Category: Games

Categories
Games

Battle Royale Model

In a battle royale game like Tetris 99 or Fortnite, a player’s rank does not absolutely reflect their skill level. Just by chance, a strong player may encounter a stronger player early on in the match. Since ranking is by elimination and time, a skilled player may be eliminated early and thus rank low.

I thought it would be interesting to model this phenomenon with Python.

In the following code, a list, “s”, of 10 members, stands for 10 players. The numbers 0 to 9 give the skill levels of players, with 0 being the strongest and 9, the weakest.

Two numbers are pulled from the list randomly, then compared.

The larger number is added to the rank list, “r”. The smaller number is added back to the pool of players.

At the end, zero is appended to the rank list because zero always wins. The rank list, “r”, is reversed to give the ranks their proper placements.

#Battle Royale Model

from random import choice

r = []
s = list(range(10))

while len(s) > 1:
    x = choice(s)
    s.remove(x)
    y = choice(s)
    s.remove(y)
    if x < y:
        r.append(y)
        s.append(x)
    else:
        r.append(x)
        s.append(y)

r.append(0)
r.reverse()

print(r)

Here is some output:

[0, 2, 8, 7, 1, 6, 5, 9, 3, 4]

Notice, Player 1 is ranked in the upper half, but barely; yet Player 1 is better than 80% of the players.

Also, although Player 9 is worst in skill, he made 8th place, rather than 10th or last place. One interpretation of this is that in battle royale games, hiding is a good strategy.

Categories
Games

Clash of Clans

Confession

I’ve spent probably around $200 on Clash of Clans.

I started playing 2 years ago and I deleted the game recently.

Gameplay

Clash of Clans boils down to two things: build time & resources.

The reward of diligent play is building on an accelerated schedule. Of course, one can also spend money to build, by purchasing gems.

The trade-off is clear. I wait hours for a building to complete or I can spend gems and complete it instantly. I spend gems to accumulate the resources needed to build when I am short.

After playing a while, one realizes that it would be foolish to spend gems for resources. The rational side started to take over. The rush of instantly upgrading buildings balanced against my bank account. I’d come to a state of equilibrium.

Season Pass

If I’m grinding every month, I might as well buy a season pass to obtain spells & potions.

Everything takes a long time to build. Logging on does not speed up the process. It feels wrong to base one’s life around Clash of Clans. I consciously log on less to play more efficiently.

At the end of the season, the season bank empties. There are more resources than needed, and all the spells & potions are gone.

Thus, buying a new season pass presents itself as an affordable option to quickly spend resources, as long as you plan on grinding. If you buy a season pass early in the month, you can also take advantage of build time bonuses.

Final Thoughts

At one point, I told myself I’d get to a fully upgraded Town Hall 10 and stop. However, sometime after I completed this, I reopened the game. I upgraded to Town Hall 11, and gave myself the same task. After a month, I quit.

Categories
Games

Comparing some Memory Games

There are three components of memory games: position of card, card, and study period. The study period refers to the presentation of information and the time allocated to players. For example, we can present all the information to be memorized at once or partially.

Take the game Memory where there are duplicates of cards in a grid; you flip up cards two at a time, memorize them, and replace them. Naturally, players learn the positions of cards overtime and are able to select them and remove them from the game. Compare this to a game where all the cards are revealed at once: a player has a chance to memorize all the cards, then the cards are flipped over and then he identifies pairs.

When playing Memory, often one remembers a card that has been revealed but not the position. Or oppositely one can remember the positions and sequences of cards that were flipped over, seeing the grid as a grid of where cards have been flipped over. Suppose, you can only remember which cards have been revealed but not their place, then a strategy is: when the sequence of cards in memory has a duplicate, to choose a card that has been flipped over, hoping that you choose the duplicate. In competitive Memory, a strategy if you do not remember the cards is to continue flipping over new cards. Now if a future player tries to reveal the duplicate and fails, then he has eliminated a possibility and perhaps has helped jog your memory as to where the duplicate truly is. The gestalt of card positions is a highly memorable feature.

Another game that is more about card positions than the cards themselves is often played on a computer with a simple grid where grid squares can be turned light or dark. In this case, the gestalt of card positions is the basis for the game. In a short frame of time, a few seconds, a player will see all the positions and then on a separate grid will try to duplicate all the positions. How someone is able to memorize all the positions so quickly is a bit of a mystery. The brighter lights sear a pattern into the visual system. If there are not too many squares, then a person can code the pattern like, “4 connected in an L starting on this square, etc.” quickly in their head.

Another separate part of the memory game is the cards themselves. The cards for example might have a sequence of numbers on them or other relations between them like color or pattern; picture, imagery. We could play a different version of Memory where we are asked by a third party to recover certain cards that may or may not have been revealed instead of just duplicates as a hypothetical example. Another possibility might be to present the information to study in different ways than all or one at a time. All cards of a type might be revealed. This lacks a kind of elegance compared with Memory as a third party is needed to give these presentations.