Random function's maximum value is reached quickly

[frew]

Hello,

I just wanted to mention what I think is an interesting observation as I did some experiments

with the Random() in AutoIt.

I'm amazed at how quickly this returns a maximum value for Random()

What does this tell us about the Random function algorithm?

I like the algorithms results, ie nicely equally distributed, but I just find it

a bit curious that it should actually reach the exact maximum so quickly,

even when each time through the loop, the value of $x becomes the new minimum value in Random()

I guess it says that the Random() algorithm is designed to reach it's maximum value sooner than

the maximum value within a reasonable amount of time for general usages of the Random()

Generally takes less than around 25 times through the loop

$x = 0
$i = 0

While 1
;each time through the loop, the value of $x becomes the new minimum value in Random()
    $x = Random($x, 1444000222, 1);1 billion, 444 million
    $i = $i + 1
    MsgBox(0, "" & $i & " times through the loop", $x, 1)
    If $x = 1444000222 Then
        MsgBox(0, "" & $i & " times through the loop", "reached maximum random value of " & $x & "")
        Exit
    EndIf
WEnd

Siimilar numbers of loops are needed to get to the maximum for 5000, interesting...

$x = 0
$i = 0

While 1
;each time through the loop, the value of $x becomes the new minimum value in Random()
    $x = Random($x, 5000, 1);only 5 thousand
    $i = $i + 1
    MsgBox(0, "" & $i & " times through the loop", $x, 1)
    If $x = 5000 Then
        MsgBox(0, "" & $i & " times through the loop", "reached maximum random value of " & $x & "")
        Exit
    EndIf
WEnd

Thanks for any ideas about this.

frew

[PsaltyDS]

I question your methods. The distribution looks pretty standard here:

Global $sMsg = "", $iMax = 1000, $iIter = 0

For $i = 1 To 100
    $sMsg &= $i
    $iIter = 0
    While 1
        $iIter += 1
        $n = Random(1, $iMax, 1)
        If $n = $iMax Then
            $sMsg &= "; $iMax (" & $iMax & ") reached in " & $iIter & " iterations" & @LF
            ExitLoop
        EndIf
    WEnd
Next
ConsoleWrite($sMsg & @LF)

[frew]

Thanks for your nice code PsaltyDS.

Yes, that shows the nice distribution very well, and how the Random() max is reached in a a way that is not more frequent than would be expected.

My code example was not to test the distribution results. I was just interested in how, when the Random() minimum value is increased each time through the loop, the Random() maximum seems to be reached so soon. I know increasing the Random() minimum value each time through increases the likelihood of getting to the Random() max sooner, but I was not expecting the Random() max to be arrived at so soon, even with the Random() minimum being increased each time through the loop.

Oh well, not that important really I guess. I was just doing some Random MouseClick tests that increment along the x axis, and noticed that the Random() max (the exact max number) seemed to be reached much sooner than I thought it would be...as in my code examples.

Thanks for your reply and for your nice code example.

frew