The Question:
So once upon a time, we were playing Yahtzee after dinner with my grandmother as we do, since Yahtzee is one of the few games she'll play with us. And I pondered, "How many games of Yahtzee in a row do we need to have to mitigate luck and show who is truly better at Yahtzee?"
Spoilers:
Like, quite possibly hundreds and hundreds, imo. Yahtzee is a ludicrous amount of luck, hahaha.
We took it to ChatGPT:
But we took this question to the great source of ChatGPT and asked it to give us a low estimate and a high estimate of the number of games we would need to play (combining all the scores at the end).
It responded: Low estimate: 20 games. High estimate: 50.
Gameplan: Add each game's total to a spreadsheet. See the results after 20 games. I also decided to keep track of 2 other important numbers outside of score: Total number of Yahtzees and Bonus Yahtzees.
Btw, Bonus Yahtzee's are BROKEN:
Bonus Yahtzee's are BROKEN. Seriously broken busted. 100 points is an insane amount PLUS you often can chuck that five-of-a-kind up on top, making making your top sooo much easier. Broken broken broken.
And So It Begins:
And so we started off on our journey. Most days after dinner, we would play a couple-few games of Yahtzee and would. After a couple-few weeks, Grandma, Mom, Eric, and I finished our 20 games of Yahtzee, and then for some wild reason, my mom, Eric, and I decided we were going to sit down and play 30 more games. Right then. We, of course, did not take turns in any form during these 30 games, which made it significantly faster, but it still took quiiiite a while. But it was kind of a blast, haha.
Stats from the 20 games:
1st Place: Mother with 5530 points (an average of 276 points per game).
2nd Place: Alex with 4962 points (an average of 248.1 points per game).
3rd Place: Grandma with 4894 points (an average of 244.7 points per game).
4th Place: Eric with 4604 points (an average of 230.2 points per game).
But the yahtzee/bonus yahtzee stats are really important here.
Mom: 7 Yahtzees, 7 Bonus Yahtzees
Alex: 8 Yahtzees, 1 Bonus Yahtzee
Grandma: 7 Yahtzees, 2 Bonus Yahtzees
Eric: 6 Yahtzees, 0 Bonus Yahtzees
After Mom got 4 Bonus Yahtzees in the course of 3 games, I knew our chances were not good.
Stats from the 50 games:
1st Place: Mom with 13633 points (an average of 272.66 points per game).
2nd Place: Alex with 12464 points (an average of 249.28 points per game).
3rd Place: Eric with 11889 points (an average of 237.78 points per game).
Mom: 23 Yahtzees, 15 Bonus Yahtzees
Alex: 21 Yahtzees, 2 Bonus Yahtzees
Eric: 18 Yahtzees, 2 Bonus Yahtzees
The fact that my mother was able to get 38 Yahtzees over the course of 50 games is actually ludicrous, with 15 of those being in the same game as other Yahtzees making them more than twice as good. Simply crazy. I was hoping that playing another 30 games would spread out the Bonus Yahtzee love, but nope. My mom just kept rolling Bonus Yahtzees.
Also minor note here: In one of the games, she crossed out Yahtzee fairly early into one of the games and then her next two rolls were yahtzees; she could've had one more Yahtzee and one more Bonus Yahtzee. Actually bonkers.
Answer to our Original Question:
Like, a bonkers number of Yahtzee games are needed to actually mitigate luck. The choices you make obviously do matter in Yahtzee -- you can't simply pick up all 5 dice and huck them for all 3 rolls. However, the base strategy is so simplistic that in order for the small decision differences between players to actually shine forth, you would need hundreds and hundreds (probably even thousands and thousands or maybe more) of games to see which players make better decisions.
Granted, as I say that, there's presumably a better way. Theoretically there's always a best move to optimize potential points. Figure this out with a computer doing tons of stat things and then create many different scenarios. Ask the players what they would do in all these different scenarios and see how accurate they are.
Training an AI with your playstyle and letting it play hundreds of thousands of games is also a potential option, I think.
How Good Can You Actually Get:
Theoretically, you can become "perfect" at Yahztee. You know the statistics so well that you always choose to roll the dice in a way that maximizes profit. The thing, ofc, about such an extremely luck based game as Yahtzee is the difference between being "perfect" and "really good" at Yahtzee is quite small. The perfect player won't win that many more games, and would need hundreds of games to show they win more often.
And getting "really good" at Yahtzee is not hard at all. It legit takes very very little study. You can't get that good at Yahtzee. And the initial getting good is 1000x easier than the final push to becoming perfect.
Additional Strategy Note:
I realize the strategy of playing a single game is a little different than playing 50+ games combined. In a single game, looking at your opponent's scores can actually become quite important. If an opponent, for example, already has scored a Yahtzee and a Bonus Yahtzee, the only way you're winning that game is if you also score a Yahztee and a Bonus Yahtzee as well. Thus, you never cross out Yahztee and you push for it in circumstances you wouldn't have had otherwise. Most of the time this will lead to an overall lower score for that game, but it will give you a chance to actually win -- which is the goal. (Granted, this dives into other topics dealing with the concepts of how playing for 2nd should be important too etc. etc., but I think that's a topic for another time.)
When playing 50+ games back combined, the strategy shifts more to what statistically gets you the most points regardless of how many points the other players have (until you're approaching the end of the 50+ games, I suppose).
Conclusion:
Okay, this post turned out way longer than I thought it was going to be; there's a surprising number of thoughts that Yahtzee brings up that I want to unpack and talk about. And there's still more I want to talk about. Why I hate Bonus Yahtzees but I'm not sure if I should (long story short, I hate them because they're completely unbalanced and stupid, but 'fun' is an important thing in games, and maybe they simply add fun to an already luck based game and that's good even though they're stupid), the whole 2nd place mattering thing, other thoughts on our final scores, and probably some other stuff too. But I'll call it here. I'll perhaps have to continue these conversations in other blog posts or maybe in a ¿¿¿video???. Idk, guess we'll see.
No comments:
Post a Comment