The first paragraph of the wikipedia mentions it's relation with entropy.
The wikipedia link itself has science related articles, none of which point to the other study you mentioned.
By reading the entropy entry on wikipedia, you'll be able to see how it directly relates to the possibility of the statistical distribution of the data.
The data you're taking into account, those 1002 reports are innacurate.
You should not take those into account, and of course, you'll need a much larger pool to start evaluating what the chances really are.
So no, we cannot detect a clear pattern, as the data cannot be taken into account.
Yes, it was designed against a high value gift, of course.
Perhaps, its how you're approaching the randomness of the gift.
Santa gives 6 prizes, 1, 2,3,4,5,6 gold, each related to the side of a six sided dice.
That means that you have the same chance to get them, all at random.
What if santa gives the the same prizes, but now, the rules are:
if you roll, 1,2 and 3 on the dice you then have to flip a coin and you'll get 1 gold if heads and 2 gold if tails.
if you roll, 4 and 5 on the dice you then have to flip a coin and you'll get 3 gold if heads and 4 gold if tails.
If you roll 6 on the dice the you have to roll another dice, if you roll 6 again, you then flip a coin and you'll get 2 gold if heads and if tails you roll another dice a 20 sided dice, if you get 20 on the dice you get 6 gold, all else, you get 1 gold.
This means you have a very, very different chance of getting the money but still, both are random, the same kind of random.
To be random and to have the same probability chance are two very different things.
And 'I guess your concept is an extremely heterodoxy approach in order to conclude that it is a random event.'
It's not my concept, I have no orthodox or heterodox way of approaching as this is a statistical discussion that can't have my views of the world, none of which I posed, ofc.
I don't have a philosophical idea about the subject nor did I mention any other approach besides the Entropy, which has no philosophical intent or view.
I merely pointed out a few things.
'Random is hard'
'C++ source code used srand(TimeInMillis);'
'Study does not apply'
'Data is not reliable'
This is a great video somewhat related to the topic.