Two dice puzzle -- Part Trois
Quote: coachbellyQuote: unJonOpen to any challenger. Money escrowed in advance with the Wiz.
I'm willing to make escrow arrangements with the Wizard.
Do you have any conditions not specified earlier?
I have just one...the exercise and settlement must be conducted with both participants (that's me & you) in attendance, in person.
Any witness is acceptable to me.
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Your extra stipulation is not acceptable to me. I stipulate to do it witnessed over Zoom or similar video conference, with the Wizard conducting the roll under video camera.
If that’s acceptable to you, advise if you want to do one bet or numerous bets, so appropriate amounts can be escrowed.
Best of luck.
Quote: unJonYour extra stipulation is not acceptable to me. I stipulate to do it witnessed over Zoom or similar video conference
I don't consider video conferencing a legitimate format for such an exercise, it should take place in person.
You should reconsider, perhaps we could renegotiate the odds?
Quote: WizardHere is your chance to prove me wrong and make some money at the time same time.
Is this bet open to any takers, ala MDawg's challenge, or is it by invitation only?
I'm willing to give it a shot...who wouldn't take a hall-of-fame opportunity like this?
Do you have any conditions not specified earlier?
I have just one...the exercise and settlement must be conducted with both participants (that's me & you) in attendance, in person.
Any witness is acceptable to me.
Quote: coachbellyQuote: unJonYour extra stipulation is not acceptable to me. I stipulate to do it witnessed over Zoom or similar video conference
I don't consider video conferencing a legitimate format for such an exercise, it should take place in person.
You should reconsider, perhaps we could renegotiate the odds?
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Thank you but no. Your stipulation is not acceptable to me. Appreciate your renewed efforts to try to meet up with me in person though.
ETA: I hope you and the Wizard work out agreeable terms.
Quote: unJonYour stipulation is not acceptable to me.
If I were to stake another member, would you agree to an in-person event?
Quote: unJonAppreciate your renewed efforts to try to meet up with me in person though.
It ain't about you...why would you think that it is?
Quote: coachbellyIs this bet open to any takers, ala MDawg's challenge, or is it by invitation only?
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I'll offer Alan's side to anyone who wants it.
Quote: coachbellyI'm willing to give it a shot...who wouldn't take a hall-of-fame opportunity like this?
Do you have any conditions not specified earlier?
I have just one...the exercise and settlement must be conducted with both participants (that's me & you) in attendance, in person.
Any witness is acceptable to me.
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I suggest that until we establish some trust, bets be settled after each shake, as long as there is it isn't a push (no twos). An alternative to that is we both escrow money with a mutually agreeable source.
I also pretty much insist this be done in person.
Also, lest loaded dice be an issue, the party NOT supplying the dice get to choose the particular face bet on. In other words, it doesn't have to be twos. It just has be declared before the shake.
Quote: coachbellyQuote: unJonYour stipulation is not acceptable to me.
If I were to stake another member, would you agree to an in-person event?
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I’m happy to let you and the Wizard work it out. Will be more legendary that way anyway.
Quote: unJonYour stipulation is not acceptable to me.
Nobody is going to take your bet without the following conditions...so what's you're angle?
Quote: WizardI also pretty much insist this be done in person.
Quote: coachbellyQuote: unJonYour stipulation is not acceptable to me.
Nobody is going to take your bet without the following conditions...so what's you're angle?Quote: WizardI also pretty much insist this be done in person.
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The angle is the +EV bet. The sweetener is ending the debate on the topic of this two dice problem. If no one would take it then no one would take it. I’m comfortable with the Wizard running the show via video.
Quote: unJonI’m comfortable with the Wizard running the show via video.
LOL...OK playa.
***: A bet is considered resolved, when a roll shows either: "one two" or "two twos" (see link here for further clarification ).
Important: The odds below are for how many "two twos" occur after 40 resolved bets (expressed as "American Odds").
Zero to Two: +235
Exactly Three: +335
Exactly Four: +370
Five or more: +220
Quote: coachbellyQuote: unJonI’m comfortable with the Wizard running the show via video.
LOL...OK playa.
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Just throwing in my two cents.
Wizard and Unjon should consider some table limits. Min and Max bet.
Otherwise some obscenely high bankrolled braggart could come along, Marty their way to a one unit profit after maybe a couple of rolls and then refuse to play on. He could then lie that he proved Wizard and Unjon wrong, while walking away with a free supper.....
Or some other mischief maker could waste several hours of Wizards time playing for ten cents a roll.
Anyway...... the wager will not happen. We've been here before Nine years ago.
If Alan or Coachbelly or his proxy manages to arrange to seriously take up the wager with Unjon or Wizard, for beer money stakes, get in touch with me before the meet.
I will send a giftcard code (or maybe paypal payment) for modest funds to cover the price of a complimentary drink to each player.
Sometimes, you gotta make concessions to keep the fish at the table.
Humor aside, I agree with OD that table min/max should be negotiated in advance.
I know. Pathetic isn't it. Offer withdrawn.Quote: billryanYou are going to cover the first round of complimentary drinks? What a sport. As they are free, why not cover the second round as well?
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I wonder if a casino would host this and give comps.
Quote: DieterI agree with OD that table min/max should be negotiated in advance.
There are currently two bets offered...see quotes below.
Once accepted, are the makers obligated to adhere to the terms that they have presented,
or can they just disregard their original offer, and change original terms, should they simply desire to do so?
Quote: WizardIt's time to put up or shup up. I'll bet whatever stakes you wish.
If you think the probability is 1/6, then fair odds would pay 5 to 1. I'll offer you 8 to 1.
Quote: unJonHere is the bet. I’ll take it if the Wiz doesn’t want it.
Two dice are rolled under a cup. Someone we both trust will report the answer to the questions:
is there at least one die showing a two?
If that person says “no”, then there’s no bet. They can show us the dice to verify the “no.”
If that person says “yes”, then there is a bet. Alan will win $70 if the roll is a hard four.
Alan will lose $10 if the roll is not a hard four, but just a two on one die but not the other.
That’s 7:1 odds that if one die is a two the other won’t be.
That’s the bet. That’s the bet you say has 1/6 of being correct, and I and others say has 1/11 of being right.
Quote: coachbellyQuote: DieterI agree with OD that table min/max should be negotiated in advance.
There are currently two bets offered...see quotes below.
Once accepted, are the makers obligated to adhere to the terms that they have presented,
or can they just disregard their original offer, and change original terms, should they simply desire to do so?
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That would seem to be between the two parties laying action.
One party lays one money
One party lays seven money (or eight money)
They agree on which number (2 has been suggested, but any number works).
Throw the dice, settle, repeat until uncle is cried.
Agreeing on stakes in advance is just a convenience so that both parties can bring enough cash money to keep playing a while, and avoid bringing a slingshot to a knife fight.
Agreeing to a different game on the day would seem to be their option, although it might not satisfy the challenge.
Refusing to play the agreed in advance game on the day would also seem to not satisfy the challenge.
Quote: coachbellyOnce accepted, are the makers obligated to adhere to the terms that they have presented,
or can they just disregard their original offer, and change original terms, should they simply desire to do so?
Quote: DieterThat would seem to be between the two parties laying action.
Members have received lengthy suspensions for reneging on wagers that were offered and posted.
We currently have 2 new wagers offered and posted.
Should the bettor not agree to changes in the maker's offer,
are there forum consequences (i.e. suspension) for the reneging maker?
Quote: coachbellyQuote: coachbellyOnce accepted, are the makers obligated to adhere to the terms that they have presented,
or can they just disregard their original offer, and change original terms, should they simply desire to do so?Quote: DieterThat would seem to be between the two parties laying action.
Members have received lengthy suspensions for reneging on wagers that were offered and posted.
We currently have 2 new wagers offered and posted.
Should the bettor not agree to changes in the maker's offer,
are there forum consequences (i.e. suspension) for the reneging maker?
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Just IMHO, All wagers between members are between members. We moderate the rules here, not litigate civil legal action.
However, if a member uses this forum to make a wager and it is thoroughly clarified and double confirmed, and is then reneged on, then Wizard might or might not impose a penalty as he sees fit. You can probably point out some precedents.
There's probably a difference between withdrawing an offer to bet and refusing to settle a resolved bet.
Quote: coachbellyQuote: coachbellyOnce accepted, are the makers obligated to adhere to the terms that they have presented,
or can they just disregard their original offer, and change original terms, should they simply desire to do so?Quote: DieterThat would seem to be between the two parties laying action.
Members have received lengthy suspensions for reneging on wagers that were offered and posted.
We currently have 2 new wagers offered and posted.
Should the bettor not agree to changes in the maker's offer,
are there forum consequences (i.e. suspension) for the reneging maker?
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I do not currently see a rule on welching on the list.
This does not mean welching is acceptable by forum standards.
Quote: DieterI do not currently see a rule on welching on the list.
I don't recall any welching, but here are a couple of suspensions for retracting a challenge....
MDawg 12/18/20 31 Challenge retraction 1/18/21
Expectedvalue 04/12/21 30 Challenge retraction 05/12/21
Thank you. Please go through all the other posts on the forum and let us know where challenges were retracted and no penalty imposed.Quote: coachbellyQuote: DieterI do not currently see a rule on welching on the list.
I don't recall any welching, but here are a couple of suspensions for retracting a challenge....
MDawg 12/18/20 31 Challenge retraction 1/18/21
Expectedvalue 04/12/21 30 Challenge retraction 05/12/21
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Quote: OnceDearThank you. Please go through all the other posts on the forum and let us know where challenges were retracted and no penalty imposed.
You are welcome.
You mentioned precedents, and I provided some.
Quote: OnceDearYou can probably point out some precedents.
Are you suggesting that forum precedent includes retracted challenges with no penalty imposed?
That's not clear from the following exchange...
Expectedvalue
April 11th, 2021 at 6:56:33 AM
Quote: ExpectedvalueI am out.
Wizard
Administrator
April 12th, 2021 at 5:58:19 AM
Quote: WizardPer forum precedent, 30 days for retracting a challenge.
Expectedvalue 04/12/21 30 Challenge retraction 05/12/21
I just wanted to give you the opportunity of quoting all the conflicting precedents. It was what passes in my head as a joke.Quote: coachbellyQuote: OnceDearThank you. Please go through all the other posts on the forum and let us know where challenges were retracted and no penalty imposed.
You are welcome.
You mentioned precedents, and I provided some.
1. First, this moderator (and I suspect all other moderators) is not going to serve as a "Forum judge" for who has won this bet. Any person agreeing to serve as a judge for a $100,000 wager of this type would open themselves up to being swept into future lawsuits.
- Again, this forum bet is not based on the outcome of a sporting event or internal forum contest for which the results can be clearly discerned and are publicly documented.
2. This wager carries a stated penalty of being nuked from this forum to the loser. To be clear, either participant has an option of self-banning themselves from the forum at any time. However, the administrative staff of this forum has no obligation to enforce suspensions on a losing party simply because it is a condition of a wager that we were not a party to.
3. On the subject of suspensions for welching on a bet that was publicly posted on this forum: The original statement of this wager involved no language that stated how the matter of proof is to be resolved to the satisfaction of both parties. TDVegas is now raising questions and challenges to what MDawg is proposing to offer. If the matter of "proof" is not resolved to the satisfaction of both parties then this is a "dispute" and I imagine the proper societal channel for resolving the dispute would be to bring suit in a civil court with appropriate jurisdiction.
If, however, both parties do eventually agree and concur on a clear winner and a clear loser to the wager then there might be an adequate basis for determining that a party is welching on a bet made on the WOV forum. We (the administrators) might (or might not) address such an issue at that time.
Any member of the 1/6 camp should incorrectly perceive a 33.3% advantage (not counting pushes). Come and get it.
I'm just now, today, seeing this entire thread for the first time.
I also, just now, read the entire "Two Dice Puzzle" thread, that initially started back in October of 2013. (It's possible I read that thread back then. But if I did I forgot about it.)
Hey, if I can get in on any of these wagers, let me know.
The initial problem is clearly stated (re-wording it is not needed) and yes, the answer to the question, "What is the probability that both dice are showing a 2?" is 1/11. It is NOT 1/6. (Sorry Alan.)
I can't do any better than some of the others in explaining WHY the probability 1/11 is correct... so I see no reason to even try.
But here's what puzzles me.
Okay, I get it. I DO understand why some people, initially, think the answer is 1/6. That initially seems correct.
But for the life of me, I don't understand why, when shown HOW and WHY 1/6 is clearly WRONG and when presented with simple simulations they can conduct for themselves, in their own home, to CONFIRM it's wrong, why they still aren't able to figure out and confirm the correct answer.
That part I just don't get.
The question reminds me of one of the logic problems on my website. "The Woman With Two Children."
Census Taker: How many children do you have?
Woman: Two.
Census Taker: And their ages?
Woman: One is five, one is two.
Census Taker: Is one of them a girl?
Woman: Yes.
What is the probability that her other child is a girl? (Assume every pregnancy has a 50/50 chance to be a boy or a girl.)
And the answer to this question is... 1/3.
Fun stuff.
In other news, I'm happy to report that LoquaciousMoFW has accepted Alan's side of the challenge. Here are some tentative details:
- Challenge to take place June 8 in Las Vegas
- LoquaciousMoFW will wager $5 per shake
- I have kindly upped the win for two 2's to 8 to 1.
- LoquaciousMoFW has agreed to keep playing until losing $200. At that point, he/she has the option to back out.
- If for some reason LoquaciousMoFW can't be present, he/she has agreed to front money and have a proxy play for him/her
If anyone would like to piggyback on LoquaciousMoFW's side, by all means, please express an interest. I'm happy to bet more on my side.
As I’ll be in Vegas then, I would like to witness this.Quote: Wizard• Challenge to take place June 8 in Las Vegas
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Can I assume this will be after the day’s activities at the Table Game Conference? If so, can we just make it an official WoV Meet-Up event?
FYI: I’d volunteer to judge but I’m not sure how impartial I’d be. Note that in this post on page 9 of this thread, I argued for both sides.
Quote: billryanWhen can he quit if he is up? Making him play until he is down $200 doesn't sound right.
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He promised to do so in the name of getting a decent sample size. I would be happy to let him quit if up $200, just to be fair, if he asks.
Quote: DJTeddyBearCan I assume this will be after the day’s activities at the Table Game Conference? If so, can we just make it an official WoV Meet-Up event?
FYI: I’d volunteer to judge but I’m not sure how impartial I’d be. Note that in this post on page 9 of this thread, I argued for both sides.
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Yes, that is a correct assumption.
I hope I may say this event planned for the small suite of LoquaciousMoFW. I'll let him decide who may attend, but as the first to ask and prospective videographer and judge, I think your odds are looking very good.
My window is wide open if anyone else wants to piggyback on LoquaciousMoFW's side.
Quote: WizardYes, this whole problem is the same thing as the "two boys" problem, but with six genders. Anyone who gets one will get the other. Anyone who doesn't get one won't get the other.
In other news, I'm happy to report that LoquaciousMoFW has accepted Alan's side of the challenge. Here are some tentative details:
- Challenge to take place June 8 in Las Vegas
- LoquaciousMoFW will wager $5 per shake
- I have kindly upped the win for two 2's to 8 to 1.
- LoquaciousMoFW has agreed to keep playing until losing $200. At that point, he/she has the option to back out.
- If for some reason LoquaciousMoFW can't be present, he/she has agreed to front money and have a proxy play for him/her
If anyone would like to piggyback on LoquaciousMoFW's side, by all means, please express an interest. I'm happy to bet more on my side.
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Nice. I thought Coachbelly accepted the wager also. Maybe he can come to town that day or use LMFW as proxy.
Quote: EdCollinsOh my gosh.
I'm just now, today, seeing this entire thread for the first time.
I also, just now, read the entire "Two Dice Puzzle" thread, that initially started back in October of 2013. (It's possible I read that thread back then. But if I did I forgot about it.)
Hey, if I can get in on any of these wagers, let me know.
The initial problem is clearly stated (re-wording it is not needed) and yes, the answer to the question, "What is the probability that both dice are showing a 2?" is 1/11. It is NOT 1/6. (Sorry Alan.)
Quote clipped. I strongly disagree the original problem is stated clearly. In fact, I know I can recreate a situation that meets every part of the original wording and have the answer be 1/6. Or frankly 1/1.
Read other threads and you will see that, regardless of clear evidence presented, there are forum members who refuse to believe:Quote: EdCollins
But here's what puzzles me.
Okay, I get it. I DO understand why some people, initially, think the answer is 1/6. That initially seems correct.
But for the life of me, I don't understand why, when shown HOW and WHY 1/6 is clearly WRONG and when presented with simple simulations they can conduct for themselves, in their own home, to CONFIRM it's wrong, why they still aren't able to figure out and confirm the correct answer.
That part I just don't get.
1) The chance of winning the ALL bet in craps is about 1 in 190. Their rationale: “No way, happens more often when I play”
2) The combined house edge of a passline bet with 3/4/5 odds is 0.37%. Their rationale : “Not true. It’s just a marketing scheme to make you think that. Besides, what kind of lunatic would play a zero-edge bet like free odds since you are just breaking even over the long run …moving money from one pocket to the other “
If you wanted a bet that represented my position use one die and see the ratio of when a 2 appears.
Use a six sided die of course and not one of those 11-sided dies available on the Internet.
Thanks.
By the way... the next time you see a spinner on a craps table don't make the mistake of saying "there's a 1/11 chance we'll make the point."
Quote: AlanMendelsonGood luck to all of you. Please keep my name out of this bet because I dont think this bet represents my postion.
Your position? What's your position? That setting one dice as a two is the same as knowing one of the dice is a two? Well, it isn't.
[Edit. Here in his own words is Alan's position]
Quote: AlanMendelson
I have to disagree with you. You didn't read the question carefully. The original question tells you one die is known to be a 2. And that is the same as throwing two dice on a craps table, one of them coming to rest as a 2, and the spinner being the unknown die. You have a 1/6 chance that the spinner will be another 2.
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That was is position in 2015. It's his position in 2022 and it will be his position on the day he dies.
He's right that the probability of his spinner being a 2 is 1/6.
Where we all see him to be wrong is where he says "And that is the same as". Because... Well because it really just is not.
Since that position is absurdly wrong, why would anyone want to create an alternate reality to prove that a 1/6 probability event is a 1/6 probability event? The question requiring testing was the one with the 1/11 probability?
No-one accepts that your position in any way represents the two dice puzzle as stated, let alone be represented by Wizard's offered wager.Quote:If you wanted a bet that represented my position use one die and see the ratio of when a 2 appears.
very drollQuote:Use a six sided die of course and not one of those 11-sided dies available on the Internet.
Thanks.
Why would anyone, for one second think the chance to make the point is 1/11. It's absolutely obviously 1/6 when you've seen one of the dice land. It's also nothing whatsoever to do with the two dice puzzle. It's like saying Next time you roll a six sided die, the probability that a coin lands Heads side up is 1/6.Quote:By the way... the next time you see a spinner on a craps table don't make the mistake of saying "there's a 1/11 chance we'll make the point."
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Quote: Wizard
In other news, I'm happy to report that LoquaciousMoFW has accepted Alan's side of the challenge.
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Big shout out to LoquatiousMoFW.
May I ask what you expect to achieve?
You do realise that when you lose your $200 or whatever, there will be no point reporting back to Alan. He will simply say that betting scenario did not match his scenario of setting one dice and so is an invalid test.
In other news, maybe of interest to Wizard....
I've looked out the post where LoquaciousMoFW very succinctly and elegantly proved that the probability is indeed 1/11 and went on to write and run his own sim.
https://wizardofvegas.com/forum/questions-and-answers/math/15508-two-dice-puzzle/2/#post448641
Which makes me wonder what his motivation is. Paying 200 for the pleasure of the game with Wizard?
I might tootle off and derive the probability of LoquaciousMoFW leaving the table $200 ahead with $5 flat bets.
That probability is a little less that 50% if the other possibility is that he loses $200. But it's not without hope.
Note to Wizard ( and i guess to LoquaciousMoFW ) If a progressive wagering pattern is followed with a good bankroll, LoquaciousMoFW could give himself a very good chance of leaving the table $200 in profit. He could almost guarantee it. Obviously at the cost of potentially losing a LOT.
Have fun guys. Good luck LoquaciousMoFW. Will there be a video?
Quote: OnceDearWhat's your position? That setting one dice as a two is the same as knowing one of the dice is a two? Well, it isn't.
It's not?
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Quote: AlanMendelsonQuote: OnceDearWhat's your position? That setting one dice as a two is the same as knowing one of the dice is a two? Well, it isn't.
It's not?
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No. It's not!
It's a simple enough concept to grasp.
If you set one of the dice as a two, then One of the dice is a two. That is 100% true. No questions asked.
If one of the dice is a two, then we cannot truthfully say that you set one of the dice as a two unless we had evidence. No evidence. No knowing.
So to say One of the dice is a two because alan set it that way would not be 100% certain to be true.. It might be true but we have no way of knowing.
So. setting one dice as a two is NOT the same as knowing one of the dice is a two.
It isn't the same.
Entertainment (And I suspect this will be less expensive than an equivalent time on strip bartop video poker.) And I like empirical evidence.Quote: OnceDearQuote: Wizard
In other news, I'm happy to report that LoquaciousMoFW has accepted Alan's side of the challenge.
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Big shout out to LoquatiousMoFW.
May I ask what you expect to achieve?
Quote:
You do realise that when you lose your $200 or whatever, there will be no point reporting back to Alan. He will simply say that betting scenario did not match his scenario of setting one dice and so is an invalid test.
I really don't expect to convince those who adhere to the 1/6 belief. But maybe it will offer clarification to others trying to understand.
And maybe we can finally close the 2 dice threads and stop the intermittent thread-rage [Cf. road-rage] episodes that emerge when the thread(s) is/(are) active.
Up to the Wizard. I have no objection to recording.Quote:
Have fun guys. Good luck LoquaciousMoFW. Will there be a video?
Quote:
Quote: OnceDear
If one of the dice is a two, then we cannot truthfully say that you set one of the dice as a two unless we had evidence. No evidence. No knowing.
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Are you sure this is your position?
Because if it is your position then what I said early on in this discussion was correct: it's a trick question.
And now I'll add this: the original question is an invalid question because it contained misinformation.
Remember-- in the original question we are told TRUTHFULLY that at least one die is a 2.
But now you're saying that might not be true?
Either at least one of the two dice is a two or isn't. Which is it?
And if you tell me the question is not truthful or valid or doesn't correctly illustrate the shaken dice in the cup then the discussion is over and this question is stricken.
Quote: OnceDearQuote: AlanMendelsonQuote: OnceDearWhat's your position? That setting one dice as a two is the same as knowing one of the dice is a two? Well, it isn't.
It's not?
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ONCE DEAR RESPONDED (BUT THE QUOTE FEATURE IS NOT WORKING):
No,. It's not!
It's a simple enough concept to grasp.
If you set one of the dice as a two, then One of the dice is a two. That is 100% true. No questions asked.
If one of the dice is a two, then we cannot truthfully say that you set one of the dice as a two unless we had evidence. No evidence. No knowing.
So to say One of the dice is a two because alan set it that way would not be 100% certain to be true.. It might be true but we have no way of knowing.
So. setting one dice as a two is NOT the same as knowing one of the dice is a two.
It isn't the same.
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----- END OF QUOTE ----
I just would like to know if at least one of the two dice in the cup is really a 2?
Quote: AlanMendelson
I just would like to know if at least one of the two dice in the cup is really a 2?
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I believe 7:1 has been offered, and it's a push if none of the dice show a 2 (or whatever point has been selected for the current round).
Quote: DieterQuote: AlanMendelson
I just would like to know if at least one of the two dice in the cup is really a 2?
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I believe 7:1 has been offered, and it's a push if none of the dice show a 2 (or whatever point has been selected for the current round).
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I'm asking about the original question in the original post.
Is there a 2 or not?
