Hat or not, the idea that there are no similarities is absurd. Both, when taken with the aim of playing well, are games of tools, strategy, psychology, and raw processing power.
You can argue that the differences are greater than the similarities, I suppose. But the number (and style) of similarities is significant, making the comparison perfectly valid.
A poker player who doesn't see the comparison with chess doesn't understand chess.
A chess player who doesn't see the comparison doesn't understand poker.
Every game has an opening.
Every game has a middle.
Every game has an end.
Name any game-Risk, soccer, Scrabble, baseball, etc. All require some skill to become good. Any game can be compared to another in this way. It does not make them similar.
In the Wikipedia article on the Elo rating system
http://en.wikipedia.org/wiki/Elo_rating_system
it is stated that: "A player's expected score is his probability of winning plus half his probability of drawing."
Why are they talking about probabilities/chances if there is no luck in chess?
The use of probability/statistics for ratings is simply to provide a mathematical model which can account for overperformance (improving players) and underperformance (aging players, players who are rusty, etc). It is a convenient way of saying e.g. two equally strong players should generally draw or trade wins, and of quantifying in some way the skill differential.
First, let me say I don't disagree with anything you wrote in your post #45. We can argue about the relative contributions of luck and skill to each game, but I think you are right in principle.
However, consider this... If two players have the same Elo rating their probability of winning or drawing is equal. Why then should one or other player win a game at all? If both players are equally skillful, isn't a win/loss due to "luck" - intrinsic (i.e. human) chance factors?
If two players' ratings differ by 200 Elo points, the more skilled player would have anything between a) a 75% chance of winning and a 25% chance of losing, and b) a 50% chance of winning, 0% chance of losing and 50% chance of drawing (according to Wikipedia). That means that, despite the 200 Elo points of skill differential, there is still a substantial chance of the lower rated player winning or drawing against the more skilled player, who would always win if chess was 100% skill. What a difference that 1% of luck makes!