Solving 8 item negotiations in 3 turns

[hajiboy]

Any math wizards here? What is the probability of solving an 8 item negotiation in 3 turns? These negotiations show up in GE Level 3, last encounter and several times in GE level 4. What is the probability of solving these without enabling the extra turn? This type of a negotiation also showed up in 2021 St. Patrick's event's daily task - 8 items=complex negotiation, 3 turns.

No matter how promising the results on the first turn were, even with 3 items eliminated as wrong goods, the solution has proved to be unachievable for me with remaining turns. So, I am curious, what is the probability of solving an 8 different goods negotiation with 3 turns?

 

[KevinP0208]

Any math wizards here? What is the probability of solving an 8 item negotiation in 3 turns? These negotiations show up in GE Level 3, last encounter and several times in GE level 4. What is the probability of solving these without enabling the extra turn? This type of a negotiation also showed up in 2021 St. Patrick's event's daily task - 8 items=complex negotiation, 3 turns.

No matter how promising the results on the first turn were, even with 3 items eliminated as wrong goods, the solution has proved to be unachievable for me with remaining turns. So, I am curious, what is the probability of solving an 8 different goods negotiation with 3 turns?

For those negotiations, my probability is 28% with my strategy (out of 236 attempts)
I got these attempts from daily challenges and expeditions btw

Use as many different items on your first turn as you can. Coins and supplies are plenty, so always use them first: E.G. Let's say your options are coins, supplies, and 6 other goods. For the first person, place coins. For the second person, place supplies. With the remaining people, use three different goods (use the goods that you have most of as priority). Next turn you should use the remaining goods you haven’t yet used to determine which ones to use and not waste goods. The goods marked as incorrect should be ignored and forgotten. Even the AI will get rid of them. If the good is marked “wrong person”, it is incorrect for the person you just offered it to but there will be one or more who want this good. (Mark these goods down because in future turns you will need them)
Once you’ve offered all the goods, you will now know which goods to use. Then use the strategy of elimination and common sense and you should be able to get it right. (Luck will also be needed btw, but using this strategy will increase your chances of success)

 

[Vger]

I wouldn't know how to do the math, sorry.
What I do know is that several of us have tracked our success rate in GBG and all came up with a success rate of around 50% for 6 item/3 turn negotiations.
So I think it is safe to assume that the extra 2 goods are going to bring that number down. But by how much? My guess, based on absolutely no facts or math is that it might be in the 25 to 35% range for success.
That does sort of fit my experience doing those (which is limited because I would only do them in DC, in GE I'm going to have the extra turn). I know it can take me 2 or 3 or 4 tries most of the time. But then again, I have no qualms about spending 10 diamonds to finish it if I already failed a couple times and know I can finish it with 1 more turn.

--- Got this far responding when Kevin posted his results above. So I'll just stop here and pat myself on the back for a SWAG that appears to be ballpark right.
Thanks Kevin!