Tuesday, February 12, 2008

Skill and Luck and Card Driven War Games

In this post, I look at luck and skill, particularly in card driven war games.

Previous Articles

I've written a number of times before about Luck:

In Luck vs Randomness, I define randomness and that which occurs randomly during a game, and luck as the amount of control one has to react to these random events.

For example, if you flip a coin and call heads while it is in the air, your winning the coin toss is entirely luck. This is because the random event happens after your decision has been made. You cannot react to the event, which decides the winner. On the other hand, if you can call heads or tails after the coin has landed, the same random event occurred, but your ability to win is no longer luck. That's because you make the decision after the random event, as a reaction to it, and you have the capability of winning (saying "heads" or "tails") regardless of what event occurs.

In Luck, I note that just because a random event happens after the decision, doesn't mean that your decision is entirely lucky. If there are three balls in a drawer, and two are red while the other is black, and you must declare which color ball will be drawn first from the drawer, victory is not entirely a matter of luck. One choice has greater chance of success than any other.

I then go on to riff that once the decision has been made, drawing the ball has become irrelevant if you play games in order to test your own performance rather than to win.

In More on Luck, I look at the middle ground of random events that sometimes give choices, sometimes constrained choices, and sometimes no choices.

The Luck in All Games

Some would argue that there are games of pure skill have no luck. E.g. Chess, or the 100 Meter Dash. In fact, many elements of luck enter into these games.

First, there are the meta-game elements. Take Chess. People are born with stronger or weaker capacities for the game. People's environments are more or less conducive to becoming better at the game: time for practice, role-models, access to literature, and so on. As a result, your ability to win a game of Chess vs a random opponent is largely a matter of luck. I.e. your skill level is based on predisposition, opportunity, character, and fortitude, all of which are largely a matter of luck.

OK, that nearly defines skill out of existence. To keep things meaningful, we will ignore situations of birth, character, and circumstance. These two guys are sitting down to play Chess. In fact, the very concept that they chose to play Chess (assuming they did) preselected them from the small pool of players with favorable circumstances. The game is now pure skill, right?

Well, you have the situation of the player at that time. Is he ill or healthy? Did he just break up? With his opponent?! Who was cheating on him with his boss, who's also a Russian hit man!!!??? Bad luck!

OK, let's ignore the meta-game elements surrounding this particular match that don't involve any actual in-game decisions. The rest is pure skill, right?

Well, no, not really. I may have studied 9,999 Chess openings and my opponent just happens to hit me with the 10,000th that I never saw. I still have to rely on my skills, but not my "memorized opening skills" but my "capacity to wing the opening skills". Assuming that my opponent chose a random opening, isn't my opponent's choice of opening bad luck for me?

While this type of situation won't happen every game, it certainly happens. Your opponent hits to your blind side, or your good side, unknowingly. If your opponent knows exactly what your strengths and weaknesses, then it's not luck hurting you but a well-prepared opponent. Unless it's just by chance that he knew ...

And then, in a Tennis game, there is the bad luck of twisting your ankle. You've done that dive successfully so many times, only this time something went wrong. Bad luck? Or poor skills?

Skill vs Luck

There's skill in performance on comfortable ground and skill in moving the field in that direction. There's one skill vs one type of strategy and a separate skill vs another.

Most importantly, there's the skill to handle whatever comes as best as you can.

Luck can still overturn more or less of the work your skill achieved, or restrict or even deny you any capacity to utilize any further skill.

Card Driven War Games

This topic came up as a reaction to my session report on Dungeon Twister. Some people had compared the game to Chess-like; I said in my review that the game is not Chess-like because, at the very least, the battle cards introduce an element of luck that isn't in Chess.

The battle cards work as follows: you have several player pieces, each of which has a battle value of 1 to 4. If you choose to attack another player, you move your piece next to theirs and attack it. On your turn, the decision to attack is entirely yours. As the defensive player, your options are only to leave different pieces at different locations on the board on your previous turn, making it more or less difficult for your opponent's pieces to attack you on his turn.

If an attack occurs, players select one of their battle cards and place it face down on the table. They have free choice among all of their cards. Cards contain a battle value from 0 to 5.

Players simultaneously reveal their cards. Add your piece and card's battle value for a total value. The higher total value wins. The win or loss of a pieces is highly significant to the game (not like Stratego, for instance). Battle cards are discarded after use, except for the 0 card, which you can play as often as you like. And will have to, if it is your only remaining card to play.

Some comments on my review disagreed with me and said that the cards are 0% luck. I was astonished; I'm still astonished. But they tried to defend themselves.

Now to me, for the battles to be "0% luck", the rules would have to be changed as follows: the attacking player selects a card and places it face up on the table. The defending player then selects a card and places it face up on the table. Continue.

There you go: 0% luck.

How can you argue that the blind bidding version is 0% luck? One commenter wrote:
What I think you're failing to realize is the intrinsic link between character positioning, abilities, dungeon rotation, and combat. All three are so intertwined that you can't focus on any one aspect of the game and analyze it in isolation.

Before combat, players analyze the situation at hand. You also analyze what combat cards you and your opponent have access to. You then take your analysis into the combat draw. That's the short version.

In the scope of the larger game, available combat cards (even outside of combat) influence the game tremendously. Players have to be very mindful of this when they go into combat. As part of your analysis of what combat cards to pull and what will be pulled on you, consider the greater impact on the game of the combat being won either way. The insight you gain from your grand analysis will not only tell you what card you're best off playing, but what your opponent is best off doing as well.

Therefore, it's not luck at all. The player who has the best grip of tactics and most successfully analyzes the whole situation is going to have the most positive outcome.
and another wrote:
I agree: Combat is bluff, hand management and calculation, but certainly not luck. If your combat cards are depleted, you'll have a tendency to avoid the fighting. If you have a strong hand and your opponent already has depleted his hand, you will be able to fight more often. If you attack a character for no reason and the opponent cleric is not far behind, you're just stupid... Of course, the bluff element plays a lot. If you play poker, you probably know that. Poker gamers make great DT gamers. But that's no luck: as attacker, you know that you take chances if you play a combat card that can result to the loss of the fight.


On the defender side, most of the time, you'll play a +0 combat card, because if the attack is declared, you have already lost the fight. The attacker won't attack if he thinks he will lose (it can happen if he doesn't remember which combat cards have been played, or if he wants that you play your highest card so he is dominant in that area, but that's another matter). So most of the time, you play +0. Sometimes, the situation can be so interesting for you if your character is not wounded that you will sacrifice your highest card, and hope your opponent plays to even the score. But against experienced players, this tactic doesn't succeed very often: chances are that if you have seen a good action to play, they have seen it too...
Aside from the statements to the effect that the battles are "not luck", I agree with most of what was said by both of these commenters.

Yes, the structure of the battles, your positions, and all the other facets of the board affect both when you battle and how you battle. In fact, they affect all your non-battle decisions, as well. But to say that the battles are not luck? Still no.

Regardless of situation, there will be battles in the game, sometimes ones you initiate, and sometimes ones that you don't. Furthermore, unless you will win the game shortly before or after your first battle, and therefore the path to victory is now clear, you do not know how many battles will occur, nor what future battle situations will be like. Therefore, you do not know with complete certainty during a battle if you can or cannot afford to lose the battle, but more importantly, if you can or cannot afford to lose a particular battle card.

Game Theory and the Example Battle

Suppose that you are attacking with a 4 battle value playing piece versus your opponent's 1 battle value playing piece. Each of you has 6 cards valued 0 to 5.

You are guaranteed a victory in the battle; you can easily select your 5 battle card, for a total value of 9. In fact, you need only select a 3 value battle card in order to total 7. Now you know that you can save your 4 and 5 cards with impunity.

Meanwhile, your opponent can only muster a total value of 6 if he plays his highest card of value 5. Your opponent knows that he can't win if you play your 3 or higher. Therefore, why waste his 5? So your opponent gives up and plays his 0, losing the battle but retaining his better cards for later battles.

But you're not dumb. You know very well that your opponent knows he can't win. You suspect that he will play his 0 for a total value of 1. If you know that your opponent's total value is going to be only 1, then why waste your 3 card? You can safely win the battle by playing your 0 card as well, saving your higher cards for later battles.

But your opponent's not dumb. He knows very well that you know that he knows he can't win. He knows that if he plays his 0, then you'll win the battle cheap with a 0 card. So he has the bright idea of playing a high card in order to snatch victory from you! In fact, since he suspects that you'll be playing a 0, he need only play his 4 card to win the battle, saving his 5 card for later.

But you're not dumb. You know he suspects that so you'll play your 2 just to ensure victory if he plays his 4, but he'll play his 5 just to ensure that you tie. But you'll play your 3. But he'll play his 0 again.

This is a vicious cycle in game theory that has no end. Your choices are between your 0, 2, or 3 cards, and all have the potential of winning or wasting resources. Your opponent's choices are between 0, 4, or 5 with the same criteria. Both of you need the higher cards for later, and both of you would like to win the battle now, too. But neither of you can do both. Which is the correct play?

The answer is that any of them are the correct play. The right card is the one that exactly trumps the card played by your opponent. And, unless you have insight into the psychology of your opponent, you have no way of knowing what he will play. (What if he simply takes three cards, mixes them, selects one at random without looking at it, and then lays it face down. Now what?)

You still have to choose. As attacker, your choice is between certain victory and loss of a middle card, versus possible victory and saving a resource. As defender, your choice is between certain defeat but saving a high card versus possible victory.

You can choose the path that offers no luck and is entirely predictable, but you can also gamble on luck. If you select a card that gives you a chance of victory, you will win or lose by luck. In fact, you may just have won or lost the game due to luck.

And that's in an uneven battle. You may find yourself each at 4 points (game is 5 points). Your opponent is going to win on his next turn by gaining his last point. Both of you have identical battle cards and two of your playing pieces with a battle value of 1 are next to two of his with the same values. You only have to win one of the battles to win the game. You attack twice. You win the game if you play your highest card in the battle in which he doesn't. If you both tie both battles, he wins the game. You select the card for your first battle ...

Can anyone show me a comparable situation in Chess?

The game is not 100% luck, of course. But saying that the battles are 0% luck is simply absurd.



Agent Easy said...

Not sure I'm with you on this one.

I think we can both agree that Dungeon Twister features no RANDOMNESS in battles (i.e. externally generated data). I think many people equate luck to the effects of randomness. In your description, you are equating luck with decision-making in any environment where a person doesn't have 100% information. From a certain point of view, I see where you are coming from, but the problem is that if you accept that hypothesis, then you ultimately have to accept that every game is luck, since you can never predict with 100% accuracy what a person's next move will be. In other words, the cycle of bluff you described could be applied just as well in a non-blind bid situation:

1) If I move my pawn, he's likely to take it with his queen, which would leave his king vulnerable. However, if he doesn't take the bait, he can take my rook in two turns and I'll be in trouble.

The correct move in this case requires knowing how the other player will react to your move. Is that luck?

Kelvin said...

I completely understand why someone who isn't familiar with game theory would think there's no luck.

However, knowing the game theory law of the mixed Nash equilibrium, I can say with 100% certainty that the battle system introduces a nonzero amount of randomness. Even with all outcomes being deterministic, by having simultaneous choice, surprisingly enough, the perfect player is required to play nondeterministically (for example, they might have to choose 3 40% of the time and 0 20% of the time). This is just like rock paper scissors where the outcome of the game is completely determined by your choice, and yet the game still has an element of luck. A perfect player can't just play rock every time. In fact, two perfect players should just pick randomly every time.