A note about probabilities

[Jellby]

I guess anyone interested already knows, or can easily work it out for themselves, but no harm in being explicit. The probability of discarding some precious sugar when you distil increases with the number of sugars. Assuming you just have N sugars (+N alcohols), 1 yeast, 1 water:

1 sugar
Probability of discarding 0 sugars: 50%
Probability of discarding 1 sugar: 50%
Probability of discarding 2 sugars: 0% (doh!)

2 sugars
Probability of discarding 0 sugars: 40%
Probability of discarding 1 sugar: 53%
Probability of discarding 2 sugars: 7%

4 sugars
Probability of discarding 0 sugars: 36%
Probability of discarding 1 sugar: 54%
Probability of discarding 2 sugars: 11%

4 sugars
Probability of discarding 0 sugars: 33%
Probability of discarding 1 sugar: 53%
Probability of discarding 2 sugars: 13%

5 sugars
Probability of discarding 0 sugars: 32%
Probability of discarding 1 sugar: 53%
Probability of discarding 2 sugars: 15%

[Aeronwy]

I must have gotten really unlucky when trying to make my signature drinks in 2 different game then...

In one, I had 4 sugars and 7 alcohols (plus 1 yeast and 1 water) - lost 2 of my sugars, but of course my signature sugar got used, but it needed 3 for the recipe, so I couldn't make it. (I'm hoping to be able to get enough grain sugar to try it again but we were already in round 5, so I'm not hopeful.)

In my other game, I had 5 sugars and 6 alcohols (and just 1 water) - again lost 2 sugars, but thankfully my signature was NOT one of the "lost" ones, so I still had 3 in the washback and was able to make my signature recipe.

[Jellby]

In one, I had 4 sugars and 7 alcohols (plus 1 yeast and 1 water) - lost 2 of my sugars, but of course my signature sugar got used, but it needed 3 for the recipe, so I couldn't make it. (I'm hoping to be able to get enough grain sugar to try it again but we were already in round 5, so I'm not hopeful.)

Probability of losing 2 sugars: 4/13 × 3/12 = 1/13 ~ 8%
Probability of losing 2 sugars and wasting the signature one: 1/13 × 2/4 = 1/26 ~ 4%

In my other game, I had 5 sugars and 6 alcohols (and just 1 water) - again lost 2 sugars, but thankfully my signature was NOT one of the "lost" ones, so I still had 3 in the washback and was able to make my signature recipe.

Probability of losing 2 sugars: 5/12 × 4/11 = 5/33 ~ 15%
Probability of losing 2 sugars and wasting the signature one: 5/33 × 2/5 = 2/33 ~ 6% (so ~ 9% or losing 2 and not wasting)

It feels really unlucky, but I think the probabilities are actually higher than what intuition says, so we probably overestimate how unlucky we are.

[c12h22o11_]

Indeed. If you play enough games, you are usually pretty safe having 1 extra sugar over the recipe. But those 5-10% chances can always happen.

[Jellby]

But those 5-10% chances can always happen.

Make it 7-15% (a proof that we underestimate the probability)

[charlimangy]

This is great, but I'm still confused about the probability with the signature sugar. I found this post on BGG:

https://boardgamegeek.com/thread/309357 ... ercentages

but I'm not sure how to interpret the odds of making a signature recipe that needs 3 sugars at the end. I've failed a number of times trying to make a 3-signature recipe using one signature ingredient + 3 regular sugars. Am I just unlucky or am I underestimating the odds of failure? Getting 4 sugars + a barrel to go with your signature ingredient is tough.

[Magrim42]

Hmm, that if interesting, maybe I'll play a little more fast and loose with my signature, I usually get enough to make it impossible to fail