Update on the best negotiation strategy.
Chances to negotiate an encounter in 3 turns:
4 resources - 95.1% (1.1 attempts on average)
5 resources - 83.1% (1.2 attempts)
6 resources - 60.0% (1.7 attempts)
7 resources - 36.0% (2.8 attempts)
8 resources - 22.0% (4.6 attempts)
9 resources - 12.7% (7.9 attempts)
10 resources - 7.8% (12.8 attempts)
The best strategy requires, sometimes, to offer at the 2nd turn set of resources, which will never be accepted. But such offer allows player to gather more information and make a better guess at the last turn.
With the best strategy, the average number of attempts needed to finish different difficulty levels is:
Difficulty 1 - 20.1 attempts
Difficulty 2 - 36.3 attempts
Difficulty 3 - 65.4 attempts
To finish all 3 difficulty levels, player needs, on average, 121.8 attempts (with standard deviation 21.4 attempts)
If a player uses all "free" attempts (24 attempts/day * 6 days + 8 initial attempts = 152 attempts), he will finish the expedition with probability 92.1%.
I'd say devs did a rather good job with this negotiation game. It's sufficiently easy for any player to play it, but at the same time it has (not obvious) strategies that significantly improve chances of a player. As with many other aspects of FoE, luck does play a role (and make things more interesting and unpredictable), but strategy is more important in the long run. Good job!
However, I think that the cost of negotiations is way too high. With over 100 attempts, 3 turns per attempt, 5 slots, and about 1-2 goods per slot, it gives over 1000 goods per week spent on the expeditions. This is too costly, and I don't think the negotiations will be very popular after few first weeks (maybe, only the first difficulty, which is rather simple). I think it would be better if the resources were subtracted only when the slot is "accepted".
