# Fundamentals

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- This page deals with the most basic operating assumptions of having a wargame such as time, distance, and determining factors.

## Time and Distance

- Time should be dealt with in a manner which fits nicely with the actual operating of the game engine. This probably means cutting up combat rounds into small unit-friendly bits of time for them to do specific things. And there is absolutely no excuse for making life tough on the player and using 60 seconds, 60 minutes, and 24 hours, etc... Having a metric unit of time only makes sense, and since metric distance already exists we may as well use that.

- Let's say that we define a year as roughly the same as an earth-year. Let's cut this up into four periods, and each of those into 100 cycles. Let's also say a cycle consists of 10 hours (2.2 Earth-hours each) which are divided into 100 ticks. This works out to be one tick equals approximately 79 earth-seconds. This seems like a reasonable medium to base game-ticks upon.

- Crossing this with the metric system, we can say that a unit moving 50 kilometers per game hour is moving 500 kilometers per cycle, or half a kilometer per tick. In the context of the game, real-world time units will be totally unnecessary.

## Dice

- Though I don't like to apply dice to the nobility of Wartime and bring it down to the level of other non-computer wargames, they are undoubtedly the best way to produce random numbers. However, one of the cleverest tricks of Wartime is present in the most fundamental use of the dice, and though it may take a little bit of wrapping your brain around it's not really that complicated.

- When you roll a single six-sided die, your odds of getting any given number is one in six. When you roll a pair of six-sided die, however, the numbers are no longer all equally likely. In fact, you are most likely to roll a 7 because there are more ways to get 7 (1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1) than to get, for example, 3 (1 and 2, 2 and 1). This follows basic laws of mathematics and probability, and the distribution of numbers is according to a bell curve. The probability of getting a 7 is the highest, with 6 being equally likely as 8, the odds of getting a 5 are the same as those of getting a 9, etc. down to 2 and 12 which are also equally likely.
- Also, there is a decrease in probability as the number moves away from 7. 4 is less likely than 5, which is less likely than 6. Likewise, 10 is less likely than 9 which is less likely than 8.

- The relation we are interested in is the relative size of the numbers to the likelihood of rolling them. To make my point, imagine that 150 riflemen are shooting at 150 other riflemen. There are a certain number that you might reasonably expect to kill given that each man will hit the enemy a certain amount of the time. Let's say that one-third of shots result in hits. So 150 riflemen can expect to kill 50 of the enemy.
- Now, roll two six-sided dice for the entirety of the 150 men (rather than one for each, as is common practice in wargames). A 7 would correspond to killing exactly 50 men, as it is the most likely outcome, with an 8 corresponding to proportionately more being killed, and a 6 to proportionately less. Note that six-sided dice are absolutely terrible for this sort of thing, because... it's based on
*six*for crying out loud.

- After considering a number of possibilities, I thought it would be best if we could somehow get this system to work out of 100, and preferably get it to be as flexible as possible. Now, there are no 100 sided dice, and nor would we want one. But five twenty-sided dice can equal 100 at the maximum, and 5 at the minimum. This creates a focal point at about 54, but the bell curve is much nicer. It's more rounded, with more variation possible. (ten twenty-sided dice may be worth considering as well, ranging from 10 to 200)
- Now, to illustrate the flexibility and utility of this method, let's say that we have a pass/fail test. To define a probability, let's say 54 +/- (plus-or-minus) 10. So from 44 to 64 means the test is passed, and anything else is a fail. Extending this is easy. If we were testing a single rifleman, this would work beautifully. It even has a built-in law of diminishing returns. The more you trained your riflemen, the larger the range gets, but an increase from 54 +/- 5 to 54 +/- 10 is much larger than an increase of 54 +/- 10 to 15 +/- 15 even though you added 5 to both sides in both cases.
- To make this system even more flexible, you might subtract a range from the middle, or declare outlying numbers within it as well, like 54 +/- 5 and 75-80 would be passing rolls.

- However, that's not the issue that was at hand. We needed to determine how many out of 150 riflemen hit their targets, with 50 out of 150 being the bell curve average. At this point, the result should be fairly straightforward. We know that rolling a 5 (five ones) means that nobody hit, and that rolling a perfect 100 (five 20's) means that everybody hit. Of course, both have a 1 in 3,200,000 chance, so don't expect to see that too often. Now we have 100 possibilities (we're skipping the bottom four to make it a cool 100- beats the heck out of using 95) and 150 men. So each number corresponds to 1.5 men. Rolling a 54 gives you 50 hits. Rolling a 55 gives you 51.5 hits, and 53 produces 48.5. Rolling a 74 then gives you 80 hits (difference of +20 from 54, and each is 1.5 hits, so +30 hits). Rolling a 34 gives you 20 hits (difference of -20 from 54, and each is 1.5 hits, so -30 hits).

- Now this isn't entirely correct because we should be counting the greater-than-50 hit portion as double the less-than-50 portion because it is twice as large. Note how a negative difference of 20 dropped the number of hits from 50 to 20, while a positive one increased it to 80. The difference is thirty in both cases, which is a perfectly reasonable situation. But the number of hits will hit the dirt at 20, a difference of 34 * 1.5 = 51, which would drop the number of hits to -1. By the same token, rolling a 100 gives you a difference of 46, which adds 69. So the maximum possible hits is 119. If we were modelling, say, the Civil War, this would be nearly perfect. The odds were in fact skewed towards hitting nobody at all, and the lethality of a salvo of rifle fire was capped fairly tightly. 150 men could hardly hope to kill 120 in a single volley- it would have been unbelievable.

- If you're confused, I don't blame you. Forget what I just said. Here it is in very simple terms-
- Get the number of men and the chance they each will hit.
- Multiply these two together to get the number who
*should*hit. - Divide the number of men by 100. This is your variation per number on the dice.
- Roll the dice and add up the pips they show.
- The median number for rolling five twenty-sided dice is 54. Is the number you rolled above or below 54? If it's above, you got more than the bell curve average. If it's below, you got less.
- Get the difference between the number you rolled and the median, 54.
- Multiply your difference by your variation per number on the dice.
- Add or subtract it from the number you were "supposed" to get, accordingly.