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Pursuing high scores – a limit case

2012/04/10

I’ve been obsessively playing Reiner Knizia’s Deck Buster on my iPad lately, despite thinking that it’s objectively not a great game, certainly not as good as his earlier offering Yoku-Gami. I think a lot of the addiction stems from the fact that I was an early adopter and managed to get the #1 global high score in one of the game modes early on… now I’ve been bumped down to #3 and, being a highly competitive person, can’t help but feel a need to try to win my crown back.

The trouble is that, when shooting for a score as high as I need to be #1 again, I find myself being forced to adopt strategies that aren’t nearly as much fun as the ones I was employing when I first started out. Whereas consistency is usually and intuitively a desirable trait in a game player, the nature of competing for high scores encourages exactly the reverse.

What I realize now is that there’s an additional problem with big group games that I failed to mention in my last post and that it’s really what’s going on here, because when the goal is a high score, a seemingly single-player game is actually more like an infinity-player game! Let me explain.

Whether or not a game contains a luck component (and most high-score based games do), the performance of a player’s brain on a given day is itself a form of luck, and a player’s results will always form a statistical distribution of some sort. Some games you do better, some games you do worse, but you have an average, and you have a standard deviation. Note that the distribution is not necessarily a bell curve, depending on the nature of the game, but let’s pretend it is to simplify the discussion.

If you’re consistent at being good at a game – which is what we’d normally call a good player, whether in chess, or poker, or soccer – what that means is that your average is high and your deviation is low; you can beat most people most of the time, and you won’t throw too many games away against weaker opponents by committing errors.

But this sort of performance actually works against you in a high score competition, whether you’re competing against others, or only against your own previous scores. Either way, your average is, by definition, lower than your highest scores; so instead of that variance in your performance being a hindrance against weaker players, it is actually your greatest asset in striving to achieve that one miracle game to add a new notch to the measuring post.

In other words, most games ask us to be consistent about being good. High scores games, rather, ask us to be good at being inconsistent. There’s no penalty for a failed gamble, except having to start another game, so the fundamental strategy in achieving high scores is to look for ways to make the gambles with the highest possible payoffs, regardless of the odds of actually winning them.

The reason this is similar to a large group game has to do with the number of separate results you’re trying to beat. In a one-on-one game, you only need to beat one other player’s score, so it’s clear that maximizing your average performance is key. The bigger the group gets, the more separate people you need to beat, so unless you’re much better than everyone, you need to start gambling a bit, unless your goal is to consistently end up in second or third. In a high score game, though, you’re trying to beat every score ever posted in the history of the game, including your own. Thus, if 100 people have each played 100 times, in shooting for the high score, you’re trying to have the highest score out of 10,000 results. This is equivalent to trying to win a normal competitive game with 10,000 players! That’s why you really have to gamble big or go home.

Back to Deck Buster, the basic gameplay here is that you’re assigning cards one at a time to one of three hands you’re building, receiving video poker style payouts in the form of additional cards. The nature of the game is that full houses are your safest bet to shoot for, because if you miss, you can still score a two-pair or three-of-a-kind, and will occasionally luck into a four-of-a-kind instead. But you receive a large bonus once you’ve created every type of hand at least once… meaning that to shoot for a high score, you need to get a royal flush and a straight flush at some point.

Flushes, particularly straight flushes, are risky to shoot for, because they mean you’ll have no pairs in your hand. If you fail to get them, then, you’ll score nothing at all (or only a pair). Fail a couple of times, and you’re doomed to end the game quickly, with a miserable score. If you were trying to perform well on average, then, you’d focus on the high-probability hands and only go for the big ones if you already had four of the five cards needed. Instead, the quest for high scores means the optimal thing is to shoot for your royal flush from the get-go, any time you’ve got the slightest shot at it, and simply abandon the game and start over if you fail to get it. This is boring, frustrating and grindy, but it’s unfortunately the best way to shoot for a big score.

One basic solution to this problem is to limit the payout from any given opportunity, and ensure that consistency will afford a player a greater number of those opportunities. Everyone knows, for instance, that in Tetris, one wants to create a deep, single-column well to drop the straight pieces into for four-line scores. There’s a certain gamble involved here, as the necessary piece may not come up, but a consistent player will nonetheless be able to construct the appropriate setup more effectively, as well as deal with the situation when the game refuses to give her a straight line piece for a while.

Another common way is to have scores ramp up as the game continues, so that bigger and riskier opportunities to gamble only come along later in. That way, the player is more likely to face a real choice. If he’s already invested 20 minutes into a given session and has been performing above his average, it’s not clear that taking a long-shot gamble is the best option… especially since surviving a little while longer would give the player a shot at an even bigger and better gamble later. This is what Yoku-Gami does, and the reason that it’s a much better game than Deck Buster.

Related: The challenges of big-group games

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