full and fed up reduction tests

[_Gunnar]

The timer added is reduced based on the humours you have gained so far in the session.

After 1 humour level-up, the timer increases at ~0.74 of the rate shown on the food
After 2 level-ups, increases at ~0.62 rate
After 3 level-ups, ~0.56 rate
After 4 level-ups, ~0.52 rate
At that point I got bored, because I think I can already see what it is.. (the numbers above are approximate)

Let n be the number of levelups, let f be the full and fed up timer modifier

if n=0: f_0=1
if n>0: f_n=1-sum{[1/4]^((1+i)/2)} where the sum over i is from 1 to n
f_n = (2^n + 1)/2^(n+1) [closed form, pointed out by Tammer]

i.e. 1 levelup: f=1-1/4 = 0.75
2: f=1-1/4-(1/4)**1.5 = 0.625
3: f=1-1/4-(1/4)**1.5 -(1/4)**2 = 0.5625
4: f=1-1/4-(1/4)**1.5-(1/4)**2-(1/4)**2.5 = 0.53125
etc
Does this formula match other peoples tests? I don't know how many other people know this, so sorry if its really obvious.

NB. it asymptotes at f=0.5 as n--> infinity, and approaches that pretty quickly. So its not at all worth eating a food if its combined gluttony reduction modifier reaches a worse value than 0.5 (as part of a normal glutton… of course it may be worth it to just top off a levelup).

[DemonEyes]

Good work Gunnar.. I was trying to link it to food items or food types, wasnt in much of a position to consider level ups

[Tammer]

Nice work Gunner.

Your sum has a closed form, by the way (since it's a geometric series):

f_n = (2^n + 1)/2^(n+1)

[_Gunnar]

doh, i forgot to post that - thanks :p

[Scilly_guy]

Hmm, I hadn't realised this, but surely it is still better to eat just enough to raise 1 Humour and wait until you can gluttony again?
Unless you can raise more than once without reducing the same groups.
Assuming you are able to log on when the timer resets.

[bashnagdul]

it seems to be a weighing of amount of food gluttoned vs amount of time full and fed up debuff and how long you are offline.
doing an extra 4 hours full and fed up debuff is better than 4 hours no debuff, but not eating either.

[Jalpha]

Hmm, I hadn't realised this, but surely it is still better to eat just enough to raise 1 Humour and wait until you can gluttony again?

That depends on how well you mix food types.

[_Gunnar]

Its also worth considering eating your low-timer food at the start of a session. The reason i'm saying "considering" is that often low-timer food has much worse reductions attached to it (see: autumn delight) so you have to plan carefully if you want to do this. I don't think there is an "optimal solution" for arbitrary humours, which is cool.

And yeah, eat a variety of food and profit. Some of the early foods have horrible debuffs which make it so that its only worth gaining 1pt per session (like: reduction to ALL FOOD), but later foods sometimes only give tiny debuffs, and often restorations too. However I'm not very good at this game myself, because i'm too lazy to make the right foodstuffs :p