Lanny's Mario Maker Rant

## Origin

On August 26th, 2017, The Game Theorists posted the video Game Theory: Super Mario Maker, BIGGER than the UNIVERSE!, in which Mat Pat tries to calculate the number of "fun" Mario Maker levels. After watching this video, Lanny, a math major, noted many flaws in Mat Pat's math and wrote a thorough reply detailing said flaws. After attempting to show Vanesa his comment, it was found that the channel had hidden his comment, which had been gaining traction before suddenly stopping.

Proof of his comment being hidden, as well a link to the original comment, can be found here.

## The Rant

First of all, he claims that you can account for the four game styles by multiplying by four. This \*would\* be true, except that different game styles have access to different items that don't always have equivalents in the other styles, or have more variants in one style than another (e.g. Goomba Shoe has eight variants, but only exists in SMB and SMB3 styles; its equivalent in other styles is the Yoshi Egg, which only has four variants). Without the same number of items/variants, you can't guarantee that one style has the same number of levels as another, thus you aren't just adding the same number four times, so you can't multiply by four.

He then makes the same mistake with level lengths (the number of tiles long a level can be). He multiplies by the number of possible level lengths, which implies that there are just as many possible levels you can make in each possible length, which is obviously not true (obviously there are more possibilities when you have more space to work with). Additionally, he makes an error when calculating the number of possible level lengths (he subtracts the min from the max, when he should be subtracting everything \*less\* than the min from the max; he should 217 instead of 216).

He doesn't explain very clearly what he does when calculating the number of possible layouts, so I can't explain exactly \*what\* he's doing wrong, but he gives the impression that he's doing something along the lines of taking all the possible things that can occupy a single tile (e.g. Goomba, bottom half of door, top-left corner of Bowser) and bringing it to a power of the number of available spaces. The mistakes he's likely to have made here are A. failing to account for the fact that certain tiles \*must\* be adjacent to certain others (e.g. bottom half of door below top half of door), B. failing to account for tile/entity limits, C. failing to account for the ability to overlay certain things on top of each other, and D. not having a proper number for the available spaces, since he's already tried to account for the length of the level.

He also fails to account for the heights of the starting and ending platforms and the ability to choose a different theme and scroll settings for the subworld than the overworld.

Now he has his number for the number of creatable levels in Mario Maker, but now he wants to narrow it down to the number of levels which are clearable and "fun". He claims to use Fermi Estimation (a process of taking known figures to estimate something; the example Wikipedia gives is estimating the number of piano tuners in Chicago using the average rate at which a piano needs to be tuned, the time it takes a tuner to tune a piano, and Chicago's population, average number of people per household, and average number of pianos per household), but really just pulls random guesses out of his a\*\*. He also thinks he can be accurate within one million, which is obviously stupid because A. Fermi estimation isn't always that reliable, B. no estimation utilizing a 12,445 digit number is gonna have that small of a margin of error, and C. he doesn't even show that many digits, so what's the point of even claiming this?

He has us assume that 0.00001% (10^-5 %) of levels are clearable, and 0.00000001% (10^-8 %) of levels are "fun". He then says that that's the same as saying that 0.0000000000001% (10^-13 %) of levels are clearable and "fun", which just shows that he doesn't know how percentages work (it should be 10^-17, or, if he wants to keep it in percentages, 10^-15 %).

He then says that he multiplies his number of levels (1.8\*10^12444) by that number to get 1.8\*10^12431 (another slip up with percentages; 1.8\*10^12444 times 10^-13 \*percent\* is 1.8\*10^12429) and claims "it barely made a dent" and "that's why Fermi estimation works." First of all, that absolutely made a dent; he goes on to explain how big this final number is, and dubs it a Marioplex, but he just subtracted 9,999,999,999 Marioplexes of levels, which I think qualifies as a little more than a dent. Secondly, even if it \*had\* "barely made a dent," the starting number being close to the final number does nothing to demonstrate that this method of estimation is in any way accurate.