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2014-10-30 19:59:13
10 votes, rating 4.8
Dynamic Gold.
I feel like this is a question I should already know the answer to, but can anyone explain the concept of dynamic gold in tournaments to me?
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Comments
Posted by Rabe on 2014-10-30 20:12:57
I'm pretty sure it just means:

You win, you get an additional 10k, added to your roster after the match.

I don't think it's more than that - maybe in a later stage of the tournament, but I doubt it.
Posted by Jauna on 2014-10-30 21:15:38
https://fumbbl.com/index.php?name=PNphpBB2&file=viewtopic&t=24663

The concept is explained as a formula in Christer's post. Please feel free to calculate the odds of getting rich fast :)
Posted by Wreckage on 2014-10-30 22:47:23
Ok, let's decipher this:

function Knockout_dynamicPrize($numRounds, $round) {
$prize = 10000 * min(10, 10*pow($numRounds,3)/125) / ($numRounds - $round + 1);
$prize = round($prize/10000) * 10000; // Round to nearest 10k
return $prize;
}

Ok, now ignore all the code stuff.

$prize = 10000 * min(10, 10*pow($numRounds,3)/125) / ($numRounds - $round + 1);

This is the important statement.

We have two functions in there that aren't defined. Min(a,b) presumably means whatever is smaller a or b. Pow should be the power function for pow(a,b)= a^b.

So, lets focus on the pow part for now.

pow($numRounds,3)

Lets say we have a 4 round tournament, so we get:
pow(4,3)= 64

for the min function we get then:
min(10, 640/125) = min (10, 5.12);
5.12 is smaller than 10, so 5.12 is used.

now lets look at this part of the $prize calculation:
($numRounds - $round + 1)
$numRounds = 4
and
$round is a variable starting at 1 and going towards 4.
This is the number the final amount of gold will be divided by, meaning in the final round it will be divided by 1 (not at all), and in the second last round by 2, third last by 3, fourth last by 4 and so on.

For round 1 we get then for:
$prize = 10000 * min(10, 10*pow($numRounds,3)/125) / ($numRounds - $round + 1);

this:
$prize = 10000 * 5.12 / (4 - 1 + 1) = $prize = 10000 * 5.12 / 4 = 12800

The whole thing is rounded now: and you get 10k in game one.

Now for games 2-4 we simply change what this is divided by:
round 2: 51200 / 3 =~ 17067 =~ 20,000
round 3: 51200 / 2 = 25600 =~ 30,000
round 4: 51200 / 1 = 51200 =~ 50,000

Posted by Wreckage on 2014-10-30 22:57:53
Now lets compare to a 3 round tournament:
All that changes is the power function again, so:
for min (10, 10*pow(3,3)/125) = min(10, 10* 27/125) = 2.16

Now for games 1-3 we get:

round 1: 21600 / 3 = 7200 =~ 10,000
round 2: 21600 / 2 = 10800 =~ 10,000
round 3: 21600 / 1 = 21600 =~ 20,000
Posted by Wreckage on 2014-10-30 23:06:33
finally would be interesting to see why there is the maximum of 10 incorporated and how many rounds a tournament needs to have until its reached. The consequence would be that any longer tournaments wouldn't sprout any additional money. I think I can about estimate it. 5 power 3 is 125, so divided by 125 and multiplied with 10 is ls already 10.

We can deduct from that that the 5 round prize money is the maximum amount of money people should recieve for this sort of tournament.

This time I'll count backwards so you can estimate the winnings for round 6, 7 etc.

Final: 100000 / 1 = 100,000
Semifinal: 100000 / 2 = 50,000
Quarterfinal: 100000 / 3 =~ 33333 =~ 30,000
Round of 16: 100000 / 4 = 25000 =~ 30,000
Round of 32: 100000 / 5 = 20,000

Posted by Wreckage on 2014-10-30 23:19:01
Ah what the hell, I almost wrote everything up, so might as well add the last bit. For the five+ round format:

Only 10,000 you'd recieve starting with the 7th round counted backwards.

And 0 bonus gold you'd recieve starting with the 21st round counted backwards.


Meaning in a 21 round KO tournament with dynamic gold you would recieve no additional gold in the first round.
Such a tournament would need 1,048,576 participants.
Posted by monk12 on 2014-10-31 01:09:32
Rated six for inspiring the piles of math in here. Thanks Wreckage! Very interesting.
Posted by Rabe on 2014-10-31 01:23:16
Well, if that's correct, there's more money in it than I thought! :-)
Posted by liquidorange on 2014-10-31 02:25:44
This is an awesomely detailed answer to a question that has bothered me for a while. Thanks, Wreckage!
Posted by the_Sage on 2014-10-31 10:53:19
What's really important here is the way the tournament is set up.
For example, compare the Warpstone open:
4 round quali, 4 round main event
to the FUMBBL cup:
8 round main event
(not sure about the actual numbers though).
The point is, even though you need to win the same number of successive wins, the latter has much bigger payouts later on.