ProzacIsBack posted...

You're quibbling over semantics now.

Rephrased as "is he the better player?", the answer is no.

If the question is "did the game pop up with Winner! and score him a point?", the answer is obviously yes; without consistency, however, who gives a ****.

The circumstances in which a lesser player can sneak out a win against overall much better players have been explained.

(which has nothing to do with pr rog 'cause rog is gdlk)

There is a massive difference between if someone 'deserved' a win and if 'is he the better player'. This has the trappings of what is called a 'straw man argument', in which you choose a different (more winnable) argument to attack instead of the one presented. But I don't really view this as an argument, as you no doubt do, because my post didn't require a response. It simply was a statement of fact.

This does however remind me of another problem, one that is of the same subordinate type (strategic consistency problems in choice systems).

Some 2 or 3 years ago when I was writing a text book on the subject, an interesting part of optimization was determining the weight of chance of success versus effectiveness of success. There are several other factors you have to take into account (binary outcomes versus variable outcomes, intensity of information stream, information availability, historical choice pattern, etc), but these two are enough to demonstrate the basic idea.

Essentially, the chance of success can be interchanged for effectiveness success only relative the sample size required of performance.

Let's say you are playing a game with a coin toss that can be tuned to give % outcomes on command. In this game, if the coin comes up heads, you get points, and tails, your opponent gets points. First one to some number of points will win.

Now if I gave you some options, which were:

1. 85% heads chance, 1 point for heads, 2 for tails. 10 points

2. 75% heads chance, 1 point for heads, 2 for tails, 1000 points.

In the first example, that seems like an easy one, you will win most of the time. In fact, if we lowered it to 66% it would come out about even, you winning half the games, him winning half the games.

In reality 85% has some inefficiency built in. The reason is its a 10 game sample with a opponent that needs to score half of what you have, you really only need about 82% to win convincingly. Many systems in life have the ability to reduce the chance of success for increased effectiveness of success, so here we can actually sacrifice 3% for some increase in points (assuming ceteris parabis, and that there isn't some choice that has better odds AND better effectiveness, we would just call that the better choice).

In the second example, we have a similar problem, but here with the 100 game sample, we actually would need about 79% to win convincingly. So we are short 4% here.

Just something to think about.