R&D Journal
"Multiplayer Mathletics"
by Nate French
Welcome back to the latest edition of the R&D Journal. This week I'd like to take a short break from the War of Five Kings spoiler series, and instead look at what kind of expectations for success different player-personalities might have going into different formats of play.
In his "Open Letter" to the AGOT community, Christian raised the analogy that a head-to-head AGOT tournament is akin to a chess competition, while a multiplayer AGOT tournament will feel more like poker. As an individual that has competed at the tournament level in all three games, I find this analogy both compelling and useful as a tool in thinking about and discussing what we're after when we sit down to play A Game of Thrones.
As in most things, our expectations for an experience will inevitably play a large role in defining our perceptions of that experience. "What we want" will influence what we feel we are (or are not) getting.
One of the more common conceptions of the competitive multiplayer game, for those that are more at home in head to head tournaments, is that multiplayer AGOT is not a contest of skill. The obvious response to this claim is that it takes a different set of skills, but even then there are those who acknowledge the different skill sets, but still aren't convinced that the multiplayer game is as much (if not more) a test of a player's ability as its head-to-head counterpart. It is for these players that I offer up the suggestion that the impact of skill on multiplayer play is (similar to the impact of skill on Poker outcome) diffused throughout a larger number of games, and therefore less readily discernible, than its impact on head to head results. In other words, the skill impact is there, but because it's more spread out, it's a lot harder to see.
To illustrate this point, I need to introduce a concept that I've come to think of as the "realistic expected outcome." The realistic expected outcome is simply a bar by which you can measure whether or not, and by how much, you're successful or failing. In a nutshell, it's your expected success rate against opposition with exactly the same level of skill as your own. Assuming that all the uncontrollable variables like good/bad match-ups, good/bad starts, top-decking exactly what you need, and so on are going to balance out over time, how many games, against equally skilled opposition, can you expect to win? (Another way to imagine it is, if you were playing against yourself, and both you and your clone of an opponent were using the same deck, how frequently would you expect to win?)
The answer, it turns out, is pretty simple. With everything being equal, you can expect to win one out of every two head to head games. This means that your "realistic expected outcome" is a 50% win rate. If your win rate is higher than 50%, you are either the beneficiary of some favorable short term luck, or you're playing with a higher level of skill than your competition. And since we've already allowed for short term luck to balance itself out in the long run, if you're winning (you're no longer playing against your clone here, but rather against other, "real" opponents) 2 out of 3 games, or 3 out of 4, over an extended period of time, you can rightfully assume that you're playing at a higher level of skill than your opponents. With a large enough discrepancy in skill levels (i.e. if you get good enough and/or your opponents are bad enough), your win rate can be pushed even higher.
Some of the game's top head-to-head players have come to expect 80% and 90% win rates in head to head play. Other than raising the issue of how the rest of you have ever allowed such a situation to develop, I will also assert that it is a player with this type of expected win rate who is most likely to overlook the skill that is necessary to perform well at a multiplayer table, as they are used to having their relevant skills pay off at a much higher rate. This is because the realistic expected outcome in a 4 player multiplayer game does not start at 50%, but rather at 25%. In other words, if you were playing against 3 clones of yourself, and you were all using the same deck, you could realistically expect to win one out of every four games. This means that in the real world, you would be a successful multiplayer competitor if you could push your win rate to 30% (3 games out of 10), and 40% (winning 2 out of every 5 games) would be remarkable. Doubling your baseline multiplayer success expectations from 25% to 50% would be akin to taking your baseline head to head winning expectations from 50% to 100%, a feat that none but the bravest (or most foolish) AGoT player would dare pursue.
Now it's time to get all "mathletic." Win rates and expected win rates are fine if we're playing in a vacuum; unfortunately, we are not. It's all well and good for Gregor to have an 85% expected head-to-head win rate against "the field," but what happens when he comes up against an opponent like Jaime, who has a 90% expected head-to-head win rate against that same field? This question raises the interesting truth that while we play against "the field" over time, in any given game we are always playing against another individual. Maybe Gregor is a player who plays up to the level of his competition, and he has a 60% win rate against players who are "better" than he is (better statistically, against the field), but he also tends to underestimate people, and throws away an occasional won game against players who aren't even cracking 50% against the field. Maybe Jaime shows no mercy and wins all of the "gimme" games, and all of his losses come against players who are performing with a high level of success: he doesn't always lose against other good players, but when he does lose, there's a good chance it happened against a quality opponent. Whatever the specifics of the match-up, something is going to give as the two players square off, and (in this example) their win rates against each other will most likely be less (as they're both strong players) than their win rates against the field.
The moral of this story is that your expected success rate is not the only determining factor on the outcome of a match (your expected success rate is going to come into conflict with your opponent's expected success rate), and that when two expected success rates clash, one (or both over time) of them has to give. The point is that in a multiplayer game, there are not just two expected success rates competing for dominance of the situation, but four. Your skill is not going up against the skills of one opponent, but those of four. This means that, from the start, your skill has its work cut out for it if it wishes to make itself felt.
Getting back to Christian's analogy, let's take a look at the games of poker and chess, and how the idea of the realistic expected outcome applies to each game.
Chess is a head-to-head game, and many believe that its outcome is determined entirely by skill. (I personally believe that, with humans playing, there is an element of luck involved, but that is a different story. Like all luck, the luck factor I perceive in chess is also short term and will balance itself out over time, making it a non-entity in this discussion.) Against a player with an exactly equivalent level of skill, a chess player can realistically expect to win 50% of the games that come to a decision. (The high drawing margin in chess will see to it that many games between equally matched players are undecided.) Therefore, playing successful chess is accomplished by pushing your win-rate against the field up above 50%. It is telling that the game of chess is most enjoyable when the players are fairly evenly matched, and that most players would rather not play against someone they are going to beat 7, 8, or 9 times out of 10. It's no challenge, and therefore not a whole lot of fun, when the going is that easy.
Poker is a game that can be played heads up, but it is frequently played with 4, 6, 9, or 10 players sitting at a table. (At larger tournaments, you will almost always find 9 or 10 players assigned to a table.) Assuming once again that all the players have an equal level of skill (you're playing against 9 clones of yourself) and that the random element of luck will balance itself out over time, you can realistically expect to win one pot out of every ten hands that are dealt. Being successful at Poker, then, involves at least one of three goals: maximizing the size of the few pots you win, minimizing or eliminating your investment in the pots you're not going to win, and/or simply winning more than your fair share of pots.
Of course, a good poker player is going to take advantage of all three of these possibilities, but trying to win more than your fair share of pots can quickly work against you if you push that angle too far. Even trying to grab 2 out of every 10 pots at a ten-handed table can quickly raise the eyebrows (and the ire) of the rest of the players at your table, leading them to believe that you're "full of it." At which point you'd better slow down, or expect to be looked up more often than not. A more patient and less conspicuous approach would be to steal an extra pot or two over the course of 100 hands, raising your percentage of won pots to 11% or 12%. This discrepancy is more difficult to see (you may not even notice it yourself if you're just "playing the cards") if your opponents are not actively watching for it.
Imagine kid who grew up winning chess tournaments. He's used to dealing with one opponent at a time. He's used to seeing an immediate return on the hours of study and practice he puts in. He's used to seeing his talent come through for him on a regular basis.
This kid gets to college, and discovers the game of Poker. Now, he's playing against 9 other players simultaneously. He just can't grasp the concept that only 1 out of every 10 pots is "rightfully" his; he's used to winning 60-70% of the time. He tries to impose his will upon the game, to dominate his opponents the way he did in chess. What does he say when he keeps losing money? Bad luck, of course, and that there is no such thing as skill in a game in which he cannot impose his will, at will, whenever he'd like. At which point the Poker players will agree, sympathize with his awful "luck," console him that it will change sooner or later, and continue to take his money.
Of course, since he's probably an intelligent kid, and a competitor who doesn't like to lose, he'll probably head back into the chess scene and mop up in a few tournaments. As he plays, he'll probably come to realize the differences between the two games, and come to understand that he was reaching for too much in the Poker game when he was using his chess experience as a basis of comparison for what he considered "successful" play. Armed with this knowledge, he was able to return to the Poker game with a new perspective, and a new appreciation of what he had to do to succeed. At this point, he was able to win some of his money back from the Poker players (who all had him pegged as a newb!); he was now one of them.
As a player who has moved from tournament chess to tournament poker and back and forth between both games throughout my life, I am frequently asked which is the better game. The answer, it seems, is whichever game I happen to be playing at the time. It is also true that the two games are not mutually exclusive, that enjoying one does not exclude the enjoyment of the other, and that, at the end of the day, my experience and enjoyment of each game is richer because of my intense familiarity with the other. This is also a case with the Game of Thrones LCG. Head to head or multiplayer? I love them both, and will continue to design cards that excite the fans of either format. The format shift, in my eyes, is not at all about the end of the chess-like, head-to-head competition, which is and shall be one of my favorite pass-times. Instead, the format shift is all about an opportunity for the other side of the game, the social and diplomatic, poker-like multiplayer game (also one of my favorite pass-times), to have its proverbial "moment of glory," and take its place as an equally valid medium of competition. Loving one format does not exclude the love of the other, and, both can give you a deeper appreciation of their counterpart.
Long live the game of Chess. Long live the game of Poker. Long live the Game of Thrones LCG.
Until then, Happy Shuffling!
