We were given 5 minutes to submit an answer to the preceding question in writing. Apparently, the selection for suitable candidates for magic has already begun even before the timeframe that was stated.

The chance of a coin flip is 50% on either side. Thus, getting two heads in a row is half of half, and three is half of half of half.

Eleven occurrences happened in a row, so the overall chance is impossibly low. But 5 minutes isn't enough time to give a correct answer to halving eleven times.

According to what he said, causing an extremely unlikely result takes a lot of exertion, and isn't likely something he can do while casually talking to us.

Nobody saw the coins before he flipped them, so there is a good a chance that these coins he used are fakes with heads on both sides, and so no magic was used at all aside from making people think they're standard coins.

The chance must be 100% that this would happen, and since no magic was needed to change the result, there would be no exertion on his part.

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'Some of these guesses are interesting, so I think I should address them so you leave this class with the correct impression.

First, quite a few of you picked up that repeatedly changing easier probabilities is easier than changing a single extremely rare event. This principle can be useful for you in the future - rather than trying to alter one occurrence, it's less exhausting to figure out what can cause it to happen to eliminate its causes separately instead.

One of you speculated that the coins I'm using have heads on both sides. This isn't true, you can check it for yourself, but it is true that you were not given a chance to check the coins before I tossed them, and in the situations you may find yourself stuck in, you may be misled if you make conventional assumptions, and you can mislead your enemies if you tempt them to make conventional assumptions.

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Another guessed that no magic was involved because I'm precise enough to flip a coin in such a way that it will land on the side I intend it to. This is a high compliment, but I'm not that skilled, even though some others in this world may be.

However, only one of you in the entire class got the correct answer to the trick question, because I indeed misled all of you into making an assumption, but it's not the coins being fake. Alicia Reinhart, would you like to explain what happened here to the entire class?'

Oh, it's the 'observing your surroundings' girl.

'Erm, this is a stone building, so the ventilation isn't very good when we came in, but when erm, sorry, may I ask your name?'

'Joshua.'

'When Joshua was speaking earlier, his hair blew in the wind, even though there shouldn't have been any wind here. While it's not impossible that it suddenly started blowing through the window, Joshua isn't sitting next to the window, so his hair shouldn't have been the one to billow. The likelihood that this can happen is not zero, but it's very low. Gwyn flipped the coin much higher than normally people need to for a coin toss, so I thought it might be possible that instead of fixing the result of the coin with magic, he simply changed the result when needed by altering the flow of wind between the coin and the table after seeing what it would likely turn into.'

'I don't think Alicia is the only person in this class who noticed this, but she was the only one to connect the dots. Make sure the rest of you learn to as well. This is magic - looking at a situation, spotting chances where you can change non-zero probabilities into reality with the least possible effort, and doing it by willing the result into reality.

Fireball is extremely inefficient to turn into reality because of the extremely unlikeliness of sudden explosions in the middle of nowhere, so people who want its effects to scare goblins and the like with normally carry bags of powder to throw before detonating them. Mist is more efficient for early morning ambushes and very exhausting to execute in the middle of the afternoon.

For every situation, there's going to be results that will benefit you more. For every result, there will be methods of achieving it that require less effort. The laziest solution is the best solution for magic, because once you run out of stamina, you'll have problems regardless of whether you're using magic as a primary method of achieving what you want, or just a support method.

The ability to think of what results are better and which methods to achieve those are lazier is what we in the adventuring business call intellect, and this is why it is important for casters to be good at this.'