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No-luck Weighted Rounding: 1/29/2022 12:26:18


καλλιστηι 
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Assume normal kill rates 60/70. U(a) is the smallest integer bigger than a. Rounding matters if the result would lead to a different amount of armies killed (for example attack 3->2 matters, but 3->1 doesn't).
If you attack a neutral territory with 3 troops, you should kill 1.8 troops. The current system either rounds it to the nearest integer or gives you U(1.8)-1.8 = 0.2 probability to round down, otherwise rounds up. I suggest a compromise between these two systems:
You have a bank you|neutral. The bank starts on 0. When you make an attack of y troops (would kill 0.6*y =x troops), Warzone checks, whether rounding matters. If no, proceed as during straight rounding. If yes, check, whether you|neutral bank is bigger or equal to U(x) - x. If yes, you kill U(x) troops and U(x)-x is subtracted from your bank. If not, 1+x-U(x) is added to you|neutral bank. You can see the current value of you|neutral bank and during the planning phase, Warzone will tell how many troops your attack will kill (if neutral doesn't deploy any troops/ attack you; both these actions could change the expected bank value).
In a game, everybody would have a bank with everybody (so there would be you|neutral, you|opponent, opponent|neutral, opponent| you, neutral|you, neutral|opponents banks in 1v1). You can see the value of any bank affecting you, assuming fog is at most normal. You can see "expected banks" (=assuming nobody but you executes orders) of everybody during the planning phase (when you select an order, "expected banks" before that order would be displayed somewhere). The host can set starting banks. This feature would have a big level requirement to not discombobulated newbies.


Example: you have 0 in you|neutral bank. You tap Uganda with 1, kill 0 and set you|neutral bank to 0.6. You attack Sweden with 3 troops, kill 2 troops and set you|neutral bank to 0.4. You attack Norway and Finland with 3, killing 2 in each and setting you|neutral bank to 0.
You attack Denmark with 3, killing 1 and setting you|neutral bank to 0.8. You attack Poland with 3, killing 2 and setting you|neutral bank to 0.6.


I think No-luck Weighted Rounding would offer a more predictable alternativity to Weighted Rounding while keeping risk management (if you make all orders with just enough armies to take a territory, a small interference from the opponent may result in a drastically different outcome) and slowing down rising as WR does. It would also present new strategies (tapping a neutral is now a relevant move to rise your bank. Order of attacking neutrals matters because of leftovers).

Edited 1/29/2022 12:33:31
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