*The First Example
*

Let’s say you and I are playing a duel of yugioh, and for the sake of argument that we both are playing the exact same deck.

Furthermore, we will play precisely the same in any given situation. In fact, we will always make the optimal play. That is that we will crunch the numbers and make the play that gives us the best chance of winning statistically. So that in any given game position, were the opposite player in each positions they would make the same play as was actually made by the other.

In this environment, what is the chance that I will win? Well, assuming no ties, the answer is .5. Were we to play an infinite number of games, I would win half the time and you would win half the time.

That is because our skill level is the same. As such all of our duels are determined by luck and solely by luck, which makes sense since we are both winning 50% of the time.

*The Second Example*

Suppose now that we introduce misplays. That is that in certain situations I will crunch the numbers incorrectly and make a play that was not the one that gave me the best chance of winning but one that gave me a lesser chance of winning.

In our analysis of the games we will play now, you will have a greater chance of winning than .5. That is, you will win more than half the time as you will play a perfect game and I will not. I will, of course, have less of a chance of winning than .5 and, assuming no ties, our chances of winning will add up to 1. I hope this concept is clear to everyone.

As you play a perfect game it is clear that any time you lose it is due to luck and solely to luck.

But what about me? Well, actually, we can go through the games we played and each time I lose we can attribute it either to a decisive misplay or luck.

That is that each game I lost was lost either due to luck, as in I played perfectly, or I made a misplay but the misplay was not decisive, that is, irrelevant. Or I lost because I made a decisive, fatal, misplay. That is, had I played perfectly, optimally, I would have won but I did not play perfectly and so I lost.

But this brings us to a radical conclusion. That is, that every game is determined either by skill alone or by luck alone. That is you can never lose due to a combination of lack of skill and bad luck. You can only lose due to either a lack of skill or bad luck.

And this principle is groundbreaking and earth shattering.

Let us call the number of games we play G and for the sake of argument G will be constant and will equal 10 and there will be no aberrations.

In the first example, our games might look this, with M being that I win and Y being you win:

MMYYMYMMYY

But if we break this down into the number of games determined by luck versus the number of games determined by skill we see this:

LLLLLLLLLL

That is, all the games were necessarily determined by luck as we both played optimally.

The second example would look more like this:

MMYYYYMYYY

As I misplayed and you did not.

Let’s look at the luck vs skill determination.

LLSLLLLSLL

As you made no misplays, any game I won was necessarily won by luck and any game where I played perfectly and still lost was necessarily determined by luck. And any games where I made a fatal misplay were, again, necessarily, determined by skill.

As you can see then just as, assuming no ties, M+Y=G, that is, the number of games I win plus the number of games you win equals the number of games total, so do L+S, the number of games determined by luck plus the number of games determined solely by skill, equal G, the number of games played total.

I hope this insight is appreciated by the community as much as I appreciate it. It really affects how you view the game and it has a number of implications for banned list design.