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MrBenn wrote:I've spent a but of time dusting off some textbooks, and have put together a quick spreadsheet that will calculate the probability of dropping a particular bonus region on a map, that also takes 'build-your-own' bonuses into consideration...
Bonus Probabilities Spreadsheet v1
I don't think I've got my formulae wrong, but it has been a few years since I did any meaningful work using probabilities like this... If people think it would be useful, I can expand the spreadsheet to allow for more regions to be calculated simultaneously?
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john9blue wrote:My preliminary test didn't work, though. Try 9 territories with a continent of 3... each player gets 3 territs in a 2p or 3p game, and 84 ways to distribute them, so the odds are 1/84, or 1.19%. Your spreadsheet says 1.23%, so you're gonna have to tweak it.
Merciless Wong wrote:the.killing.44 wrote:Merciless Wong wrote:The issue is not just the cities. Its the Cities and the Challenges. The Cities is a 9% chance of giving someone an edge.
The Challenges, another 9% or so (2/27). So your chance of having no starting bonuses or so is about (1-9%)^2.
So you are talking about a 18% chance of either 1 or 2 starting with an advantage - which would beat the 10% level you quoted
I'm not going to go into your other complaint, but your math is wrong. If you're saying that it's 9^2 with a max of 18, 9^2 = 81. Which is blatantly wrong.
.44
I'm not sure if you noticed but ^ is the power symbol.
(1-9%)
=91%
91%^2
=approx 81%
Chance of no bonus is 81%
Chance of bonus is 100% -81% = 19%
.
Here's my working:
2^5 = 32. There are 5 provinces with cities, assuming conquer club will place them all with on player or the other there are
2x2x2x2x2 possibilities.
In 1 of them player 1 has it all
In 1 of them player 2 has it all
In 5 of them player 1 has 4 of the 5 cities
In 5 of them player 2 has 4 of the 5 cities
That's my 12 out of 32 = 37%
The reamaining 20 out of 32 are scenarios where player 1 has 3 cities (10 possibilities)
and player 2 has 3 cities (10 possibilities)
If you wish to model the number of neutals in 1v1 (I presume its 1 out of 40+ territories) it should make a slight difference.
If its 3 starts (1 neutral, meaning neutals will be 1/3 of the board):
3^5= 243 scenarios (focuing only on non hard coded neutral provinces that matter for city bonus)
2 of them they have it all
5 of them p 1 has 4, neutrals have 1
5 of them p 2 has 4, neutrals have 1
5 of them p 1 has 4, other has 1
5 of them p 2 has 4, other has 1
Makes it 22 out of 243 = 9.1%
the.killing.44 wrote:
Merciless Wong wrote:
The issue is not just the cities. Its the Cities and the Challenges. The Cities is a 9% chance of giving someone an edge.
The Challenges, another 9% or so (2/27). So your chance of having no starting bonuses or so is about (1-9%)^2.
So you are talking about a 18% chance of either 1 or 2 starting with an advantage - which would beat the 10% level you quoted
I'm not going to go into your other complaint, but your math is wrong. If you're saying that it's 9^2 with a max of 18, 9^2 = 81. Which is blatantly wrong.
.44
I'm not sure if you noticed but ^ is the power symbol.
(1-9%)
=91%
91%^2
=approx 81%
Chance of no bonus is 81%
Chance of bonus is 100% -81% = 19%
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