the odds of rolling yahtzee seem way too high.

[justanotherjo]

Is it just me or does the dice randomizer seem off? In this online version I roll a yahtzee (not natural, but within 3 rolls) maybe once every 8 or 9 games. In the real world, this happens so rarely I can't even guess at the frequency of it, once every 100 games? And, forget about a second yahtzee. I think I have done that twice in my 40+ years of playing the game in the real world, yet i've done it 4x in the past month online.

[dschingis27]

If you roll a Yahtzee only every 8 or 9 games, you are actually off in a way that you roll too few Yahtzees. And you seem to have had extraordinary bad luck in your real life or you played with screwed dice. Probably you lean to heavily towards straights or something else.

https://www.thoughtco.com/probability-o ... ee-3126593
"The probability of a Yahtzee in one roll is 0.08 percent, the probability of a Yahtzee in two rolls is 1.23 percent and the probability of a Yahtzee in three rolls is 3.43 percent. Since each of these are mutually exclusive, we add the probabilities together. This means that the probability of obtaining a Yahtzee in a given turn is approximately 4.74 percent. To put this into perspective, since 1/21 is approximately 4.74 percent, by chance alone a player should expect a Yahtzee once every 21 turns. In practice, it may take longer as an initial pair may be discarded to roll for something else, such as a straight."

[Silene]

And don't forget that real life play is much slower. That means that you usually play much fewer games while still having the feeling of having played "a lot". Your brain translates having played a long time into having played many games while in fact it was only something like 5 games. While when having played online you have the same feeling of having played a lot only after something like 15-20 (fast) games. In online-fast games you have more games to find an extraordinary pattern while in real life it takes much longer.

[justanotherjo]

If you roll a Yahtzee only every 8 or 9 games, you are actually off in a way that you roll too few Yahtzees. And you seem to have had extraordinary bad luck in your real life or you played with screwed dice. Probably you lean to heavily towards straights or something else.

https://www.thoughtco.com/probability-o ... ee-3126593
"The probability of a Yahtzee in one roll is 0.08 percent, the probability of a Yahtzee in two rolls is 1.23 percent and the probability of a Yahtzee in three rolls is 3.43 percent. Since each of these are mutually exclusive, we add the probabilities together. This means that the probability of obtaining a Yahtzee in a given turn is approximately 4.74 percent. To put this into perspective, since 1/21 is approximately 4.74 percent, by chance alone a player should expect a Yahtzee once every 21 turns. In practice, it may take longer as an initial pair may be discarded to roll for something else, such as a straight."

While the odds are 1/21, real life doesn't follow the odds. If you flip a coin the odds are 50% you will get heads, yet if you flip a coin 100x, you'll see that the results are not as close to 50% as you might think. When rolling dice in the real world, it is not an even die roll every time. How you hold them when you throw them, what position the pips were in when you threw, how hard you throw them, what they bounced off of all affect the results. In a computer simulation, these real world variables do not exist in a die roll, so the results will be much closer to statistical probability.

[dschingis27]

If you roll a Yahtzee only every 8 or 9 games, you are actually off in a way that you roll too few Yahtzees. And you seem to have had extraordinary bad luck in your real life or you played with screwed dice. Probably you lean to heavily towards straights or something else.

https://www.thoughtco.com/probability-o ... ee-3126593
"The probability of a Yahtzee in one roll is 0.08 percent, the probability of a Yahtzee in two rolls is 1.23 percent and the probability of a Yahtzee in three rolls is 3.43 percent. Since each of these are mutually exclusive, we add the probabilities together. This means that the probability of obtaining a Yahtzee in a given turn is approximately 4.74 percent. To put this into perspective, since 1/21 is approximately 4.74 percent, by chance alone a player should expect a Yahtzee once every 21 turns. In practice, it may take longer as an initial pair may be discarded to roll for something else, such as a straight."

While the odds are 1/21, real life doesn't follow the odds. If you flip a coin the odds are 50% you will get heads, yet if you flip a coin 100x, you'll see that the results are not as close to 50% as you might think. When rolling dice in the real world, it is not an even die roll every time. How you hold them when you throw them, what position the pips were in when you threw, how hard you throw them, what they bounced off of all affect the results. In a computer simulation, these real world variables do not exist in a die roll, so the results will be much closer to statistical probability.

While your statement is in general not incorrect, there can be of course some weird way of flipping a coin that biases results slightly away from pure chance, it's very hard to imagine how this could appear in dice rolling for a Yahtzee. Like you would need to systematically roll the dice in a way that avoids pairs, triples, quadrupels.
To be clear, I don't say that your real-life experience of very few Yahtzees is impossible, I just say that if it's true, it means you had a lot of bad luck.

[dschingis27]

While the odds are 1/21, real life doesn't follow the odds. If you flip a coin the odds are 50% you will get heads, yet if you flip a coin 100x, you'll see that the results are not as close to 50% as you might think. When rolling dice in the real world, it is not an even die roll every time. How you hold them when you throw them, what position the pips were in when you threw, how hard you throw them, what they bounced off of all affect the results. In a computer simulation, these real world variables do not exist in a die roll, so the results will be much closer to statistical probability.

To be clear once more: I would say that real life DOES follow the odds in the long run. And it will usually be as close to statistical probability as a simulation is, unless there is some weird environmental influence. It's just that normal human beings usually do not play as many dice games in their real life in a lifetime as they would need to reach a long run in statistical terms.

[frogstar_A]

I'd expect a yahtzee more often than 8-9 games! Maybe every 3-4?

It's also influenced by how you play too - remember any time you hold two different numbers a yahtzee is jmpossibe. If you often hold say 1122 trying to roll for a full house, or hold 234 trying to roll for a straight you will not get so many yahtzees. Even holding a single 6 reduces your chances of getting a yahtzee because you can only roll one on 6s now.

[Jellby]

Even holding a single 6 reduces your chances of getting a yahtzee because you can only roll one on 6s now.

Not really. The probability of a yahtzee from scratch is (1/6)^5, times 6 because there are six possible ones, so (1/6)^4. The probability of a yahtzee once you hold a 6 is (1/6)^4. So it's exactly the same.

[frogstar_A]

Even holding a single 6 reduces your chances of getting a yahtzee because you can only roll one on 6s now.

Not really. The probability of a yahtzee from scratch is (1/6)^5, times 6 because there are six possible ones, so (1/6)^4. The probability of a yahtzee once you hold a 6 is (1/6)^4. So it's exactly the same.

On roll 2 the odds of a yahtzee are the same whether you hold a 6 or reroll all 5 dice , agreed.

However you maximise your chances of rolling a yahtzee across rolls 2 and 3 by rerolling all five dice.

This is because you might roll two or three or four of a kind of another number, and could have got yet another of the same had you rerolled the six.