Let Poor Rudolph Join In This Goblin Game!

Those of you younger than, say, sixty, may not know exactly what an actuary is or does. Well, I’ll tell you. An actuary is an expert in when exactly you are going to die. Using complex statistical and mathematical models as their diseased cow intestines, these modern soothsayers can ask you exactly two and a half questions and then divine the exact day and manner of your death. (“You’re a smoker and have three kids, you look married, lessee…June 12th, 2048, slip in your bathtub and impale yourself on your own pipe.”)

Actuaries work for insurance companies, who want to know when you’ll die so they can pretend to care. That said, actuaries themselves can be wonderful people. Two examples are Todd Petit and David Hanson, friends from our Magic group who thought the exact same thing I did when we saw Goblin game: “Hey, look, game theory!” We would like to be among the first to examine what may look like a random mind lapse of Wizards, and explain why it is, in fact, continuing evidence of R&D having a friendly laugh at your expense. Understand this article, and maybe you can join in the laughter.

***

Many casual, and perhaps pro players, have been intrigued by the most erratic card in Planeshift:

GOBLIN GAME. 5RR Sorcery, Rare. Each player hides at least one object, then all players reveal them simultaneously. Each player loses life equal to the number of objects he or she revealed. The player who revealed the fewest objects then loses half his or her life, rounded up. If two or more players are tied for fewest, each loses half his or her life, rounded up.

Notes from the DCI FAQ imply that players should choose small, non-game objects like coins or beads and just hide them in your hand. Don’t get fresh and take your opponent’s library. And be honest, for crying out loud.

Goblin Game represents a”game within a game.” Nothing like Shahrazad, mind you, but an interesting diversion nonetheless. Bottom line, you are betting your opponent(s) that you can afford this detour into chance more than they can. And unlike Chaotic Strike and all those other annoying coin-flip cards, Goblin Game actually has a strategy behind it.

Game theory is a familiar concept to many of us. The Prisoners’ Dilemma, formulated by mathematician Albert W. Tucker, is perhaps the best-known corner of game theory. There’s a good link at http://www.princeton.edu/~mdaniels/PD/PD.html. Read it if you don’t know what the dilemma is about. You should know this anyway, if you’re going into (or God forbid, already in!) any career involving economics, political science, environmental science, evolutionary biology, and hey, sure, crime-fighting, too.

[Space to think about why it should be necessary to scroll down if you’ve (a) read the link and are ready to continue, or (b) skipped the link since you already know game theory well enough and would just like to get on with it.]

The Goblin Game, like the Prisoner’s Dilemma, is NOT a zero-sum game. (If you don’t know what a zero-sum game is, or why it should matter that Goblin Game isn’t one…GO BACK AND READ THE LINK. Look, now you have to scroll UP all that extra space…Wouldn’t it have been easier if you were honest with yourself?) In other words, cooperation may or may not be rewarded. Unlike the Dilemma, however, in Goblin Game you may not always be trying to minimize your jail sentence (loss of life).

Some initial observations about the card:

* It costs too much to be practical as a duel tournament card. This is regrettable and people are welcome to prove us wrong; we’ll be among the first to cheer.
* The least life you will lose from this card is two. Anyone who only hides one object (the minimum) will lose one life for that object, and then will lose half of their life rounded up since they’re certain to be tied for the least. That will be at least another one; and it will only be one if you are at one or two life, in which case you’ll be dead.
* The card is red because red can typically afford to play this sort of masochistic lose-lose proposition. (Todd would like everyone to know that it could also have been blue, given the”intelligent” nature of the card. Anthony would like everyone to know that Todd is a goober. Neither Todd nor Anthony have consulted much with Dave in this respect, but we can reasonably assume that Dave would like everyone to know that people in goober houses shouldn’t throw chocolate-covered peanuts.)
* People are free to hide as many objects (and lose as much life) as they want. The card sets no maximum. And you are losing the life, not paying it, so there is no general rule against this, either. While bidding more money than you have is considered poor form at a formal auction, we all seem to be free to lose as badly as we’d like, here.

Effective play in duel is possible, and only a little complex. You essentially try to get your opponent down to about four life, where you’ve got him theoretically pinned…And then realize that two Shocks or a Fireblast would do the job at least as well.

Effective play in multiplayer, well, depends on what you mean by”effective.” We will focus on group play for this card, since we find the decision-making more fascinating there.

Here are your options, and in a very relevant way your opponents’ options, when someone plays this card in, say, a five-player chaos game:

RISK AVERSION. Also known as the”min-max” strategy, the goal here is to minimize the maximum loss of life. (To illustrate, you may care very much whether you lose more than ten life; but you don’t care so much if you lose two or ten.) The”min-max” approach is nearly identical to a Stop-Loss insurance policy, the mating call of the actuary.

A min-maxer wants a guarantee that there is an end to the pain, somewhere. Goblin Game gives very few guarantees; but one that it does make is that you can limit your life loss to 1+ half your life. That’s the min-maxer’s goal: Accept that bad fate, and avoid the worse one of trying to gamble with three or five objects and STILL losing half your life.

So if you are at eleven life, your accepted maximum is six. If you are a min-maxer, you will hide one object, lose one life to go down to ten, and then intentionally lose half your life to get to five, where you’re apparently comfortable. Better this, in your mind, than hiding two or four objects and finding out you still have the minimum, which would take you down to four or three life, respectively.

If your life total is even, you may as well bid two life. That’s because the second loss of life, for those with the minimum, rounds up. (In the example above, if you are at twelve life and bid one, you go down to eleven…and then lose another six, ending up at five again.) What you gain from having even life is the chance that as you bid two, at least one of the other players will be a min-maxer, bidding one…Which will make you look very, very smart as you stick at ten life.

Use Necropotence to adjust your life total to an even amount?!?! You heard it here first, folks.

RISK EMBRACER (GAMBLER). The opposite of the”min-max” is – no fair peeking ahead – the”max-min”. This strategy maximizes the chance of minimum damage. That’s a fancy way of saying this gambler will play along with the spirit of the card. Their goal is to find a number of objects to hide that should leave them better off than a max-min player in their place.

Using the eleven-life example above, the gambler will calculate 1+ half of her life, so she knows what the risk-averse people are bidding (six). Then she will choose a number less than six, but more than one, which she feels maximizes her chance of paying ONLY that much.

And how much, exactly, is that? There is no formula, or certainly not an easy one in a game with four opponents. There are too many variables going on. But you can move your hunch into a certain comfort zone, with a little help.

If you’re a gambler in a situation like this, you can feel better about hiding only two objects (instead of three, four, or five) if:

* Other Life Totals Are In The 5-10 Range. As people drop into the low two digits or single digits range, two beautiful things happen for gamblers. First of all, risk-averters’ maximum will be lower than six, pressing you into a smaller and more certain range anyway. Secondly, there will be more of them, which increases the chances of at least one player bidding one. However, once life totals drop below five, you get a third kind of gambler…Which we’ll get to in a moment.
* Very Few Players Have Demonstrated Life Gain. Of course, the player using the Goblin Game may very well supplement his deck with life gain, just to be clever. Set her aside for a moment. If no one else is playing life gain, you are dealing with opponents who can afford to risk very little. That means risk-averse people, which means greater chances of someone bidding only one. Shoot for two! (Unless they have even totalled-life, in which case you’re bidding three, right?)
* The Game Is Aggressive. If the game has been one of lots of creatures, tramplers, direct damage, and what not, then other players are likely to anticipate more of the same in the near future. They’ll find their maximum threshold and go for it. Underbidding them should be easier.

Of course, the more people get used to Goblin Game, the greater the chance that every single player will make similar calculations: The guy who would normally be risk-averse figures everyone else will, so he gambles. Four more people do that, and you have your five-way Prisoners’ Dilemma again.

Outguessing your opponents in this respect is a never-ending challenge. And here’s something to make it tougher:

THE BANKRUPT BOMB. Just about every group has their particularly unpredictable soul. More often than not, THAT will be the guy playing this spell!

Here’s how it plays out. You are in the same five-player game and Goblin Game has just resolved. Glancing around the board you notice that Pete, poor guy, is only at four life. You smile inwardly, thinking that he can’t bid higher than two, since if he bids three and is the lowest, he is out of the game. (Four is a critical threshold for the card, particularly in duel. If you have a single opponent at five life, he has options of one, two, or three life. At four life, he’s only at one or two…Which makes your call easier.)

Since you are a super-lucky guy who gets to play at a table where everyone else is an actuary (and higher than four life), you know everyone else knows the same thing. So everyone bids three life.

However, we are talking about Pete here. This is the man that sacrificed all of his permanents and cards in hand to take one of the authors out of a lively four-player game! And you forgot that, you dork, so you are both astonished and horrified when Pete goes over to the closet, drags out a huge trunk…

…And dumps a Dr.-Evilesque”one meeeeeelllleeeeon” beads onto the floor!

Yes, the Bankrupt Bomber is now out of the game. But he has also seen all of you lose three plus half of your life, which probably waxes someone else and at the very least pushes you out of your comfortable zone of a perfectly-ordered, mathematically-rigorous world.

Of course, a player at four life (or three life) still has the option to play nice, hide one object, and go down to one life while you all snicker at him. But even the most laid back players are likely to go ballistic once they hit two life…Because they just lost anyway, and unlike a Steam Blast, Goblin Game gives them some say in how flashy their departure is.

Enough about players and game theory strategies. Goblin Game is a fun card that can get around annoying red hosers like CoP: Red and Worship. What will make this card even more fun?

ZERO-LIFE CARDS like Lich and Soul Echo let you pay as much life as you like. If you face this combo, your best bet is to just hide a single object. (We suggest your head.)

REVEALED HANDS is another, more intricate ploy. Best bet is Wandering Eye, but you can work around Noxious Vapors as well. Of course, you can play alone by using Cinder Seer and other”reveal X” cards from Urza’s Destiny. If you know that the caster of Goblin Game also has a Fireblast in their hand, the floor of the game has been raised from zero to four (and to avoid becoming a future Goblin Game bomb, from four to eight). Now there is a”game within a game within a game”…

Mr. White has 35 life. Ms. Red has seven, and sports a Fireblast. Doctor Green, Father Blue, and Sister Black are all at ten life.

Utility theory, anyone? Here’s a primer: Utility theory places”weights” on potential gains or losses, depending on the situation. Bill Gates doesn’t care much if he loses $100,000 in a speculative deal. Any one of this article’s authors, however, would care a great deal. Lifestyle changes would be in order. And so you might say the $100,000 loss represents a greater loss of useful resources, or”utility,” than it does Bill Gates. (The fact that people care about $100,000 losses leads to other evils, like insurance companies and actuaries. If there’s a one in 10,000 chance that a fire will consume your $300,000 house in the next year, you have an expected loss of $30.00. But you’ll pay more than $30 per year for the relevant insurance, because you hate the idea of losing that house so freaking much. You’ll pay up to $100 or more for it. Hey, we don’t blame you. But this is what makes insurance companies profitable. They are like Bill Gates, with massive resources. Your house goes down, they lose $300,000 and don’t mind so much.)

Getting back to the game, Mr. White is the clear Bill Gates of the group at 35 life. A strong bid wouldn’t hurt him so much, so you can expect him to hide about ten things without too much worry.

What does this mean for other players? First of all, they all hate Mr. White’s guts; but this is probably not unusual. After they get past those initial feelings of class revulsion, they will recognize that Mr. White will probably not be the low bid. Each of Father Blue, Sister Black, and Doctor Green have to find a way to minimize their loss of life and NOT go below five. None of them want to lose to Mrs. Red and her cheesy direct damage spells!

Let’s ally ourselves with Father Blue. Does he bid the min-max of two? (It would be one, remember; but he’s at an even life total.) If he does, he will almost certainly be tied with the Sister and Doctor and will slip from ten to eight to four…Bad mojo for all three of them!

Okay then, three. Or four. Or five. The optimal solution here for Father Blue seems to be five, since he can’t go any lower without defeating the purpose of his strategy, and it’s as far away from two as he can get.

The problem is, Father Blue knows that his green and black colleagues hate the idea of going down to four life just as much as he does. How far they will run away from two life (all the way up to five) depends on how much they really hate that life loss. It also depends on permanents on the board, cards in hand, expectations from the library, etc. But the most likely scenario is that all three players will bid five, and then lose another three since they were tied for the lowest.

Mrs. Red, of course, knows all of this. She will bid six, and happily go down to one life. When’s the last time a red mage looked at their life total, anyway?

And the second-guessing can continue, of course. If Father Blue, Sister Black, and Doctor Green are all of the same mind (i.e., they are all prisoners who know each other well enough in these dilemma situations), they can all bid seven life, which sounds insane since it’s more than one plus half their life… But it does put Mrs. Red out of the game before she can cast her Fireblast! Hey, we all have our game objectives.

This is where game theory starts to mutate into something more along the lines of Rock, Paper, Scissors. It’s a little less interesting then to some, and more interesting to others. Some players will continue to work the calculations and probabilities in their head, certain that they can predict most players’ behavior. (Ergo Bart Simpson: “Good ol’ rock! Nothing beats rock!”…His futile logic is immortalized on the Visions card Rock Slide.) Others will decide it is futile to overguess and simply pick a range of hidden objects that makes sense, choosing randomly within that range. Still others will build decks around Goblin Game in such a fashion that they are Mr. White, watching everyone else apply whatever theory (or lack thereof) they like. In any event, it reveals a great deal about how each player approaches the game. Not many Magic cards do this so well.

As far as the authors are concerned, we were among the group who hoped this card was real when we saw it on the spoilers. The modest confusion that may arise as players adjust to it is a small price to pay for an unusual gem like Goblin Game. Time Walk once went through this difficulty in the early Magic days, as some people mutated”take a turn after this one” to”skip your opponent’s turn” to”opponent loses their next turn”, which if you emphasize the right word -“loses” – means something very different. Wizards has since tried to be very careful about ambiguously worded, game-changing cards. They failed fabulously with cards like Lifeline, and hit the mark beautifully with cards like Thieves Auction and the new Waterspout Elemental.

But like we said, there will still be confusion! On the night the group looked over the card on the spoiler, Carl, a very logical computer programmer (is there any other kind?), commented that he really liked the card as well and envisioned great fun in everyone running around the room hiding various objects in a flurry of decidedly non-secretive activity. Taking Carl’s vision a step further, everyone would have to run around once more to pull out the objects they’d stuffed in closest and under sofa cushions and dump them all on the floor.