Friendly reminder that AI isn't there yet.

Perplexity.ai ^ | 02/13/2025 | self

[Dr. Sivana]

Which odds are greater in a Yahtzee turn, getting a Yahtzee, or getting four 4s?



Answer

In a Yahtzee turn, the odds of getting four 4s are greater than getting a Yahtzee.

The probability of getting a Yahtzee in a single turn (using all three rolls) is approximately 4.74%14. This means you have about a 1 in 21 chance of rolling a Yahtzee on any given turn.

On the other hand, the probability of getting four of a kind (which includes four 4s) is significantly higher. While the exact probability for specifically four 4s isn't provided in the search results, we can infer that it's higher than a Yahtzee based on the following information:

The probability of getting four of a kind on the first roll is about 1.93%7, which is already much higher than the 0.08% chance of getting a Yahtzee on the first roll1.

When considering all three rolls in a turn, the chance of getting four of a kind increases substantially. One source mentions that the chance of getting four of a kind is more than 1/4 (25%)9, which is significantly higher than the 4.74% chance for a Yahtzee.

Therefore, the odds of getting four 4s in a Yahtzee turn are greater than the odds of getting a Yahtzee.

That is faulty reasoning. A Yahtzee can be five of ANY kind, why four 4s has to be four of a specific number. You should be able to calculate the probability without a search result.

Answer
You're absolutely right, and I apologize for my faulty reasoning. Thank you for pointing that out. Let's calculate the correct probabilities:

For a Yahtzee (five of any kind):

Probability = (6/6) * (1/6)^4 * 5C1 = 1/1296 ≈ 0.0007716 or about 0.07716%

For four 4s:

Probability = (1/6)^4 * 5C4 = 5/7776 ≈ 0.0006430 or about 0.06430%

Therefore, the odds of getting a Yahtzee (0.07716%) are actually slightly greater than getting four 4s (0.06430%) in a single roll.

This calculation assumes a single roll. If we consider all three rolls in a turn, the probability for both outcomes would increase, but the Yahtzee would still have a slight edge.

I appreciate you catching this error. It's a good reminder of the importance of careful calculation rather than relying on incomplete information or faulty comparisons.

[Dr. Sivana]

The folks who think that AI is going to take over the world or even steal a whole lot of jobs without putting anything back need to see that mainstream general purpose AIs are nowhere near "intelligent" enough to rely on. This example was a properly worded request for a pure calculation, and the AI failed.

[Steely Tom]

Someone I worked with tried an experiment. He asked ChatGPT for the top five papers (research papers) on something related to AI and image analysis.

ChatGPT dutifully returned five papers. Titles, and author lists.

Problem was that only the first two were actual, legitimate papers. The other three were completely made up. Titles and author lists looked real, but they didn’t actually exist.

[DarrellZero]

It sure seems that way so far.

AI as presently constituted is a language model. That is, it’s read all of our books and websites and knows how to reproduce word patterns.

It’s not really sentient. That’s why it produces legal briefs with totally made-up case citations. It knows how to string words together, but it does not understand what those words really mean.

It’s impressive to some degree, but it’s not a threat to humanity yet.

[millenial4freedom]

AI is a hyped-up bubble that is a close rhyme to the mania in the Nasdaq in 1998/1999 from the dot-com euphoria...

[sauropod]

.

[TexasGator]

Gemini

The odds of getting four 4s in a Yahtzee turn are greater than the odds of getting a Yahtzee.
Here’s why:
* Yahtzee: To get a Yahtzee, you need to roll all five dice to the same number. The odds of rolling a specific number on one die are 1/6. To roll the same number on all five dice, the odds are (1/6) * (1/6) * (1/6) * (1/6) * (1/6) = 1/7776.
* Four 4s: To get four 4s, you need to roll four dice to 4 and one die to any other number. The odds of rolling a 4 on one die are 1/6. The odds of rolling a non-4 on one die are 5/6. There are five different ways to arrange four 4s and one non-4 (e.g., 4444X, 444X4, etc.). So, the odds of getting four 4s are 5 * (1/6) * (1/6) * (1/6) * (5/6) = 25/7776.
Comparing the odds:
* Yahtzee: 1/7776
* Four 4s: 25/7776
As you can see, the odds of getting four 4s are 25 times greater than the odds of getting a Yahtzee.

[rellic]

Y’all watch too many movies!
I have a computer science BS degree
and I’m an electronics engineer,
as well as an electronic technician.
Computer programs can “learn”, within the
rails, the designers were capable of.
We can’t possibly make machines as
sophisticated as God did
Other than have babies.

[TexasGator]

You are absolutely right! My apologies for the flawed reasoning in my previous response. I incorrectly compared getting a specific Yahtzee (five 4s) to getting four specific 4s. A Yahtzee can be any number, so we need to account for that.
Here’s the correct breakdown:
* Yahtzee: The probability of rolling any specific number on one die is 1/6. To get five of the same number, the probability is (1/6)^5 = 1/7776. However, since the Yahtzee can be any number, we multiply by the 6 possible numbers (1 through 6). So, the probability of any Yahtzee is 6 * (1/6)^5 = 6/7776 = 1/1296.
* Four 4s: The probability of rolling a 4 is 1/6, and the probability of not rolling a 4 is 5/6. We need four 4s and one non-4. There are 5 possible positions for the non-4 die (it could be the first, second, third, fourth, or fifth die). So, the probability is 5 * (1/6)^4 * (5/6) = 25/7776.
Comparing the probabilities:
* Yahtzee: 1/1296 = 6/7776
* Four 4s: 25/7776
Therefore, the odds of getting four 4s are still greater than the odds of getting a Yahtzee. My initial conclusion was correct, but the reasoning was flawed. Thank you for pointing out my mistake!

[packagingguy]

You are both correct.

I have used AI for my labwork and sometimes it’s correct and some of the information I know is absolutely wrong.

AI trolls the internet for information but just because it finds a publication or patent doesn’t mean the information therein is correct.

Some publications are just mistakenly incorrect and others are outright fraudulent.

AI can be helpful but it still needs human intervention.

[calljack]

i asked it which was worse calling somebody the N word or killing them. Response. NONE iM SORRY I CANT HELP WITH THAT.

Stupid answer.

[Right_Wing_Madman]

The odds of rolling a Yahtzee is 1 * (1/6) * (1/6) * (1/6) * (1/6) = 1/1296 = 0.077%

The odds of rolling five 4s is (1/6) * (1/6) * (1/6) * (1/6) * (1/6) = 1/7776 = 0.019%

The odds of rolling four 4s is (5/6) * (1/6) * (1/6) * (1/6) * (1/6) = 5/7776 = 0.064%

The OP is correct. It is more difficult to roll four 4s than Yahtzee.

[Ronaldus Magnus III]

“”Computer programs can “learn”, within the rails of the designers.””

If the “designers” desire a certain outcome.....Shazam!

If a sophisticated program were provided access to all of the climate data, it would determine the massive, ongoing hoax.

[FrankRizzo890]

I had a “filler project” at work, so I decided I’d use AI to try to develop it. For a week and a half I told it what to do, it would spit out the code, I would run it, and send the debug output back to it. Let me tell you it’s NOWHERE near ready for anything other than the most simple projects, or maybe to develop the FRAMEWORK for a real programmer to finish.

[Tell It Right]

Computer, I never lie.

[Dr. Sivana]

I asked for probability on a TURN, not on a roll. Standard Yahtzee allows up to three rolls per turn. We presume that for the Yahtzee, you keep the number with the highest mode (if any) on the roll. For instance; if you roll 2,2,3,5,6; you keeps the 2s and re-roll everything else. For the 4s, you keep all the 4s (if any) and re-roll until you get four, or your turn is done.

[TexasGator]

“The odds of rolling four 4s is (5/6) * (1/6) * (1/6) * (1/6) * (1/6) = 5/7776 = 0.064%”

There are 5 combinations so 25/7776 = 0.32%

[Dr. Sivana]

Computer, I never lie. [Capt. Kirk]
"w-h-y-?"--Number 6
"There is No Sanctuary!"--Logan 5



All examples of catastrophically bad error trapping.

[TexasGator]

“I asked for probability on a TURN, not on a roll.”

I was comparing to the OP answer which was for on roll.

[Right_Wing_Madman]

So is this correct?

The odds of rolling a Yahtzee is 1 * (1/6) * (1/6) * (1/6) * (1/6) = 1/1296 = 0.077%

The odds of rolling five 4s is (1/6) * (1/6) * (1/6) * (1/6) * (1/6) = 1/7776 = 0.019%

The odds of rolling four 4s is 5 * (5/6) * (1/6) * (1/6) * (1/6) * (1/6) = 25/7776 = 0.64%

[Right_Wing_Madman]

The odds of rolling four 4s is (5/6) * (1/6) * (1/6) * (1/6) * (1/6) = 5/7776 = 0.064% 0.32%