuck with two possibly correct answers. If you guess, you've got a 50% chance. Overall, assuming you're going to go for the answer no matter what, you've got a 75% chance of getting a correct answer.
SUMMARY
According to these admittedly hurried calculations, I think:
- DD and 50:50 are identical if you can't eliminate anything.
- 50:50 is probably better if you can eliminate 1 choice, since you have a shot at getting a guaranteed correct answer, even though overall the DD gives better odds to guessing.
- DD is definitely better if you can eliminate 2 choices.
So which is better? I guess it depends on how much you know!
* If you can eliminate D, and the answer is A, then the three possible post 50:50 outcomes are A-B, A-C, A-D. You'll never choose D. Therefore, there are 3 out of 5 correct outcomes (the 3 A's).
What happens if the 50-50 eliminates two of the answers randomly? Well, it gets a bit complicated depending on which answer is actually right.
Let's assume for the moment that I'll always make a guess and I'll always guess the favorite from my initial ordering (I'll always choose A if it's there and I'll choose B over C or D and C over D). Now, my chances of getting this question right are:
When A is correct: .65*(.33*1 + .33*1 + .33*1) = .65 plus
When B is correct: .20*(.33*0 + .33*1 + .33*1) = .133 plus
When C is correct: .15*(.33*0 + .33*0 + .33*1) = .05,
for a total chance of .833, a bit worse than the DD.
But I still have the chance to walk after seeing the 50-50. Let's say I still pick A whenever it shows up and walk whenever B and C are the two choices. Now, my results look like:
Correct: 76.7%
Walk: 11.7%
Wrong: 11.7% (results don't add due to rounding).
Is that a better result than the simple 85% with the Double Dip? It depends on your risk preferences and on the level of the clue. If you are going for $50K, you'll never walk and so DD clearly is better. At other levels, the situation varies.
And, of course, if you use different assumptions for the relevant probabilities, results will be different. I haven't worked out any others yet but I suspect you can jigger the probabilities such that the 50-50 is clearly better than the DD. Maybe I'll do some of that analysis later.
Which I still messed up...

It was my intuitive sense of the way most good players would play their hunches that let me to think the DD is preferable -- you'd pick your top two choices, which in principle would give the best odds -- but now I'm left a bit befuddled...
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Playing with some probabilities in my spreadsheet suggests that in the situations where you can completely eliminate one response, DD gives the better outright chance of getting the question right. If you are of the "Million Dollars or Bust" variety, DD works better here. The 50-50 gives a lower chance of getting the question right but also a lower chance of getting the question wrong. The decision there will then depend on your personal risk preferences. So, there is no "correct" answer.
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Yes, that's a good point, too. Though, on the other hand, you could discuss what to double dip with the expert or a PAF.mikehardware wrote:I believe there's another problem with the Double Dip.
The 50/50 could be used first, before an ATA or PAF, to narrow down the choices. That could make it easier to get a correct answer.
Now, if you're combining lifelines, the Double Dip must be the last one used.
And how about this scenario. A contestant is at 16K, down to either a Double Dip or 50/50. There's no downside to using the 50/50, so that would be used.
Now, if the person has no clue and is still wanting to gamble, would they be more likely to go for it with only 2 answers showing, or with 4? We know the odds are the same, but the perception of the average player might be different.
I guess we'll soon get some empirical data in terms of finding out if people actually do get more questions right with the DD lifeline than they did using the 50:50 lifeline. And find out how people use the DD.
I do agree with others who pointed out that many contestants might leave the DD on the table, since it compels you to answer the question. None of the older lifelines forced you to answer.
Overall, it appears that the benefits of DD vs 50:50 is highly dependent on individual psychology, and the contestant's specific knowledge profile about the question. But since I think it will be more fun to watch, it's probably a win for the show.
- silverscreenselect
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There are a number of high dollar questions that you can "reverse google" to get the right answer quickly, but you can't google each answer separately. For example, suppose this is a 250K question
Osama bin Laden's family have been major stockholders for many years of which well known American company?
A-Coca Cola, B-IBM, C-General Motors, D-AT&T.
this is not a real question
If you try googling "Osama bin Laden family own stock" or something similar, you might or might not get a hit in 30 seconds which gave you the answer. On the other hand, if you used your 50/50 to narrow it to two choices, A & B, then googled "Osama bin Laden family own stock IBM" you would probably either get a quick answer indicating you were right, or, if not, you could be pretty sure that Coca Cola was the correct answer. The Double Dip takes that away, and it also takes away the prospect of narrowing a high $ question down to two choices before giving the audience a shot at it.
Osama bin Laden's family have been major stockholders for many years of which well known American company?
A-Coca Cola, B-IBM, C-General Motors, D-AT&T.
this is not a real question
If you try googling "Osama bin Laden family own stock" or something similar, you might or might not get a hit in 30 seconds which gave you the answer. On the other hand, if you used your 50/50 to narrow it to two choices, A & B, then googled "Osama bin Laden family own stock IBM" you would probably either get a quick answer indicating you were right, or, if not, you could be pretty sure that Coca Cola was the correct answer. The Double Dip takes that away, and it also takes away the prospect of narrowing a high $ question down to two choices before giving the audience a shot at it.
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You mean, when you have a strong hunch among the remaining three? That seems right.slam wrote:Playing with some probabilities in my spreadsheet suggests that in the situations where you can completely eliminate one response, DD gives the better outright chance of getting the question right.
I definitely agree you're modeling the most likely situation of a person in the chair. My intuition was that DD was usually better, if you had a strong hunch.
Heh heh... trickier than it looks...
- MarleysGh0st
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Does Ask the Expert have the same 30 second time limit that the PAF lifeline does? Can the Expert see the Q&A over the web link, instead of relying on having it read by the contestant?LastMinuteRequest wrote: Yes, that's a good point, too. Though, on the other hand, you could discuss what to double dip with the expert or a PAF.