Mathematics vs. Luck

I like randomness to scale with effect. Less random = more reliable, less spectacular, and vice-versa, like picking between a card that always does 1 damage and another that has a X% chance of doing 3. There is always a point where I will choose poorer odds if the result is more interesting than the certain outcome, or if I am desperate and near to losing anyway.

Mathematics and luck are not totally opposite, it depends about how much luck is involved. I dont like the pure mechanical not human-friendly games as some abstract strategy games as chess or baduk.

I dislike too the games based purely on luck, i.e. the victory or lose is completely uncontrollable.

To me a perfect game must be based on some random variables (but not luck), by example as in many PYL, bid or role playing games.

The difference, in therms of game theory, is if the game have perfect information or not. I will avoid, except some rare cases, the perfect information games because they generally implies a lot of learning and experience to play them in a good competitive level.

If, in general, the objective definition of a game revolves on competence (the subjective definition may implies "have fun", by example) then I want a game where I can be competitive easily. Cause this the experience required to play it cannot be so much.

And, moreover, the subjective definition of "have fun" implies the concept of "surprise": to me any kind of good game must have surprises involved.

These two aspects of the game, objective and subjective, are the negation of "mathematical" games, aka perfect information games when it level of "mathematicality" is the maximum.

A good balance between randomness and determination is achieved in games as Stratego or GOPS, games that are not based directly in random variables if not in absence of information: you know that your opponent can play something, but you dont know WHEN he will play it.

Anyway these examples (Stratego and GOPS) are limited in the amount of "surprises" that you can see it.

By the other hand a game with surprises need to be constructive in some way: you can put somewhere random events or some probable changes of the rules of the game, etc. In this sense a game is completely dynamic and organic. By example economy or politic themes are good examples to develop these kinds of organic games.

In short: is hard to design a good game, where the balance between determination/luck and all the others aspects lead to a game easy to pick, fun and enough complex to not be boring.

But commenting your example questccg, I think that throwing dice in a card game can make the game unnecessarily long to play if you dont craft the mechanic very carefully.

Dice seems fine but the nature of a card is the lack of knowledge (information) of the opponent about what you will play, this is a kind of implicit randomness. Then you are adding extra randomness, explicitly, with the dice.

Anyway only the experience playing the game can show us how appropriate is this mechanic of cards+dice. So you will test to know.

So, in resumen, I dont see this decision in the axis of mathematics/luck. I see it more in the axis of playability/simmulation.

I feel as long as there's no One Solution to become the winner of the game, then pure Mathematics is fine - because you prevent it from becoming a puzzle. When done effectively, the game becomes less about playing the odds and more about choosing the proper tools at your disposal to put yourself in a winning position.

GOPS (Game Of Perfect Strategy) and Stratego were both already mentioned, and I think those are great examples. They avoid turning the game into a puzzle, by allowing players to either configure their pieces on the board as they wish, or choosing a specific card from their limited (and ever-shrinking) set of choices to make a move.

Carcassonne (though there is random tile-drawing) and a lesser-known game called Hijara are also good examples of this.

A great thing about pure mathematics games is that very frequently they delve into the head-space of an opponent. Typical thoughts in the heads of mathematics games players when squaring off against their opponents:
What are they thinking?
When will they play their big-win card?
How can I encourage them to waste their high-value cards on something I don't want to win anyway?
How can I conserve my big-win cards for when I really, really want to use them?
Can I take this territory and hold it until I can score it/until the end of the game?
Should I do it NOW?

These kinds of questions make for intensely captivating games and excellent memories.

When you allow chance in to the equation, you find entertainment in different ways and don't always have an opportunity to ask any of the above questions. Fortunately, there seem to be audiences for all sorts of games.

It's a fascinating topic for me personally, and I think about this a lot.

Agreed, and well-written. I personally want to out-think my opponent during serious gaming. In more light-hearted gaming, though, I'm 100% fine with rolling the dice to see how many buildings in Tokyo I get to destroy, for example.

I don't know that it's less prominent, and variance is ever-present in tournament games (luck of the draw, luck of matchup, etc.). I just know that I do not enjoy games where luck is as or more important as skill in determining the victor.

I've never played Pokemon, so I can't speak to it. Hearthstone is an example that perhaps we both can relate to? In Hearthstone, the "RNG" effects are less desirable to me than not having them, but I must admit they made for some truly epic interactions. They're also fairly limited as to power level, but they can still be infuriating when you're on the wrong side of them. That could be appealing to some as others have mentioned.

The challenge for tabletop games is successfully implementing random effects of that scale that make you say, "holy crap!" without feeling too clunky. You can't just, "play a random creature that costs 5," because the typical method of randomization is card-draw or rolling dice; there's no computer doing the work for you.

So, in your examples, successful attacks rely on die rolling (is this a RPG style game? Seems like it). Obviously this isn't a new concept, but what, in your game, can I as the player do to mitigate the chances of failure, thereby increasing my chances of success? If nothing, and I'm at the mercy of the die roll, that is unappealing to me in a competitive environment.

Football players compete in most part with their athletic ability and skill. The bigger, stronger, more-skilled, and/or faster player will almost always beat the lesser opponent.

Chess players have perfect information in front of them, so the competition lies in anticipating their opponent's moves and luring their opponent into sub-optimal lines of play.

In your game, if I am a better player than my opponent, we are on an equal playing field, and I make no mistakes throughout the game, am I still just as likely to lose due to rolling poorly with dice? If so, that (in my opinion, purely subjective) is not an appropriate game for competitive play.

Well presumably, if you're playing in a tournament, there is some reward structure similar to being paid to play if you place highly. I think this comes down to whether or not the OP is trying to make a tournament-level competitive game, or simply a fun-natured, social tabletop competitive game.

My point is, in a TOURNAMENT game, I believe skill should be the major determining factor of who wins. Variance and random chance should be only minor influences.

In any other type of game, random effects are just fine.

I dont know exactly what does the multiplier but a percentage of 65% is more close to chaos (pure luck) than rare event.

Notice that 50% means absolute randomness and 25 or 75% is the intermediate point between pure randomness and determination (0 or 100%).

When you move from 25% (or 75%) to 50% you are moving to the chaos. And when you move from 25% (or 75%) to 0% (or 100%) you are moving towards determination.

It depends on the mechanic that "chaos" mean "based on luck" or not.

Masacroso has it right, that's how you calculate the probabilities. In this case, because it's such a simple problem (10 cards, 1 of which is the target are you don't care what order the cards are drawn in) it's much easier to calculate. If you were looking for multiple cards or you cared what order they were drawn in, the calculation becomes more complex.

Kris, I strongly recommend taking a statistics course of some kind. It will help enormously in figuring this stuff out (I did one pre-university and didn't think it would be much use until I later got into game design and then I was very glad to have it!)