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Topic: Rebalancing the tribes?

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king_of_nowhere
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Joined: 2014-09-15, 18:35
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 Posted at: 2016-02-21, 16:23

your values are within a 1% from the ones I calculated (which, by definition, are exact). I was going to suggest that you increase the number of simulations to get more accurate values, but really, those are more than good enough for our purposes. It's not like we're going to say "omg the chance of winning was 51% instead of 52%! now we have to rebalance everything!"

Let's see how that changes if barbarian attack at level 10 is increased by 7.5

Edited: 2016-02-21, 16:23
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einstein13
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Posted at: 2016-02-21, 17:23

Full calculations (40'000 fights)

Calculations for old values:

vs. bar_00 bar_02 bar_07 bar_10 emp_00 emp_02 emp_07 emp_10 atl_00 atl_02 atl_07 atl_10
bar_00 57.0% 5.0% 0.0% 0.0% 41.7% 1.5% 0.0% 0.0% 31.7% 0.6% 0.0% 0.0%
bar_02 97.0% 53.0% 0.1% 0.0% 93.3% 31.9% 0.0% 0.0% 90.6% 20.9% 0.3% 0.0%
bar_07 100.0% 100.0% 53.9% 12.4% 100.0% 99.7% 52.8% 13.8% 100.0% 98.7% 64.7% 11.6%
bar_10 100.0% 100.0% 91.4% 54.3% 100.0% 100.0% 79.3% 40.5% 100.0% 100.0% 87.6% 36.2%
emp_00 70.3% 9.6% 0.0% 0.0% 56.5% 3.2% 0.0% 0.0% 43.2% 1.0% 0.0% 0.0%
emp_02 99.2% 73.0% 0.5% 0.0% 97.9% 51.9% 0.2% 0.0% 96.5% 37.0% 1.1% 0.0%
emp_07 100.0% 100.0% 53.7% 25.3% 100.0% 99.9% 52.8% 15.2% 100.0% 99.7% 62.1% 12.0%
emp_10 100.0% 100.0% 89.5% 67.2% 100.0% 100.0% 88.1% 53.5% 100.0% 100.0% 93.0% 49.6%
atl_00 78.3% 13.0% 0.0% 0.0% 68.1% 5.0% 0.0% 0.0% 55.5% 2.0% 0.0% 0.0%
atl_02 99.7% 82.8% 1.7% 0.0% 99.4% 66.4% 0.4% 0.0% 98.7% 52.0% 2.0% 0.0%
atl_07 100.0% 99.8% 41.5% 15.6% 100.0% 99.1% 43.3% 8.7% 100.0% 98.6% 52.8% 7.6%
atl_10 100.0% 100.0% 91.3% 70.4% 100.0% 100.0% 90.2% 56.8% 100.0% 100.0% 94.2% 53.3%

New values for barbarian attack (8.5 instead 7.0):

vs. bar_00 bar_02 bar_07 bar_10 emp_00 emp_02 emp_07 emp_10 atl_00 atl_02 atl_07 atl_10
bar_00 56.8% 4.9% 0.0% 0.0% 41.5% 1.4% 0.0% 0.0% 31.3% 0.6% 0.0% 0.0%
bar_02 96.9% 52.7% 0.1% 0.0% 93.7% 31.3% 0.0% 0.0% 90.9% 20.6% 0.3% 0.0%
bar_07 100.0% 100.0% 54.1% 21.1% 100.0% 99.7% 52.9% 24.4% 100.0% 99.7% 75.1% 21.7%
bar_10 100.0% 100.0% 84.4% 54.3% 100.0% 100.0% 90.1% 52.6% 100.0% 100.0% 95.3% 50.9%
emp_00 70.1% 9.5% 0.0% 0.0% 56.2% 3.3% 0.0% 0.0% 43.0% 1.1% 0.0% 0.0%
emp_02 99.1% 73.0% 0.3% 0.0% 98.0% 52.7% 0.2% 0.0% 96.6% 37.3% 1.1% 0.0%
emp_07 100.0% 100.0% 53.4% 12.7% 100.0% 99.9% 52.7% 15.3% 100.0% 99.7% 62.1% 12.5%
emp_10 100.0% 100.0% 80.5% 55.4% 100.0% 100.0% 88.0% 53.6% 100.0% 100.0% 93.0% 49.3%
atl_00 78.4% 12.8% 0.0% 0.0% 67.6% 5.1% 0.0% 0.0% 55.2% 2.1% 0.0% 0.0%
atl_02 99.8% 82.6% 0.5% 0.0% 99.4% 66.9% 0.3% 0.0% 98.7% 51.4% 2.0% 0.0%
atl_07 100.0% 99.8% 30.5% 6.2% 100.0% 99.2% 43.0% 9.0% 100.0% 98.5% 52.7% 7.2%
atl_10 100.0% 100.0% 82.9% 56.6% 100.0% 100.0% 90.0% 56.9% 100.0% 100.0% 94.3% 53.1%

Only level 10 soldiers (50'000 fights):

Old values:

vs. bar_10 emp_10 atl_10
bar_10 53.8% 40.4% 36.3%
emp_10 66.7% 53.0% 49.0%
atl_10 70.2% 56.5% 53.4%

New values:

vs. bar_10 emp_10 atl_10
bar_10 55.0% 52.5% 50.7%
emp_10 55.3% 53.5% 49.5%
atl_10 56.3% 56.8% 53.3%

einstein13
calculations & maps packages: http://wuatek.no-ip.org/~rak/widelands/
backup website files: http://kartezjusz.ddns.net/upload/widelands/

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einstein13
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Joined: 2013-07-29, 00:01
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Posted at: 2016-02-21, 17:28

king_of_nowhere wrote:

your values are within a 1% from the ones I calculated (which, by definition, are exact). I was going to suggest that you increase the number of simulations to get more accurate values, but really, those are more than good enough for our purposes. It's not like we're going to say "omg the chance of winning was 51% instead of 52%! now we have to rebalance everything!"

Yes, my calculations aren't exact. They are a bit random. I can increase number of simulations, but I don't think that it is necessary now... Maybe I will let them to be 1 milion for each? face-grin.png

Let's see how that changes if barbarian attack at level 10 is increased by 7.5

For me, the results are almost equal, so it is MUCH BETTER face-smile.png

Oh... I've forgotten: the small project is on github (https://github.com/einstein13/wl_soldiers). Feel free to find any bug there face-tongue.png

And one more thing: some math

S1 - soldier 1, with all stats
S2 - soldier 2, with all stats
Example: S1 = barbarian, level 10; S2 = atlantean, level 10
Probabilities of win:
P1 = 36.3% (S1 starts fight and win)
P2 = 70.2% (S2 starts fight and win)
P1+P2 = 106,5% > 100%

It seems to be wrong, but it isn't. P1 and P2 are DIFFERENT SITUATIONS. So the probability doesn't have to sum to one (1.0). Even from the background math and physics (or rather biology) here, we can say that with any S1 and S2:

P1+P2 > 100%

Because in all situations we have "P_X = S_X starts the fight" (X = 1 or 2). So there is always a chance that starting soldier will kill enemy just before his death (and finally he will survive).

Edited: 2016-02-21, 18:08

einstein13
calculations & maps packages: http://wuatek.no-ip.org/~rak/widelands/
backup website files: http://kartezjusz.ddns.net/upload/widelands/

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king_of_nowhere
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Joined: 2014-09-15, 18:35
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 Posted at: 2016-02-21, 18:31

yes, i also agree that the new values are much better. chances among fully promoted soldiers are roughly equal, and among lower soldiers they are not affected.

Also, nobody spoke against the proposal of rebalancing, so I'd say we can implement the new values. The only question is whether to do it before or after buil 19.

By the way, we stopped mentioning it, but I suppose also the proposal of swapping two other resources for 2 gold in the price of the atlantean labirynth is accepted.

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GunChleoc
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Joined: 2013-10-07, 15:56
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Posted at: 2016-02-21, 19:03

king_of_nowhere wrote:

yes, i also agree that the new values are much better. chances among fully promoted soldiers are roughly equal, and among lower soldiers they are not affected.

Yes, this looks much better.

Also, nobody spoke against the proposal of rebalancing, so I'd say we can implement the new values. The only question is whether to do it before or after buil 19.

By the way, we stopped mentioning it, but I suppose also the proposal of swapping two other resources for 2 gold in the price of the atlantean labirynth is accepted.

I already implemented both face-smile.png

Busy indexing nil values

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