I worry about trying to apply lessons learned from zero-sum strategy games involving direct head-to-head conflict to more general domains.
To elaborate, the lessons seem specific to when 'maximizing utility' is the same of maximizing the probability of something. If 'how much' you win or lose by is important, then the lessons are much less applicable.
The opponent is attacking you with a big army. You have a choice: you can let the attack through and lose in two turns, or you can send your creature out to die in your defense and lose in three turns. If you were trying to postpone losing, you would send out the creature. But you're more likely to actually win if you keep your forces alive ... [a]nd so you ask "how do I win?" to remind yourself of that.
This specific bit on it's own is probably quite fruitfully generalizable. You have so many heuristics and subgoals that, after holding them for a long time, they may be partially converted by your brain into intrinsic values and top-level goals. When things get hairy, it's probably normal to lose sight of your initial purpose that generated those heuristics and goals and to follow them when they no longer apply.
Because your victory is now the default, the options for your opponent are very limited. If you have a big army, they need to play a card that can deal with lots of creatures at once.
Or they could play several powerful direct damage spells and fry you in the two turns they have remaining. For decks with such cards this falls under the "How do I win?" reasoning you suggest for the players likely to lose. Rather than take out a couple of your creatures and delay the inevitable loss for a couple of extra turns they may calculate that if they pick up exactly the right two cards and you don't happen to have one particular defensive card they will be able to finish you next turn. It may be a long shot but it is better than the inevitable somewhat slower defeat.
If you have nothing to lose, consider desperate high risk options. If you are in a comfortable position consolidate and avoid risk.
If you have nothing to lose, consider desperate high risk options. If you are in a comfortable position consolidate and avoid risk.
I have, in fact, seen this given as investment advice. If you are going to go broke in a big way, take risks; this is the time to play the lottery, you probably won't win, but you might and by this point you have nothing to lose. If you have plenty of wealth, and aren't playing for the thrills, this is when you play safe, no more need to take significant risks at this point.
I have, in fact, seen this given as investment advice. If you are going to go broke in a big way, take risks
Absolutely. This also applies if you have an insane government that will bail you out if your risky investment doesn't pay off.
Sure, this behavior seems "insane" if you assume the maximand of states is something like "the general welfare", but that is simply a bad assumption.
Sure, this behavior seems "insane" if you assume the maximand of states is something like "the general welfare", but that is simply a bad assumption.
One can label a collective process "insane" without so labeling any or all of the self interested actors participating therein. While many of the individuals involved may be acting more or less rationally the outcome is a clear instance of "People Are Crazy, The World Is Mad".
It may very well have been game-theoretic rational for the individual rogue trader to just keep gambling once things got sufficiently bad, although his co-workers would certainly have wanted him to stop long before then.
Hm. I would disagree - you only ask "how do I lose" when you're close to winning and winning is a "stable" state (like going on a fun vacation), and you only ask "how do I win" when you're close to losing and losing is a known stable state (like having to call a tow truck to pull you out of a muddy canyon). When you're in situations without a convenient "floor" (or ceiling) to stand on, then you stick with the middle question, which is "what will put me ahead?"
I've edited something like this into the post.
Or they could play several powerful direct damage spells and fry you in the two turns they have remaining.
Or play a congregate, and delay their death by a couple turns, buying them more time. I hated that card when I played MTG.
Or they could play a combination of cards which locks you into an infinite draw and discard cycle, decking you in a single turn.
Not that it particularly affects the message of the article, but I was under the impression that Magic has evolved away from decks that focus on using lots of creatures to deplete all the other player's life points being viable, unless you have some mechanism for playing them very early into the game when they have hardly any mana.
Modern-day Magic sets are actually very creature focussed. The Vintage format (which lets you play cards from any set) is something of another matter, but it's also not very popular (mainly due to cost).
ShardPhoenix is correct: The R&D team for Magic has explicitly upheld a design philosophy that favors using lots of creatures to win, in contrast to the older style of winning with few to no creatures.
How old is this older style?
It's been a few years since I followed the game, but it seemed to me like it was gradually moving further and further away from creature focus since I was first introduced to it in elementary school.
tl;dr: The game was dominated by spells from 1995-2003, so the philosophical change began ~8 years ago in 2004.
I believe Ice Age [1995] marks the beginning of the "spells win" era - but I'm not familiar with what sort of tournament scene existed before that point. This peaked with the Urza's Saga block in 1998, largely considered the single most unbalanced set ever printed. Mirrodin [2003] was meant to be a return to creatures, and almost succeeded. Unfortunately, a small number of severely broken cards warped the format in to something that was still focused almost entirely around combo decks.
I believe Kamigawa [2004] marks the first block that wasn't dominated by combo/spell strategies, and actually valued creatures, although "Magic 2010" [2009] was probably the first block that truly captured the new "creatures win" focus of the game - from then on, it's pretty much indisputable that the focus of the game had changed.
Although there it's more often "how do I draw?", which is the same principle with renormalized baselines. (I searched for a more accurate term than "renormalization" and happened upon this paper, which for some reason I find funny. Anyway how do I correctly say what I was trying to say?)
Probably the best example of how do I win. In this match, the gut reaction would be to use the direct damage spell in hand to clear away one of the creatures, and hope for either a big creature draw, or some other game changing spell. Instead, knowing the ONLY way he could win is if the card on top of his deck is direct damage, he spent the direct damage spell in hand directly at his opponent, and then just flipped over the top card- if you only have one path to victory, you have to ignore all other paths, no matter how tempting, or how much it feels like the wrong play.
...without losing sight of the fact that having allowed myself to get into a position where my only path to victory requires a low-probability event that I don't control was already a huge mistake that I should confidently expect to result in my failure.
This is a very fine line to walk, especially in magic. Finding the places you could have made better decisions, while understanding what decisions you could not have made better with the information you had at the time, is not an easy task- although at my skill level, it is generally easier to assume I made a poor decision and find it.
I don't know much about magic, but yes, when games have a significant random element it's often difficult to tell the difference between an optimal strategy that just happened to lose this time, and a suboptimal strategy.
An excellent habit that I've noticed among professional players of the game Magic: The Gathering is asking the question "how do I lose?" - a sort of strategic looking into the dark.
Imagine this situation: you have an army ready to destroy your opponent in two turns. Your opponent has no creatures under his command. Victory seems inevitable. And so you ask "how do I lose?"
Because your victory is now the default, the options for your opponent are very limited. If you have a big army, they need to play a card that can deal with lots of creatures at once. If you have a good idea what their deck contains, you can often narrow it down to a single card that they need to play in order to turn the game around. And once you know how you could lose, you can plan to avoid it.
For example, suppose your opponent was playing white. Then their card of choice to destroy a big army would be Wrath of God. That card is the way you could lose. But now that you know that, you can avoid losing to Wrath of God by keeping creature cards in your hand so you can rebuild your army - you'll still win if he doesn't play it, since you winning is the default. But you've made it harder to lose. This is a bit of an advanced technique, since not playing all your cards is counterintuitive.
A related question is "how do I win?" This is the question you ask when you're near to losing. And like above, this question is good to ask because when you're really behind, only a few cards will let you come back. And once you know what those cards are, you can plan for them.
For example, suppose you have a single creature on your side. The opponent is attacking you with a big army. You have a choice: you can let the attack through and lose in two turns, or you can send your creature out to die in your defense and lose in three turns. If you were trying to postpone losing, you would send out the creature. But you're more likely to actually win if you keep your forces alive - you might draw a sword that makes your creature stronger, or a way to weaken their army, or something. And so you ask "how do I win?" to remind yourself of that.
This sort of thinking is highly generalizable. The next time you're, say, packing for a vacation and feel like everything's going great, that's a good time to ask: "How do I lose? Well, by leaving my wallet behind or by having the car break down - everything else can be fixed. So I'll go put my wallet in my pocket right now, and check the oil and coolant levels in the car."
An analogy is that when you ask "how do I win?" you get to disregard your impending loss because you're "standing on the floor" - there's a fixed result that you get if you don't win, like calling a tow truck if you're in trouble in the car, or canceling your vacation and staying home. Similarly when you ask "how do I lose?" you should be standing on the ceiling, as it were - you're about to achieve a goal that doesn't need to be improved upon, so now's the time to be careful about potential Wraths of God.