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Subject: Probabilities and Combat Resolution rss

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David Perez
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As everyone else here on this forum I too want to design my own game. Then somewhere along the you ask your self, How do i resolve combat or assign damage, or model hitting. The real question you should ask yourself is what probability do I want to model? Looking at the many different aspects


Part I: Random Variables

Deterministic:

In this case, the resolution is that the same outcome will happen every single time for the given scenario. Very good examples of this are:

Chess: Where if you land on top of someone you kill the other piece and win the battle.
P(x)= 1, x= Move into opponents square [Win]
P(x)= 0, x !=Move into opponents square [Lose]

Diplomacy: Where nothing happens on a tie, but who ever has the most strength/army and is winner take all.

P(x)= 1, x= Have more total armies than opponent [Win]
P(x)= 0, x= Have less or equal armies [Lose+Tie]

Antike: You trade armies at a 1:1 ratio,strongest wins at a cost, with everyone losing on ties.

Nice things about deterministic resolution is that they are very fast to resolve. So fast to resolve that you could resolve 17 possible permutations of what could happen next turn. Deterministic combat systems push the focus on maneuver and other aspects of the game, so that players force the desired outcome.Depending on who you ask this can be a good or bad thing. Having the game be to deterministic can result solving the game ahead of time Tic-Tac-Toe or have an initial set of optimal moves.

Pros:
Simple to Understand
Fast to resolve

Con:
Can actually slow the game down. Players search the possible permutations of 'actions' to choose the optimal one.


Non deterministic
By introducing randomness in the game, from any source you are reducing the ability to predict the future and play the game to far in advance, pushing the player to thing more about now than turns from now. The more randomness/variance will each game unique and not turn out exactly the same.

Dependent Random Variables
These methods of generating random numbers, where each result influences the chances for the next result and so on. These easiest to think about this is that it has a 'memory effect', the current result will take into consideration all the past results.

Players
You must have these players to play games with, a solo deterministic game which be solved eventually and is more like a puzzle.Sudoku
Humans are really really bad at generating independent sequences of numbers

Pros:
Cheap to include in your games
Have lots of re playability
They Buy games = $$$

Cons:
Randomness hard to predict ahead of time, strategies may not be coherent
Each additional player increases play time (some players more than others)

Cards/Bags of Chits/Bingo Balls
Poker Cards are perfect example of dependent variables. In a poker deck there are 13 cards of 4 types of 'suits' for a total of 52 cards. Once a card is drawn the probability of that card being drawn again is '0' until there is a reshuffle.

Scrabble In scrabble you have several wooden blocks in a bag with letters on them. The letter distribution is fixed and you start the game with the same set of letters, each player draw one.

Bingo A spherical chambers stores several enumerated balls, each one unique. Each player has a card to record the balls that have come out, an individual ball can not come out multiple times.
This allows going through each of the possible outcomes if the game is long enough. So over the short term the game is random, as more cards are exhausted it becomes deterministic.

This also means that you will cycle through the same number of bad/good events, unless the pool is shared between players. The pool will remember what has been drawn, not by who.

Pros:
Self Correcting "Bad Luck" is pleasurable (according to the believers)
>Cards can contains instructions or complex outcomes

Cons:
>Cards have a high component cost
Reshuffling/Pool size design decisions affect cost and reshuffling/downtime
More players sharing a pool, reduces the self correcting nature

Independent Random Variables
These are systems that have no 'memory' to them, a coin doesn't know how many times its been flipped. Each time you generate a random number its has no bearing on any future numbers.

P(heads)= .5
P(Tails)= .5

Coins/Dice as the most common form of Independent Random Variables. Each time you roll a dice you get an new result. Dice tend to be cheap plentiful and can be reused in multiple games. Unfortunately for some using them requires regular sacrifices to http://en.wikipedia.org/wiki/Fortuna (Lady Luck)

Pros:
Cheap/Plentiful

Cons:
Limited number of Outcomes
Some refuse to play games with Dice.
 
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David Perez
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Just Saving Space

Part II: Distributions

 
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David Perez
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Part III: Putting the Mechanics together
 
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Nigel Buckle
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Thornton Heath
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NSKN are publishing my next game :)
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Omega Centauri Published in 2014
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Deterministic combat doesn't always slow a game down though.

Depends on the number of units in the game, size of the battles, number of types of unit, and additional factors you might have (special powers, cards etc).

In Omega Centauri I use a combat system like Civilization & Antike, but technology alters things a bit (so with the right tech you fire first, inflict a double hit or ignore the first one). In my game the stacks of units are usually small (defender will have at most 4, more often 3 or less, and attacker is likely to bring at most 6).

Deterministic combat means you work out the result before you attack, with a random system you have to work out the odds of winning, then attack and then resolve the combat ... which takes longer.
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