Took me less than a minute to create what I assume is a very similar spreadsheet.
Took me less than a minute to create what I assume is a very similar spreadsheet.
The problem with the spreadsheet is that it does not apply to the original problem. The language of the original question is the cause of conflicting answers.
Now consider this:
After rolling one die a 2 the odds of rolling a second die as a 2 are 1/6.
The odds of rolling two dice to show 2-2 are 1/36.
And after rolling two dice when at least one die shows a 2 the odds that the other die is a 2 are 1/6.
No one disputes the first two statements but while the third statement is effectively the same situation as the first statement there are so many who say it must have a different answer of 1/11.
So it all comes down to language because all of the math is correct.
I agree that language or logic is the problem here - I would point out that the people who argue that points one and three produce different answers are also arguing that points one and three do NOT represent "effectively the same situation" at all.
I know you haven't seen my spreadsheet, but did you happen to look at the post I made here about how I would set it up? It's clumsily written but I could find no flaws when I reread it today.
You are most welcome.Originally Posted by Rob.Singer
I did not say I was in my right mind.
It took less time to assemble than any one of my 'wordsmith' posts.
I did it as a direct and full reply to Alan as a favour to him. I'm that kinda guy.
I figured that a yes/no answer to 'Will the wizard clean up' would not quite be enough.
Back to point 1. There is some merit to what you say. It extends to 'Why would anyone in their right mind spend all that time posting to Alan's forum and generating free content for him'. That one is rhetorical!
Synergistic -- agreed.
Arc got it right also when he commented about the language of the question.
I remember back in the late 1960s there was an issue about the wording in a national standardized test -- I believe it was the SATs and they resolved the disputes from various high schools by throwing the question out and adjusting students' scores.
Now what will be interesting is what will happen if anyone actually bets against the Wizard? The problem now is that language does not equal how dice can roll. And variance could make the Wizard win or lose. And the same variance in rolling two dice could make a 1/6er win or lose.
Early in the discussion on the Wizard's forum I said this was a trick question with the question "set up" using the coin problem being misleading. Now I am certain it was a trick question.
As I pointed out the original poster's "essay" in his spoiler made me suspect hanky panky.
There is a saying in poker that you can play the cards or play the player. If I play the player and if the 1/11-ers also play the player they'd also realize we've all been had.
I said the original poster must be having a good laugh about what he caused. It's very curious and funny how he never returned to the thread he started.
To answer his question you play the player.
I agree. The problem is logic.Originally Posted by synergistic
The correct answer is not immediately obvious. It is just the same with the two-coin puzzle -- first you'd think 50%. Also, quite similar to the Month Hall problem or the scene in the movie 21.
Alan, you keep saying stuff like, "Enough! Just prove to me it's 1/11. No games or spreadsheets etc. Just prove it!" [Not verbatim.] And that's exactly what we're constantly doing....but, you are unable to see the truth. You can lead a horse to water but you can't make it drink.
Just try the experiment.
By the same token... or flip side of the coin... you refuse to recognize the logic that the answer is 1/6.
It was a "bad question."
You can defend 1/11 forever and I can defend 1/6 forever. And the actual bet that the Wizard says he'll bank is subject to variance.
So what if the bet that he (and I) are willing to bank are subject to variance. Every bet has variance [except for very few, like maybe betting $1 on every number straight up on roulette]. The end result, though, is we'd be having a significant advantage in such a scenario. But, I'll book that bet all day and all night (as long as the bet wouldn't be some huge part of my BR).Originally Posted by Alan Mendelson
Alan, you're saying the original question was worded poorly. Ok -- perhaps it was (I don't think so).
But, how about this, if it was worded differently (I'm not sure how else you'd word it...been worded a million times here and on WOV).....then would you agree, the answer would be 1/11? I hope this is the case.
Rob, I'm not sure what or why you're even trying to argue. I don't think there's a legitimate gambler/AP, mathematician, statistician, etc. that takes what you say seriously at all. But, to each his own.
Last edited by RS__; 04-20-2015 at 03:02 AM.
I think the question was intentionally worded to be deceptive. It was a trick question. How you view the event will prompt a different answer. And that's clearly what happened. If we ever hear from the original poster again he will tell us he had a good laugh.
Regarding the bet? I wouldn't bank it nor would I participate in the exercise. It's just a roll of the dice, isn't it? You can debate logic and language but you can't debate how the dice land. Either side could win... or lose when dice are rolled.
And to be honest when rolling two dice the answer is not 1/6 or 1/11 but 1/36.
Of course, either bet can win. But, I'd rather put my money down when I have a positive return.Originally Posted by Alan Mendelson
I agree, it is 1/36 when rolling two dice. But what if we're only interested in the rolls where "at least one die is a 2"? Only counting those rolls, what do you say is the chance of rolling a 2-2? Is it 1/6, 1/11, or other?
Well we are back to square one. It depends how you look at the problem. There is the case for 1/6 when one die shows a 2 yet we all agree rolling 2-2 is a 1/36 event.Originally Posted by RS__
What makes the bet a winner for the banker is this:
In a real casino a roll of 2-2 pays 8 to 1 which is the same as the Wizard. But in a a casino you lose the 2-2 bet only when 1-3, or any 7 rolls.
With the Wizard's bet you lose any time a number is rolled that contains a 2 on one die. That's 10 losers with the Wizard vs
7 losers with the casino.
Yesyesyes, this! With the wizard's bet, there are ten losers and one winner - only one winner out of eleven total possibilities. Follow that thought around to the paradigm shift.Originally Posted by Alan Mendelson
And this brings us back to the WORDING of the original question. I am going to ask you to read the question for what it is. When you do the answer is 1/6.Originally Posted by synergistic
No one should take what I will now call The Wizard's Bet.
I have to correct myself. The ways to lose a hard-4 bet in a casino are:
1-3
3-1
2-5
3-4
4-3
5-2
6-1
1-6
And that's a total of 8. And the hard 4 actually pays 7 to 1. The Wizard's Bet is much worse for the "player" with a pay of 8 with ten ways to lose. It's not clear if the Wizard pays 8 to one or 8 for one but either way it's worse than the casino bet.
Maybe Alan is just trying to increase the number of hits on this forum.
RS (that's funny): First, I don't argue with self-absorbed know-it-alls; I only talk facts. Alan's done a superb job arguing every aspect of the issue for his forum--both here and there--in spite of the mistreatment & insults WoV members have responded with about him-a WoV member BTW. You ought to ask beachbumbas, mission, wizard and face why they haven't used their "suspension powers" instead of flattering me with how "gambling AP's" don't take me seriously. The only thing that matters in gambling is winning money, and that's exactly why the collection of all that so-called intellect over there couldn't face me in person when it came to my challenge of playing my strategy in front of them to prove it.Originally Posted by RS__
Just as you did here RS, you folks are quick to talk theory and criticize others, but when it comes time to walk the walk all you can do is resort to the anonymous chest pounding. Alan won this round big time, even to the point about how the wording of the question could have been interpreted several ways similar to the Monty Hall problem, when all you guys cared about was calling him and us stupid because we wouldn't see it "your" way. Think about that the next time you guys want to argue common sense issues outside your sacred little world of self-annointed geniuses.
Last edited by Rob.Singer; 04-20-2015 at 06:12 AM.
You really didn't look at it then, and by the tone of once dear's response, I think he took issue with your "less than a minute" comment. Regardless, his excel effort was done with only one baseline considered, and I believe WoV members have all finally acquiesced to the fact that the question proposed was deceptive and could be interpreted several ways. The 1in11 folks preferred the more complicated route, for reasons my articles state.Originally Posted by synergistic
Looks like they're all reading this thread from WoV now, which in turn has ramped up their being humbled. For a site that likes to pride itself on being "sensitive" to others--such as to gays, transgenders, atheists, agnostics, the poor, along with other freaks of society--it hasn't taken very much for them to denigrate & namecall this forum's members simply because we're far too common sense based to see everything exactly the way they want others to see it.
Calling that spreadsheet which only told their flawed side of the story "Alan's Folly" when theorists get frustrated, is lame, and they're even going the extra mile to pick on Dan. But hey, when you belong to a forum run by an admin. who apparently had his AP gambling/better to lose $$ on a "good bet than to win a -EV bet" fail him (what's new) so he had to resort to the desperate measure of begging members for money, it's no wonder all that perceived intellect they like to project is taking this so hard. Maybe when they realize that 2+2=4, even on Mars, they'll be able to handle discussions like adults--even if they don't (horror of all horrors) "prevail".
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