Two Dice Puzzle: Part Deux
Quote: AlanMendelson
But that is a side issue, because when rolling dice anything can happen. It's all random.
Umm....sure...
Quote: AlanI still think that's 1/6 and not 1/11. Unless you have an 11-sided die, I am going to stick with 1/6.
And here lies the logic why casinos are able to make so much money off of ploppies. If it wasn't for them, AP's wouldn't be able to make money.
Quote: RSAnd here lies the logic why casinos are able to make so much money off of ploppies. If it wasn't for them, AP's wouldn't be able to make money.
Exactly.
Every single hand of video poker I played today had and expect payback of OVER 100%. But every game I played had a negative EV payscale. I wonder if the 1/6ers can explain that one? And no, comps, cashback nor anything else factored into it.
Progressives? I'd say those are part of the payscale though...Quote: IbeatyouracesExactly.
Every single hand of video poker I played today had and expect payback of OVER 100%. But every game I played had a negative EV payscale. I wonder if the 1/6ers can explain that one? And no, comps, cashback nor anything else factored into it.
Quote: AlanMendelsonWhen you read THAT QUESTION what do you consider? Do you think of two dice combinations or do you think of one die? I think of one die.
I know you do. You are wrong to do so, and the reason you are wrong has been explained many, many times. I'm not going to do it again.
A long time ago, before the Star Trek Experience was at the Las Vegas Hilton, some of their craps tables had what they called "Hilton Bets." The bet was simple: put your chip on a number from 1 to 6. If exactly one die on the next roll shows that number, you win 2-1. If both dice on the next roll show that number, you win 4-1. If neither dice show the chosen number, the bet loses.
If you can calculate the house edge for that bet, you should be able to understand why your interpretation of the two 2s question is wrong. If you can't, I don't think any further explanation will suffice.
Quote: MathExtremistProgressives? I'd say those are part of the payscale though...
No. But you're not a 1/6er either :-)
Some of them are even in the 96-low 98% range too.
Quote: IbeatyouracesNo. But you're not a 1/6er either :-)
Some of them are even in the 96-low 98% range too.
Nevermind, I just saw the other thread. Technically the instantaneous paytable is what you're playing against on any given hand, so if there's a big progressive or a 4x multiplier, that's part of the game. It's more accurate to say that the average paytable is 98% (because it's not the base paytable, the base paytable is worse than the average to balance out the times when it ticks positive). Just like playing an accumulator slot like Vacation USA with 9 out of 10 of the bonus triggers isn't really a 93% game.
EGM vulturing is the electronic equivalent of card counting - it takes into account the fact that, unlike most slot games, the RTP on certain games fluctuates with game state and sometimes turns positive. Just like blackjack. And craps when one of the dice shows a 2. :)
Quote: IbeatyouracesYou look at both, not one.
But you know that at least one is a 2. Doesn't that mean you only have to consider the other die which has only six faces?
Of course we have been over this same point dozens of times.
Quote: AlanMendelsonBut you know that at least one is a 2. Doesn't that mean you only have to consider the other die which has only six faces?
Of course we have been over this same point dozens of times.
How do you only consider one die with 6 faces when you don't even know which die is the for-sure-deuce die? You have to consider both dice.
Quote: RSHow do you only consider one die with 6 faces when you don't even know which die is the for-sure-deuce die? You have to consider both dice.
RS if you really believe that it makes a difference which of two dice shows a two, when there are only two dice in the problem, then there is nothing left for us to discuss. As I wrote many times before, if one die shows a two then the chance that a 2 shows up on the other die is 1/6. If you want a more specific answer: If die A shows a 2, the chance of die B showing a 2 is 1/6. And if die B shows a 2, the chance of die A showing a 2 is 1/6. And if both die A and die B are showing a 2, then when you look at either die A or die B the chance that either of them landed on 2 was 1/6.
Quote: AlanMendelsonBy the way, if you insist it matters which die the 2 appears on, how can you possibly conduct the bet I have with the Wizard? I think you guys will have to make up your mind about whether or not it matters if the 2 appears on a certain die and which die it is.
It doesn't matter. If 2-2 is rolled, you win. If 2-1, 2-3, 2-4, 2-5, or 2-6 is rolled, you lose. Any other outcome is a push. Just remember though. You have only one way to win and Mike has 10.
Yes. Question 1: What is the chance that die A, alone, does show a 2?Quote: AlanMendelsonIf die A shows a 2, the chance of die B showing a 2 is 1/6.
Yes. Question 2: What is the chance that die B, alone, does show a 2? Is it the same as the answer to question 1?Quote:And if die B shows a 2, the chance of die A showing a 2 is 1/6.
And now Question 3: what is the chance that either die A or die B (or both) show a 2? Is it the same as the above answers?
Don't make any pseudo-logical arguments about looking at one or two dice. There are numeric answers for each of those three questions. Write them down.
1/6Quote: MathExtremistQuestion 1: What is the chance that die A, alone, does show a 2? .
1/6Quote: MathExtremistQuestion 2: What is the chance that die B, alone, does show a 2?.
Yes the answer to question 2 is the same as the answer to question 1.Quote: MathExtremistIs it the same as the answer to question 1?
This is a different situation than question 1 or question 2 because it is not a one-die question. You are not asking specifically about either die. Individually, each die has a 1/6 chance to show a 2.Quote: MathExtremistAnd now Question 3: what is the chance that either die A or die B (or both) show a 2? Is it the same as the above answers?.
Since there are 36 combinations of two six-sided dice we know that the chance of 2-2 is 1/36. And there are 11 of 36 combinations of two dice that show at least one 2.
Quote: MathExtremistDon't make any pseudo-logical arguments about looking at one or two dice. There are numeric answers for each of those three questions. Write them down.
I am sorry, but there are different answers depending on the questions asked. Whether you want to label them as pseudo logical or not is up to you. But the answers depend on the wording of the questions.
Which brings me back to the original question. It is worded so that the answer is 1/6.
And let me also comment about the "bet": I am willing to gamble on this since the Wizard will award me 8 "points" for each time a 2 shows after there is already a 2 showing on one of the two dice. I consider that a good bet. He'll "pay" 8 "points" for what I think is a 1/6 occurance. Are there in fact 11 combinations of dice where at least one 2 shows? Yes. And that's the gamble.
I just am amazed that in a two-dice problem some of you think it matters which of two dice the 2-face shows up on.
Quote: IbeatyouracesIt doesn't matter. If 2-2 is rolled, you win. If 2-1, 2-3, 2-4, 2-5, or 2-6 is rolled, you lose. Any other outcome is a push. Just remember though. You have only one way to win and Mike has 10.
For the bet it doesn't matter, and that's the gamble I am taking. I am just amazed that some of you are saying it matters which of two dice a 2 shows on.
Quote: AlanMendelsonFor the bet it doesn't matter, and that's the gamble I am taking. I am just amazed that some of you are saying it matters which of two dice a 2 shows on.
Regardless, you'll both get a nice meal out of it.
Quote: IbeatyouracesRegardless, you'll both get a nice meal out of it.
It will be my pleasure to buy the Wizard lunch and to enjoy the time.
Quote: MaxPenDo you spend alot of time in the Keno lounge?
Never played it in my life.
Quote: AlanMendelsonIt will be my pleasure to buy the Wizard lunch and to enjoy the time.
You never know. You might beat the odds!
It's also very possible that if he were to explain it to you in person you'll understand it. There are numerous things that don't make sense when you tell them to me, but if you show me, I'll "get it."
Quote: IbeatyouracesYou never know. You might beat the odds!
It's also very possible that if he were to explain it to you in person you'll understand it. There are numerous things that don't make sense when you tell them to me, but if you show me, I'll "get it."
I've also tried to show you, through my video, that even when one die shows a 2 there is still a 1/6 chance that the "other die" will show a 2. No one here seems to get that, yet others do agree with my point.
Yes, there are 11 different combinations with at least 1 die showing a 2. But whenever one die is showing a 2, there is always a 1/6 chance that the other die will show a 2.
I think that also wraps up the Q&A above with Math Extremist.
Quote: AlanMendelsonI've also tried to show you, through my video, that even when one die shows a 2 there is still a 1/6 chance that the "other die" will show a 2. No one here seems to get that, yet others do agree with my point.
Yes, there are 11 different combinations with at least 1 die showing a 2. But whenever one die is showing a 2, there is always a 1/6 chance that the other die will show a 2.
I think that also wraps up the Q&A above with Math Extremist.
How would you change the wording of the original question to get to the 1/11 answer then?
Question #1: How many different combinations of 2 dice will show 2-2? (Answer 1 out of 36 possible combinations or 1/36)
Question #2: How many combinations of two dice include at least one 2? (Answer 11 out of 36 possible combinations or 11/36)
Question #3: Ouf of the 11 possible combinations of two dice showing a 2, how many combinations will show 2-2? (Answer 1 out of the 11, or 1/11)
Question #4: When you have two dice rolled and one die is showing a 2, what are the chances that the other die is also showing a 2? (Answer: there are six faces on the other die with one of the faces showing a 2, so it's 1/6)
So, do you agree or not?
This is all you need to know. The ratio of the first event (1/36) to the second event (11/36) is 1/11. That's the answer.Quote: AlanMendelsonSince there are 36 combinations of two six-sided dice we know that the chance of 2-2 is 1/36. And there are 11 of 36 combinations of two dice that show at least one 2.
Now all you need to do is accept that this is the question that was being asked and you'll have it.
Quote: AlanMendelsonQuestion #3: Ouf of the 11 possible combinations of two dice showing at least a 2, how many combinations will show 2-2?
Question #4: When you have two dice rolled and at least one die is showing a 2, what are the chances that the other die is also showing a 2?
After adding the phrase "at least" where appropriate, you don't think those questions are asking the same thing? Because they are, and that's why the answer is also the same.
3: 12 to 1.
2: 2 to 1.
1: 1 to 1.
0: Loss.
I'd be interested to see Alan's analysis of this bet.
Quote: WizardIn Sic Bo there is a bet on the number of twos in the roll of three dice. It pays according to the number of twos, as follows:
3: 12 to 1.
2: 2 to 1.
1: 1 to 1.
0: Loss.
I'd be interested to see Alan's analysis of this bet.
You're asking the wrong guy. I have no idea what that game is.
Quote: MathExtremistThis is all you need to know. The ratio of the first event (1/36) to the second event (11/36) is 1/11. That's the answer.
Now all you need to do is accept that this is the question that was being asked and you'll have it.
I am sorry, but I cannot accept this answer when considering the six faces on one die.
Quote: AlanMendelsonQuestion #4: When you have two dice rolled and one die is showing a 2, what are the chances that the other die is also showing a 2? (Answer: there are six faces on the other die with one of the faces showing a 2, so it's 1/6)
Have you tried this yet?
Write down how often this happensQuote:When you have two dice rolled and one die is showing a 2
Write down how often the other die is a two, or in other words, write down when both dice are a two.Quote:what are the chances that the other die is also showing a 2?
this will measure the probability that one die is a two when the other die is a two.
no logic, no thinking, just data collection.
After you have done this for a while, maybe 10 or 20 minutes depending on how fast you roll and record the dice, check the ratio of one number to the other one.
And again, it's not the math but the WORDING of the question that has him arguing.
Quote: IbeatyouracesThat's too much work for him..
Yeah yeah, far to much work for him.
Besides, all it would prove would be the longest and most consistent run of bad luck in the history of dice.
Quote: WizardNice! I think this is the first WoV "video response." Let me try to draw some more attention to it below.
Before anybody takes this post out of context, the probability IS 1 in 11.
The next time I see a larcenous hand, coming in to pilfer a die out of the scenario, I swear I'm going to burn the livin' s*** out of it with my red-hot cigar.
You have three 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 all three dice are showing a 2?
If I understand Alan's reasoning, since one of the dice is already known, he would look at the other two dice and ask "what are the chances of two 2s on two dice" and arrive at 1/36.
Alan, is that right?
Quote: MathExtremistI wonder if Alan's reasoning would extend to 3-dice games. What if the game were this:
You have three 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 all three dice are showing a 2?
If I understand Alan's reasoning, since one of the dice is already known, he would look at the other two dice and ask "what are the chances of two 2s on two dice" and arrive at 1/36.
Alan, is that right?
What? You mean as opposed to the absurd answer 1/115?
Don't be daft. You've eliminated 1 die, leaving two dice.
1 dice has 6 faces and the other dice has 6 faces
Look at those two dice
They have 12 faces all together, Not 36 and not 115
So, obviously it's 1/12.
$:o)
Quote: RSYou're both wrong. Each die only has 6 sides. Let's say there's a red, green, and blue dice. If the red one is known to be a deuce, we examine the green. How many sides and how many sides with a 2? It's 1/6. What about the blue die? Same thing, 1/6. So for the three dice puzzle, based on the wording, it's 1/6. That's all there is to it. No thinking, no logic. It's so simple! Always 1/6!
Oh Yeah.... It's all in the wording. I must pay more attention. I feel a right Mendelson now :o)
Quote: indignant99Quote: WizardNice! I think this is the first WoV "video response." Let me try to draw some more attention to it below.
Before anybody takes this post out of context, the probability IS 1 in 11.
The next time I see a larcenous hand, coming in to pilfer a die out of the scenario, I swear I'm going to burn the livin' s*** out of it with my red-hot cigar.
Just watched this video. It's impressive, as it answers a different question to that posed... something Alan keeps arguing against!
Quote: OnceDearWhat? You mean as opposed to the absurd answer 1/115?
Don't be daft. You've eliminated 1 die, leaving two dice.
1 dice has 6 faces and the other dice has 6 faces
Look at those two dice
They have 12 faces all together, Not 36 and not 115
So, obviously it's 1/12.
$:o)
Are you willing to bet on your 3 dice problem? You can be the casino paying 100 to 1. Any roll with no twos pushes. Any roll with 1 or 2 twos I pay you $1. Any roll with 3 twos you pay me $100.
Quote: mipletAre you willing to bet on your 3 dice problem? You can be the casino paying 100 to 1. Any roll with no twos pushes. Any roll with 1 or 2 twos I pay you $1. Any roll with 3 twos you pay me $100.
It's not MY 3 dice problem!
And no. 100: 1 doesn't give me enough house edge to pay for my time and energy.
Do any of these under-the-cup rolls qualify for "At least one of the dice is a 2"?
Do any of these results qualify for "At least one of the dice is a 2"?
Which ones do?
Which ones don't?
Which ones win Alan a spectacular 9-to-1 payoff of his wager?
Which ones lose Alan his paltry one-unit wager?
A shooter at the craps table just threw 99 hard 4s in a row. What are the odds that the next roll of the dice will be a hard 4?
If 99 hard 4s in a row make the problem too difficult, let's try version B:
A shooter at the craps table just threw 3 hard 4s in a row. What are the odds that the next roll of the dice will be a hard 4?
Quote: AlanMendelsonA shooter at the craps table just threw 3 hard 4s in a row. What are the odds that the next roll of the dice will be a hard 4?
1/36
But if you ask the following:
A shooter at the craps table threw at least 3 hard 4s in four rolls. What is the probability that he threw 4 hard 4s?
Then the answer is
You are having real difficulty with the phrase “at least”...which has a huge impact.
Quote: AlanMendelson...A shooter at the craps table just threw 99 hard 4s in a row. What are the odds that the next roll of the dice will be a hard 4?
100%. All 12 faces are 2's! :-)
Quote: PeeMcGee1/36
But if you ask the following:
A shooter at the craps table threw at least 3 hard 4s in four rolls. What is the probability that he threw 4 hard 4s?
Then the answer is1/141
You are having real difficulty with the phrase “at least”...which has a huge impact.
You got it. The difference is in how the question is asked.
Quote: AlanMendelsonYou got it. The difference is in how the question is asked.
Then why are you ignoring that difference?
Question A: The shooter throws one die. It shows 2. The shooter throws a second die. What are the chances both dice show 2?
Question B: The shooter throws two dice. At least one shows 2. What are the chances both dice show 2?
The actual problem is Question B. You're answering Question A while also (incorrectly) suggesting that the two questions are equivalent.
Quote:
A question about odds and two dice:
You have two 6-sided dice in a cup (standard dice). You shake the dice, and slam the cup down onto the table, hiding the result. An independent judge peeks under the cup, and announces truthfully, "At least one of the dice is a 2."
What is the probability that both dice are showing a 2?
Just in case. The answer is still 1 in 11 given this question. Dice are out, thrown, and we get information about a group of two dice, not information about a single die.
Relax. Grab your favorite snack.
(popcorn, chips, fries, pretzels, sliders, burgers, ribs, tacos, snickers, trail mix, pizza, asian take-out, ethnic-of-your-own-choice, you-know-better-than-me. )
Relax. Grab your favorite beverage.
(None, Water, Beer, Spirits, Wine - white, blush/rose, red - you-know-better-than-me. )
Relax. Grab your favorite "squeeze."
(fave-boy, fave-girl, fave-pet, fave-toy, fave-relative, fave- you-know-better-than-me. )
This is a tale of nuances, gently-shaded meanings, that might be in stark contrast to assessments that conclude certainty of thinking among evangelistic theists.
This is a recent history of assertions/rebuttals by the world-renowned ALAN MENDELSON, regarding deuces on a pair of thrown-dice.
Quote: DweenYou 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?
Quote: AlanMendelsonI don't think it's a matter of looking at all
of the combinations that have a deuce showing...
We see one die come to rest on, for example,
the 6 -- while the second die spins.
Quote: AlanMendelsonIn the original post we are told that it is known
that at least one die is a 2. That limits the possibility to 1/6.
It's a matter of English.
Quote: AlanMendelsonNow if you want to think that way, that's fine.
But if you were working for me I'd fire you. In fact, if I knew
you even thought that way and ignored the basic information
in the question, I wouldn't even hire you.
Quote: AlanMendelsonIf I roll two dice and one shows a "2" and
the second die is a spinner, what are the chances that the
"spinner" will settle on another "2"? I think 1/6.
What do you think? Are there 11 sides on the spinner?
Quote: AlanMendelsonThe question is the second die.
Quote: AlanMendelsonwhat simulations?
Quote: AlanMendelson...it doesn't matter how the question is worded...
Quote: AlanMendelsonYES. We can agree that the peeker saw both dice.
But that doesn't change anything.
Quote: AlanMendelsonWhy are you doing this with two dice?
...therefore the question pertains to the second die.
LOOK AT THE NEXT TWO COMMENTS.
Quote: AlanMendelsonThis is not a question about two unknown dice.
This is a question of figuring the odds with at least one die known.
There is a problem here with reading comprehension.
Quote: AlanMendelsonNow, you tell me why looking at just ONE DIE
would not be the right way to answer THIS QUESTION ??
Quote: AlanMendelsonIt doesn't matter which die is the two.
Quote: AlanMendelson...I have two dice in front of me and
I have set one showing a 2, and I am looking at the other die.
That "other die" has 6 faces,...
| ______________________________________________________________________ |
|---|
Quote: AlanMendelsonThe ORIGINAL QUESTION deals with TWO DICE under a cup
with at least one of them showing a 2. YOU MUST address the problem
using a pair of dice with at least ONE DIE showing a 2.
If you don't do this you are altering the question.
| _____________________________________________________________________ |
|---|
Quote: AlanMendelsonThe pushes don't matter. There is still only one way
to win and 10 ways to lose. And the win is paid 8-to-1.
You can debate this with the not-so-smart members of my forum.
Quote: AlanMendelsonI like the idea of being paid 9 for 1
for what I think is a 1 out of 6 chance...
Quote: AlanMendelson2(dice) - 1(die) = 1(die)
Quote: AlanMendelsonBut you guys who say the answer is 1/11 are not answering
the question that is written. You are adding your own interpretation
that is not there in plain, simple English. Sorry.
You fail in reading comprehension.
Quote: AlanMendelson1/11 refers to the combinations of dice with at least one 2
showing. That's a different question and answer. Once one die is known
to be a 2, the odds of the second die are always 1/6.
Quote: AlanMendelsonTake two dice and roll them until at least one of the two
dice shows a 2. Take that die that shows a 2 and put it in your pocket and
then look at the remaining die. If both dice showed a two, take one of the
two dice showing a two and put it in your pocket.
Quote: AlanMendelsonThe question wants you to remove one die and look at the
second of the two dice. 1/11 is indeed the combination of 2-2 when you have
the 11 dice combinations showing at least a single 2.
But 1/11 does not answer the question.
Quote: AlanMendelsonBut that's not the original question either. It's not
a question of how often the other die is a two, or how often it is not a two.
The question is what is the probability. Thank you for recognizing it is
a ONE DIE problem. And that one die has six sides.
Quote: AlanMendelsonIf die A shows the 2 then it's a question of what shows
on the 6 sides of die B. If die B shows the 2 then it's a question of what
shows on the six sides of die A.
Quote: AlanMendelsonAll of you who tell me that 1/6 is not the answer are
changing the question. I'm sorry to say it, but you are.
What The F*** do these next three comments mean, taken together?
Quote: AlanMendelsonIt's not about rolling two dice.
Quote: AlanMendelsonIt's a two dice question.
Quote: AlanMendelsonIf you simply isolated one die,
Quote: AlanMendelson...when we are told at least one of the dice is a two
we only have to be concerned with what the other die is showing...
Again, 1/11 is a valid answer if you are looking for the various combinations
of two dice with at least one die showing a 2. But the question is asking you
to isolate the problem to one die and only one die.
Quote: AlanMendelsonI used the example of a shooter throwing two dice with one
coming to rest immediately showing a two. The second die is a spinner and spins
like a top. While spinning you say to yourself "there is a 1/6 chance of the
spinner landing on a 5 for a 7-out," or "there is a 1/6 chance of the spinner
landing on a 1 for a 3" or "there is a 1/6 chance of the spinner landing
on a 2 for a hard 4." ...I said that the 1/11 answer would be correct if the
question were asked differently.
Quote: AlanMendelsonI have been arguing this information all along --
that once the judge/partner truthfully says at least one die is a two
the problem shifts to the remaining die (there are only two) and that is
the 1/6 answer... On the other hand, the 1/11 "faction" claims we need to know
which of the dice is showing a two. How that can matter when we start with only
two dice is what I can't understand.
Quote: AlanMendelsonIf the judge/partner sees one die as a deuce --
and it doesn't matter which die -- the decision still rests with
the other die which is 1/6.
THIS IS NEITHER GERMANE, NOR ANALOGOUS. JEEZUS.
Quote: AlanMendelsonA shooter throws two dice. One lands behind a stack of chips
and you can't see the result. One die is a spinner and eventually lands on a 2.
What are the chances that the die behind the stack of chips is also a 2?
It's 1/6.
Quote: AlanMendelsonThis is ridiculous.
More changing of the question. In fact, each of you seems to be changing
the question your own way to fit your own argument.
I am not changing the question at all, or the conditions of the question.
Quote: AlanMendelsonYou are looking at two-dice combinations. God bless you.
I am looking at one die and one die only... Unless you have an 11-sided die,
I am going to stick with 1/6.
Quote: AlanMendelsonRoll two dice. If one shows a 2, what are the chances of
a two on the other die? Is it still 1/11 ?? Do you understand that 1/11
is an answer to a different question? I guess not.
Quote: AlanMendelsonI am going to ask you a different question: Why do you
interpret the original question to consider more than one die in your answer?
It's the same question I have for the Wizard and for everyone else who says
the answer is 1/11.
Quote: AlanMendelsonME your lessons are all very informative but answer this
question please: why do you insist on looking at two dice instead of one die?
Quote: AlanMendelsonYou can interpret the question anyway you like,
but the way it was written tells me to look at one die.
Quote: AlanMendelsonAs long as one die shows a 2 the question now applies
to the other die...
Quote: AlanMendelsonDo you think of two dice combinations or do you think
of one die? I think of one die.
I really want to know what makes you consider two-dice combinations?
Quote: AlanMendelsonRS if you really believe that it makes a difference
which of two dice shows a two,...
Quote: AlanMendelsonI just am amazed that in a two-dice problem some of
you think it matters which of two dice the 2-face shows up on.
Quote: AlanMendelsonI am just amazed that some of you are saying it matters
which of two dice a 2 shows on.
Quote: AlanMendelsonYes, there are 11 different combinations with at least 1 die
showing a 2. But whenever one die is showing a 2, there is always a
1/6 chance that the other die will show a 2.
Quote: AlanMendelsonQuestion #1: How many different combinations of 2 dice
will show 2-2? (Answer 1 out of 36 possible combinations or 1/36)
Question #2: How many combinations of two dice include at least one 2?
(Answer 11 out of 36 possible combinations or 11/36)
Question #3: Ouf of the 11 possible combinations of two dice showing a 2,
how many combinations will show 2-2? (Answer 1 out of the 11, or 1/11)
Question #4: When you have two dice rolled and one die is showing a 2,
what are the chances that the other die is also showing a 2? (Answer: there are
six faces on the other die with one of the faces showing a 2, so it's 1/6)
So, do you agree or not?
IRRELEVANT. MORE TANGENTIAL B*LLSH*T. APPLICABLE TO NOTHING.
Quote: AlanMendelsonA shooter at the craps table just threw 99 hard 4s in a row.
A shooter at the craps table just threw 3 hard 4s in a row.
Quote: AlanMendelsonYou got it. The difference is in how the question is asked.
Quote: indignant99Okay, everyone.
Relax. Grab your favorite snack.
(popcorn, chips, fries, pretzels, sliders, burgers, ribs, tacos, snickers, trail mix, pizza, asian take-out, ethnic-of-your-own-choice, you-know-better-than-me. )
Relax. Grab your favorite beverage.
(None, Water, Beer, Spirits, Wine - white, blush/rose, red - you-know-better-than-me. )
Relax. Grab your favorite "squeeze."
(fave-boy, fave-girl, fave-pet, fave-toy, fave-relative, fave- you-know-better-than-me. )
This is a tale of nuances, gently-shaded meanings, that might be in stark contrast to assessments that conclude certainty of thinking among evangelistic theists.
This is a recent history of assertions/rebuttals by the world-renowned ALAN MENDELSON, regarding deuces on a pair of thrown-dice
Well done. Alan's just making stuff up as he goes along.
Quote: indignant99
This is a tale of nuances, gently-shaded meanings, that might be in stark contrast to assessments that conclude certainty of thinking among evangelistic theists.
This is a recent history of assertions/rebuttals by the world-renowned ALAN MENDELSON, regarding deuces on a pair of thrown-dice.
One day historians and psychiatrists will look back at the etymology of certain figures of speech and try to define them with examples:-
"Talking complete and utter M********s."
"What a load of M********s"
"A classic case of M******** thinking"
"Doing a M********"
"The M******** problem"
A place in history has been carved out.
Meanwhile, somewhere in a padded cell, with all the padded walls covered with two columns of numbers, a fellow sits tossing a pair of dice with a plastic cup waiting, forever waiting, for the rolling average of 1/11 to revert to its correct long term value of 1/6.
Meanwhile in a crowded padded cell just down the hall, a crowd of fools jabber and scream "1/11 IT'S AT LEAST ONE F***ING DIE"
