Generate and use pseudo random numbers

Basic idea

It is very difficult for a computer to generate truly random numbers. However, functions exist which are computationally efficient and generate numbers which seem reasonably random statistically-speaking. These functions are called pseudo random number generators, and the numbers they generate are called pseudo-random numbers. The methodology of how these functions generate these numbers is a computer science topic, beyond the scope of this class. However, given an already-existing pseudo random number generator, it is not difficult to use the function effectively. You just need to understand a few basic principles:

The pseudo random number generator is truly a function. It accepts one number as input and generates one number as output.
The input number is called the random seed.
The output number the function generates is the pseudo random number and is automatically used by the function as the input for the next time the function is called.
If we do not initially set the random seed, it may continually default to 0, meaning the function will always generate the same set of random numbers every time. In a game environment this would be deadly, because it would mean we basically have the game behaving exactly the same way every time we play.
To avoid this, we must start with a reasonably random random seed. Once we have this, the function will happy generate pseudo-random numbers.
One way to create a random seed is to use a very fast counter to time how long it takes for a user to hit a key. The resulting counter value will be random enough to serve as a reasonable seed.

Application

Application is demonstrated in hello-random.asm

Basic Generation of Random numbers

add to your main code, after a SECTION declaration (perhaps right in front of or behind memory.asm):
```
INCLUDE "gbrandom.asm" 
```
In your main code, perhaps right before your main loop, create a screen which tells the user in some sense "press any key to continue."
- This could be your title screen for your game.
- Print this screen to the display, as you have now done many time, perhaps using mem_CopyVRAM
immediately following your call to mem_CopyVRAM, add to your code:
```
        call    MakeRandomSeedByTimingKeypress 
```
- this will set a random seed by running a tight loop, counting how long it takes for the user to press any key.
when you want a random number, add to your code:
```
        call    Rand16          ; put rand # in hl 
```
- as the comment explains, this will put a random word in hl.

Using random numbers

when you call Rand16, hl is loaded with a random word i.e. a number between 0 and 65535.
- if you need a number between 0 and 255, just use h or just use l.
- You can use bitmasking to easily change the range of your random number to any power of 2 minus 1 (1,3,7,15,31,etc.). For example, if you need a number between 0 and 15, do a bitmask of #00001111 on either h or l and use the result:
```
     call     Rand16
     ld       a,l        ; use h if you have something against the letter l
     and      %00001111  ; now a contains a random number between 0 and %00001111=15.
;    and      %00000011  ; If we did this instead of the above line, a would contain a random number between 0 and 3.
```

if you want something to happen with a certain probably, one way is to use the carry flag. Examples:

50% probability:

     call     Rand16
     ld       a,l
     cp       128        ; a - 128
     jr       c,whatever ; our random number between 0 and 255 is less than 128

25% probability:

     call     Rand16
     ld       a,h        ; it doesn't matter whether we use h or l
     cp       64         ; a - 64
     jr       c,whatever ; our random number between 0 and 255 is less than 64

25% probability:

     call     Rand16
     ld       a,l
     cp       64+128     ; a - 192
     jr       nc,whatever ; our random number between 0 and 255 is greater than or equal to 192

4ish% probability:

     call     Rand16
     ld       a,l
     cp       1        ; a - 1
     jr       c,whatever ; our random number between 0 and 255 is less than 1 (i.e. == 0

For those of you who love the z flag and don't care for the carry flag, you can use bitmasking to set your probability

50% probability:

     call     Rand16
     ld       a,l        ; use h if you have something against the letter l
     and      %00000001  ; a now contains a random number between 0 and 1.
     jr       nz,whatever; it's not 0, so it must be 1. We got a 50/50 chance.

75% probability:

     call     Rand16
     ld       a,l        ; use h if you have something against the letter l
     and      %00000011  ; a now contains a random number between 0 and 3.
     jr       nz,whatever; it's not 0, so it must be 1,2, or 3. We got a 75% chance.