1, 296 and Yahtzee - Numberphile
video description
Also I find it interesting that most of the dices(whats the prular? die? lol dont know i am not a native speaker: P ) just fall and were 3 and only the last one actually spinned and result out of luck (or propability however you like to state it) and lead also to be a 3
what I am trying to say is that MAY BE (I bold that because I dont have the slightest idea besides my intuition about that: P ) there are other factors when we apply propability on the real world. because now we have to deal with gravity, size, friction etc.
so maybe there was an other probability scheme encapsulated in the bigger propability (of needing 1296 rows to get a yahtzee at 63% success rate) when cause of physics all other dices feel facing up with 3 (like a constant state for this particular row analysis) and you had to do calculate the propability of the 5th dice that was still spinning turning out to be the same as the 4 already concluded dices
and that having in mind how much energy you gave it its physical properties and if it interacts with anything else (like while spinning and touching slightly an other dice and for how long and how did the state of the touched dice change etc)
in order to know the -true- probability.
So maybe its far more complex than basic rules of probabilty dictate it to be.
or maybe all the above are mambo jumbo dont know hahahahahahahaha
Date: 2022-04-08
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Comments and reviews: 9
dbzelda123
i had a little extra fun with this and decided to try all the amount of dice up to five, and also how long will 5 dice take me with yahtzee rules. the number in the parentheses is the dice number i succeeded. here are my results:
1 die: 1 throw (4)
2 dice: 2 throws (3)
3 dice: 22 throws (5)
4 dice: 287 throws (3)
5 dice yahtzee: 31 turns = 93 throws (4)
5 dice 2nd yahtzee: 9 turns = 27 throws (3)
5 dice single roll: 1697 throws (4)
i did the yahtzee roll twice because i thought that the first one was maybe too lucky. turns out that the second one was even luckier. there is quite a leap from 4 dice to 5 that's for sure.
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i had a little extra fun with this and decided to try all the amount of dice up to five, and also how long will 5 dice take me with yahtzee rules. the number in the parentheses is the dice number i succeeded. here are my results:
1 die: 1 throw (4)
2 dice: 2 throws (3)
3 dice: 22 throws (5)
4 dice: 287 throws (3)
5 dice yahtzee: 31 turns = 93 throws (4)
5 dice 2nd yahtzee: 9 turns = 27 throws (3)
5 dice single roll: 1697 throws (4)
i did the yahtzee roll twice because i thought that the first one was maybe too lucky. turns out that the second one was even luckier. there is quite a leap from 4 dice to 5 that's for sure.
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Anonymous71475
The probability for you to success after a certain amount of rolls is this:
1 - (1 - -the chance-)--the tries-)
Which. very weirdly. if -the tries- is equal to -1/the chance-, the bigger those numbers, the closer it is to a certain number which I don't know, around 63%.
Trying 2 times on something that has 1/2 chance has 75% success rate.
Trying 6 times on something that has 1/6 chance has around 66% success rate.
Trying 10000 times on something that has 1/10000 chance has around 63. 21% success rate.
To Numberphile, to what value is it approaching?
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The probability for you to success after a certain amount of rolls is this:
1 - (1 - -the chance-)--the tries-)
Which. very weirdly. if -the tries- is equal to -1/the chance-, the bigger those numbers, the closer it is to a certain number which I don't know, around 63%.
Trying 2 times on something that has 1/2 chance has 75% success rate.
Trying 6 times on something that has 1/6 chance has around 66% success rate.
Trying 10000 times on something that has 1/10000 chance has around 63. 21% success rate.
To Numberphile, to what value is it approaching?
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Eat
So I made a silly python script to roll 10 000 Yahtzees (NO, not 10, 000 rolls 10, 000 yahtzees. I made it so it rolled nonstop until a yahtzee, then I counted the number of tries. Rinse and repeat for 10k times.
Well, the results were that the average number of tries to get a yahtzee was 1294. 5786, as expected. A two streak happened FIVE times, no 3 yathzee streak though: ( and finally the slowest yahtzee happened after 15, 719 tries.
Now in the real world I'm to lazy to even try to roll 2 dice.
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So I made a silly python script to roll 10 000 Yahtzees (NO, not 10, 000 rolls 10, 000 yahtzees. I made it so it rolled nonstop until a yahtzee, then I counted the number of tries. Rinse and repeat for 10k times.
Well, the results were that the average number of tries to get a yahtzee was 1294. 5786, as expected. A two streak happened FIVE times, no 3 yathzee streak though: ( and finally the slowest yahtzee happened after 15, 719 tries.
Now in the real world I'm to lazy to even try to roll 2 dice.
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Quantum
I always consider probabilities to be 50/50 because what it all comes down to is as Yoda says -Do or do not, there is no try- meaning just that. you succeed or you fail, it doesn't matter how many times you do something because you either get it right and succeed or you fail and must start again until you do! Even with calculated odds there still is no guarantee that you will ever succeed within the number of chances. it will happen or it won't! The probability will always be 50%
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I always consider probabilities to be 50/50 because what it all comes down to is as Yoda says -Do or do not, there is no try- meaning just that. you succeed or you fail, it doesn't matter how many times you do something because you either get it right and succeed or you fail and must start again until you do! Even with calculated odds there still is no guarantee that you will ever succeed within the number of chances. it will happen or it won't! The probability will always be 50%
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Mephistahpheles
-Dice have no memory- yet he also says, -I know I'm getting closer-. No, you're NEVER closer. Once rolled, the odds of getting what you want in the -first 1296- rolls DECREASES, since some of them (the ones you've done) are no longer a possible success. They are now DETERMINED to be failures.
Your odds of getting it in the NEXT (not including what you've done) 1296 is always the same.
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-Dice have no memory- yet he also says, -I know I'm getting closer-. No, you're NEVER closer. Once rolled, the odds of getting what you want in the -first 1296- rolls DECREASES, since some of them (the ones you've done) are no longer a possible success. They are now DETERMINED to be failures.
Your odds of getting it in the NEXT (not including what you've done) 1296 is always the same.
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Robert
The 1, 269 odds against, on the first roll, are on every single roll of 5 dice out of the cup. Those odds can still be correct after 126, 900, 000, 000, 000, 000-10 rolls. There really is nothing in the universe that guarantees you will ever roll a yahtzee: 5 dice, straight out from the cup. Lastly, there is nothing that prevents you from rolling 50 of them in a row; literally nothing.
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The 1, 269 odds against, on the first roll, are on every single roll of 5 dice out of the cup. Those odds can still be correct after 126, 900, 000, 000, 000, 000-10 rolls. There really is nothing in the universe that guarantees you will ever roll a yahtzee: 5 dice, straight out from the cup. Lastly, there is nothing that prevents you from rolling 50 of them in a row; literally nothing.
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Yoan
Rolled 200 times 5 dices and seen 2 times 4 of a kind in less than 10 minutes. That was quite physically engaging to roll that fast, using only hands over a pool table. Then it turns out that I tried to roll two 20 faces dices instead (D&D FTW) and happened to roll 2 1's at my third roll. I think I'm done with it, double critical fail in such a short amount of time lol!
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Rolled 200 times 5 dices and seen 2 times 4 of a kind in less than 10 minutes. That was quite physically engaging to roll that fast, using only hands over a pool table. Then it turns out that I tried to roll two 20 faces dices instead (D&D FTW) and happened to roll 2 1's at my third roll. I think I'm done with it, double critical fail in such a short amount of time lol!
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BrainAtrophy
Doing this in 627 rolls has a probability of about 38. 37%. So, fairly lucky, but not like insanely lucky.
You can calculate the probability of rolling a yahtzee in n rolls by finding P(n) = 1-(1295/1296)-(n. You can pretty quickly see that you're never guaranteed a yahtzee. The probability asymptotes to 1 as n tends to infinity.
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Doing this in 627 rolls has a probability of about 38. 37%. So, fairly lucky, but not like insanely lucky.
You can calculate the probability of rolling a yahtzee in n rolls by finding P(n) = 1-(1295/1296)-(n. You can pretty quickly see that you're never guaranteed a yahtzee. The probability asymptotes to 1 as n tends to infinity.
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Kevin
A question: I understand that a 1/1296 chance of throwing a one-throw Yahtzee does not mean that you are guaranteed to have one one-throw Yahtzee every 1296 throws (because each throw is an independent event, but how do you calculate the chance of getting at least one one-throw Yahtzee in 1296 throws? Is there a formula for this?
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A question: I understand that a 1/1296 chance of throwing a one-throw Yahtzee does not mean that you are guaranteed to have one one-throw Yahtzee every 1296 throws (because each throw is an independent event, but how do you calculate the chance of getting at least one one-throw Yahtzee in 1296 throws? Is there a formula for this?
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