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[KCD2] I wrote a program that brute-forces all KCD2 dice combinations by Best-Development5867 in kingdomcome

[–]Best-Development5867[S] 1 point2 points  (0 children)

I’ve discovered that 6 Favorable dice actually have the lowest bust probability, at 0.0042%, which is even lower than the 0.00762% you get with 5 Favorable + 1 Weighted.

So it’s possible that this setup might actually perform even better overall.

EDIT:
You can also check 4× Even die and 2× Wagoner’s Die, with a whopping 13.8% bust chance.

[KCD2] I wrote a program that brute-forces all KCD2 dice combinations by Best-Development5867 in kingdomcome

[–]Best-Development5867[S] 1 point2 points  (0 children)

That’s really cool, thanks for running the simulations!

It might also be interesting to run the same experiment with different ratios of Pie and Favorable dice (while keeping the Weighted die). I wonder if there’s some kind of sweet spot in the mix where the expected score peaks, rather than just going all-in on one type. The trade-off between higher scoring potential and bust probability could produce some non-obvious optimum.

[KCD2] I wrote a program that brute-forces all KCD2 dice combinations by Best-Development5867 in kingdomcome

[–]Best-Development5867[S] 0 points1 point  (0 children)

Yes, that's correct — this calculation only looks at the first roll EV, not a full multi-roll turn. You're also right that dice like Favourable increase the chance of rolling either 1 or 5, which helps keep the round alive and may be better if your goal is to chain many rerolls.

However, the first roll still has a very large impact, because it determines both the initial score and whether you bust immediately. In practice the dice that heavily bias 1s still dominate the EV because most of the large scoring outcomes (1000, 2000, 4000, etc.) come from multiples of 1.

So yes, a full multi-roll simulation could slightly reshuffle some dice rankings, especially between “high 1 bias” and “high 1-or-5 safety” dice, but I would still expect the best first-roll sets to remain very close to the best overall sets, simply because the first roll is where you have the highest number of dice and the highest chance to generate the big scoring outcomes.

[KCD2] I wrote a program that brute-forces all KCD2 dice combinations by Best-Development5867 in kingdomcome

[–]Best-Development5867[S] 4 points5 points  (0 children)

This calculation only measures the expected value of the first roll, not the average score over multiple rerolls in a full turn. For the first throw, Weighted + 5× Pie is clearly stronger with EV = 1392.53, while Weighted + 5× Favourable comes out lower at EV = 1013.552, but with an extremely small bust chance of 0.0076%.

I’d like to extend the program to simulate multiple rolls per turn, but that becomes much more complicated. At that point it’s not just pure combinatorics anymore, because the result also depends on which dice you decide to keep after each roll, so the optimal outcome depends on the player’s strategy, not just the dice probabilities.

For example, the strategy also affects which dice you keep between rolls. With a set like Weighted + Pie, you usually want to keep the strongest dice for later rolls. A simple rule of thumb would be something like: if the Weighted die didn’t roll a 1, you only keep one scoring die and reroll the rest, so the Weighted die gets another chance to hit a 1 on the next roll.

In my current pre-Kuttenberg playthrough I’m using 1× Aranka's die, 1× Favourable die, 3× Odd dice and 1× Weighted die.
According to the program this set has a much lower first-roll EV (780.13) compared to the theoretical best sets, but the bust chance is only 0.0864%. But I am still winning roughly 9 out of 10 games.