The Wizard will bank this bet: 1/6 vs 1/11

In our epic thread I posted about a proposed bet that I think will monetize the difference of opinion between those who believe the answer is 1/6 vs. those who believe the answer is 1/11.

I asked on the WOV forum who would bank the bet? The Wizard has reponded he would and here is the post with the bet and his response in italics:

Quote: Rawtuff
A person puts two dices in a cup, shake and slam the cup on the table.

A second person peeks under the cup and truthfully announces if there is at least one deuce showing or not (he will later lift the cup and show to all he wasn't lying).

If "at least one deuce" is announced, the 1/6-ers will wager 1 unit on the premise that there are two deuces under the cup( a one in six probability according to them). If they're right, they get 9 units back. If they're wrong, they lose the 1 unit wagered.


I'll bank that. The minimum bet (against me) is $10 and my maximum is $100. I will be prepared to do this for hours. Wagers must be settled after each roll. I'm flexible on any public location in Vegas. I am also flexible on the time.

Alan: If we assume that the proposed wagers will actually carry though in deed as described in the words above, you will soon see one of the reasons why the Wizard Shackleford was able to sell his website for over $2 million.

I am waiting to hear who will accept this and bet against the Wizard.

Regarding the sale of his website, that's for a different thread and if you'd like to start it I'd be happy to talk about it.

Where are those identifying items I asked for? We spent days going back & forth about how the question is to be interpreted. Does the 1st die get eliminated once a "peeked at" 2 is announced? If so, as I said, I will bet Shack any amount he desires with that 9-1 payout. If not--and I strongly suspect WoV wants the guidelines to be the Burger King way--then make the payout for two 2's 11-1. And tell him I'll do it in Tahoe this weekend.

Rob, it's spelled out. The only question is 9-for-1 or 9-to-1 and the Wizard says it doesn't matter to him.

Gone are the "old rules". This is a new bet and quite frankly I like it.

Let me answer your questions specifically and I am sure this will be the understanding:

1. Two dice are in a cup or other device, shaken and in the cup placed on the table.
2. A witness will peek. If a 2 is shown the bet is on.
3. If a 2 is not shown, there is no betting.
4. In both cases, the cup will be removed and the dice can be viewed. This will prevent the original dice from showing 2-2 and the witness lying.
5. With one deuce the bet is on (#2) and if there is not a second bet the "player" will lose their bet.
6. With one deuce the bet is on (#2) and if there is a second deuce the "bank" will pay either 9-to-1 or 9-for-1 (the Wiz doesn't care.)

My own personal thought: I can't imagine why the Wizard agreed to this? There is a 1/6 chance that when one die shows a 2 that the other will also be a 2 yet he is willing to pay 9-for-1 or 9-to-1.

Is it possible he misread this bet the same way I suspect he misread the original question? Somebody wake me up from this (bad) dream.

The Wizard says he will do it in any public venue in Vegas and he limits the bets from $10 to $100 each.

I revert back to my last post. I need to know which interpretation of the "OQ" is being used as a baseline. If it's mine, where the peeked-at die showing a 2 gets eliminated, then 9-1 is too generous, even for a kind soul like Shack. I'll take that action until the cows come home.

But, if as I suspect, we don't get to see which die has the original 2 until after the bet, then 9-1 is a punk bet because two 2's, after knowing half the outcome at that point, is an 11-1 event in this case.

I expect wizard would enjoy a trip up here while getting out of that chaotic city, but I can't believe he's serious if the first interpretation prevails.

Rob: the bet isn't "on" until the peeker says there is at least one die showing a 2.

In all cases -- no matter what the peeker says -- the cup will be removed so everyone can see what the two dice were. This will prevent the peeker from lying when the dice show 2-2.

When the bet is on you would put in your bet, from $10 to $100.

If there is a pair of 2s, you win 9-to-1 or 9-for-1.

If there is not a pair of 2s you lose your bet.

This is what the bet is.

It is in fact the same (in my opinion) of rolling one die after the first die shows a 2. And frankly I am surprised the Wizard agreed to it.

Now, with that said, the bet is being further discussed on the WOV site. And I am wondering if there was a misunderstanding about it and I have asked that.

In the meantime the Wizard has asked why I am not participating and I said honestly that I do not bet against people, and only casinos, with the exception of when I play live poker.

Wizard said he wants it to be a flat bet -- and that was my idea. The same amount bet each time. I suggested $10 per bet.

Quote:

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Originally Posted by Alan Mendelson

Rob: the bet isn't "on" until the peeker says there is at least one die showing a 2.

In all cases -- no matter what the peeker says -- the cup will be removed so everyone can see what the two dice were. This will prevent the peeker from lying when the dice show 2-2.

When the bet is on you would put in your bet, from $10 to $100.

If there is a pair of 2s, you win 9-to-1 or 9-for-1.

If there is not a pair of 2s you lose your bet.

This is what the bet is.

It is in fact the same (in my opinion) of rolling one die after the first die shows a 2. And frankly I am surprised the Wizard agreed to it.

Now, with that said, the bet is being further discussed on the WOV site. And I am wondering if there was a misunderstanding about it and I have asked that.

In the meantime the Wizard has asked why I am not participating and I said honestly that I do not bet against people, and only casinos, with the exception of when I play live poker.

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Alan, there is a difference, which is why I asked about the interpretation--which IMO can be taken two ways. It appears the WoV interpretation reigns, and from the looks of things, the wizard is only paying 9 units for something that has 11-1 odds.

If we're at this point, I'll explain why. When two dice are peeked at and we're informed that one of them is a 2, if that die is removed from the scene then we're left with a single die that no longer has a numerical relationship to the die showing a 2. This is the way I interpret the problem with the wording from the OP, and the odds that 2nd die will be a 2 is 6-1.

However, if you take the WoV interpretation, simply telling you that one of the dice shows a 2 does not remove it from its numerical relationship with the die with the unknown number showing. Whereas rolling 2-2 is a 36-1 possibility, knowing half the outcome, ie. one of the dice is showing a 2, reduces the odds to 11-1 since it is no longer a single die event. You now have to consider all combinations of the two dice where either one of them shows a 2.

Of course, the mensas all followed wizard's lead since he was the first to offer an interpretation. And because that type of analysis gave a chill up the leg of his liberal troupe, they went with it and it is now the basis of their challenge.

Tell them I'll still do it at the $10 bet amount, if they finally will accept my challenge that I can win at least $2500 playing one of my SPS sessions, which is about 5% of my session bankroll. This bet will be for, of course, $2500.

Rob, what are you talking about? The "bet" is the same thing that we have been talking about that you and I and regnis all say is 1/6. Now you are saying it's 1/11 ??

I made the initial post in this thread at 7:30pm Pacific time Monday. I am going to give it 24 hours for someone to say they will make the bet with the Wizard.

I personally won't because of my personal choice not to make bets with individuals. This is something I grew up with. My parents did make bets between themselves such as a nickel (5 cents) on the World Series. But actual betting was only done in a casino. I remember my father staying out of the craps games that his friends got into when they came over to the house for dinner parties. When they played Pinochle or Gin on Sunday afternoons they played for pennies and nickels.

$10 per bet is too much for my personal boundaries for a bet against an individual. In a casino I don't blink at $10 bets. So this is why I won't be involved with the Wizard's bet. If the Wizard would make the bet for nickels, I'm in. If he wants to do a certain number of rolls and the winner buys lunch -- well then I am in too. It's a personal ethics thing and I am not going to change it.

As offered on WOV

For the UK venue, I will arrange the venue, bank the bet, slam the cup, and peek the dice.
For the US venue, I'll accept Wizard as escrow and Wizard as peeker if that's acceptable to you and to him. I won't be betting against the Wizard.

If Alan would care to do it for nickels as a live video conference, I'm sure we could arrange that too.

Oh... And if it's announced that 'at least one of the dice is a deuce', I'd be happy for that die to be pulled from under the cup immediately and before the bet.

OnceDear I would do the bet for nickels or for lunch. I just can't do it for "real money." Lunch would be a perfect for me.

If you want the die pulled from under the cup immediately and before the bet it sounds okay to me too -- but that's not what the Wizard agreed to. But practically it's the same thing. Because that means the bet is simply this: can you roll another 2 and be paid 9X for an event that is supposed to happen 1/6 times?

And that's all this bet is.

This "business" about rolling the dice in a cup first to see if at least one 2 shows up is only a trigger for that bet. Once there is that trigger of at least one two the question is simply is there a 2 on the other die?

Those who believe there is a 1/6 chance that there is a 2 on the other die will accept the bet with the 9X payoff. Those who believe that the chance of another 2 is 1/11 will happily offer the 9X payoff.

(Note I said 9X payoff because the Wizard said he didn't care if its 9-for-1 or 9-to-1. And I don't care either even though there is a difference.)

By the way, and you can post this: I can be in Vegas late this Friday night or Saturday for this. On Sunday morning I must be back in LA to bowl in a charity fundraiser. Yes, I bowl Arc. Not well, but I bowl. I even have my own ball, bag and shoes... not that this indicates any ability.

Quote:

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Originally Posted by Alan Mendelson

Rob, what are you talking about? The "bet" is the same thing that we have been talking about that you and I and regnis all say is 1/6. Now you are saying it's 1/11 ??

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That's because it is 1-11. Here are the situations .... 1-2, 2-2, 3-2, 4-2, 5-2, 6-2, 2-1, 2-3, 2-4, 2-5, 2-6 .... How many situations are there and how many are a pair of 2s?

It doesn't make any sense to debate this anymore. Both sides have stated their case. Now, the Wizard is willing to host and bank a real money test. If it were a test and the stakes were lunch I would do it. Or if it were bragging rights, I would do it. But the bet is $10 per hand and I can't do that.

Rob has talked about making bets -- and big money bets at that. And now that we have a real money bet proposition, all of a sudden Rob doesn't recognize that this is what he was talking about the whole time? That it is the 1/6 situation he's been advocating? He needs to explain it to me now -- and to everyone.

I will put up "lunch" for the bet and it could be a $100 lunch. I just can't put up $100 in cash for ten trials because of the way I was brought up and what I truly believe in as far as betting between individuals. I just can't do it. Rob on the other hand has been offering cash bets for years. And here's your chance Rob... unless of course you're saying that it's not 1/6 ????

But Arc just to be sure you understand: the bet doesn't start unless there is already ONE two showing. And frankly that means you have a 1/6 chance. Nuff said.

Alan, I told you in my last post that the 6-1 position has always been only if they removed the die showing the 2 from the scene. One die remaining = six opportunities to yield a 2. That should be clear, and this is always been how I've interpreted the OQ.

The "WoV camp" has always used the interpretation that it is always a two-dice event without removing the die showing a 2 from play. I've said many times I didn't believe the OP meant the problem to be like this, but I guess you've agreed that it should for betting purposes.

Look at the combinations arci just posted--those are the 11 possibilities when both dice remain in play. In this case, naturally 9-1 is bad odds. In your discussions with the WoV folks, when & where did you stop talking about one of the dice being removed from play? I've said I'd take the bet at 9-1 only if the original die showing a 2 were removed from play, "until the cows come home". But I just looked at wizard's site, and of course the poster named "RS" cut & pasted snippets of my post here that is incomplete, not all correct, and said in a way that shows he's irritated. He also left out their Achilles heel about betting that I'll win with my strategy. I said I'd take the bad bets for $10 IF there was the bet on my strategy this weekend in Tahoe. I'd love to do that because at $10/roll my losses wouldn't be much, but I'd likely win $2500 from them on my vp play.

Do you understand this now? Remove one die = 6-1; keep both dice = 11-1. That has always been why the question was "tricky". Two interpretations.

Hi Rob,
For the elimination of doubt, nothing about any wagers.
The original question verbatim from Alan's first post:-

Quote:

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I got into a rather heated exchange over on the Wizard's forum on this question:

You have two 6-sided dice in a cup. You shake the dice, and slam the cup down onto the table, hiding the result. Your partner peeks under the cup, and tells you, truthfully, "At least one of the dice is a 2."

What is the probability that both dice are showing a 2?

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The original question as posed on Wizard's forum first post:-

Quote:

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You have two 6-sided dice in a cup. You shake the dice, and slam the cup down onto the table, hiding the result. Your partner peeks under the cup, and tells you, truthfully, "At least one of the dice is a 2."

What is the probability that both dice are showing a 2?

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Verbatim the same.

Quite different to the one on your comments page: I don't know where that came from.

Quote:

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This time it was about two dice, where after the shake one of them was "peeked at" and known to be a 2, and the question was "what is the probability that both die are showing a 2"?

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There was never a question about 'the second die' being a two.

There was a question about the remaining pair of dice :-

'What is the probability that both dice are showing a 2?'

There was never any mention of taking or setting aside one of the dice. There was never actually mention of 'peeking at ONE of the dice' in the OQ

Quote:

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Originally Posted by Rob.Singer

Alan, I told you in my last post that the 6-1 position has always been only if they removed the die showing the 2 from the scene. One die remaining = six opportunities to yield a 2. That should be clear, and this is always been how I've interpreted the OQ.

The "WoV camp" has always used the interpretation that it is always a two-dice event without removing the die showing a 2 from play. I've said many times I didn't believe the OP meant the problem to be like this, but I guess you've agreed that it should for betting purposes.

Look at the combinations arci just posted--those are the 11 possibilities when both dice remain in play. In this case, naturally 9-1 is bad odds. In your discussions with the WoV folks, when & where did you stop talking about one of the dice being removed from play? I've said I'd take the bet at 9-1 only if the original die showing a 2 were removed from play, "until the cows come home". But I just looked at wizard's site, and of course the poster named "RS" cut & pasted snippets of my post here that is incomplete, not all correct, and said in a way that shows he's irritated. He also left out their Achilles heel about betting that I'll win with my strategy. I said I'd take the bad bets for $10 IF there was the bet on my strategy this weekend in Tahoe. I'd love to do that because at $10/roll my losses wouldn't be much, but I'd likely win $2500 from them on my vp play.

Do you understand this now? Remove one die = 6-1; keep both dice = 11-1. That has always been why the question was "tricky". Two interpretations.

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That's all cool and dandy.

You can remove the (or one of the) dice showing deuce after the establishment roll has been made. No probs whatsoever.
The bet remains the same as outlined on WoV with the addition that when "at least one deuce is showing" is declared the peeker will reach and remove that (or any of the two in event there are two twos) dice of the cup.

You in in THAT scenario? Nice.
Put your money where your mouth is , I'm sure the Wioz and co will be happy to oblige with this addition to the rules.

Even though removing one/any dice in a particular/any case is never mentioned AT ALL, ANYWHERE, in the original question, so I really don't know where the hell is this character RS getting/demanding this from, even though - there will be no problem granting his wish. He wants removing the dice showing two from the cup? Done.
Any more wishes?
One needs to be able to comprehend simple stuff before making claims he understands stg better.