ellipsix informatics

Optimal strategy in quantum tic-tac-toe

Here's something I discovered recently: quantum tic-tac-toe is a variant of tic-tac-toe which allows players to make multiple moves at once, in an attempt to simulate quantum entanglement and superposition. Apparently it was invented in part to provide a way of visualizing quantum concepts. In that respect, it seems to be a decent but imperfect conceptual aid, but it's a pretty interesting game in its own right.

Anyway, tic-tac-toe is one of the simplest games there is, so the optimal sequence of plays have been known for a long time (in particular that if both players play optimally, the game always ends in a draw). But what about quantum tic-tac-toe? This question recently popped up on Board & Card Games Stack Exchange, and I'm rather curious to see what answers it comes up with. Currently it has a 100-point bounty attached, which means if you contribute the winning strategy, you could get 100 free reputation to get your start on Stack Exchange!


Guess the author: a (drinking+physics)/sqrt(2) game

Big news out of the CTEQ school tonight: we discovered that the various Twitter feeds which announce new arXiv papers only show you the title of the paper, not the author — not until you click on the link, anyway. So here's a neat way to have fun at parties: someone who has a smartphone (or tablet) with a Twitter app brings up one of the aforementioned feeds, like HEPExperPapers, picks a paper title, and everyone tries to guess who the authors are, or at least which research group or institution is behind it. Anything with \sqrt{s} = \unit{7}{\tera\electronvolt} doesn't count. Converting this into a drinking game is easy, you just drink every time you get it wrong. (i.e. every time) Or every time you get it right. (i.e. never) Or just have a beer in hand. I'm sure that's within the error bars.

Oh, and for the record: one of the people behind this brilliant idea happens to be the chair of a major university's physics department.


Hall Pong: Doubles

I bought a set of four new hall pong paddles today, and you know what that means... or maybe not. It was time to try out 2v2 hall pong!

Since its inception early this year, hall pong has always been a 1-on-1 sport. (Simply because we always had only 2 paddles) The thing is, when playing 1-on-1, whenever you work the ball up the court, you're abandoning the defense of your goal, which means that if you don't score, your opponent has a clear shot. It tends to lead to rather quick points. Besides, there's only so much creativity involved in the kinds of plays you can make — basically it's just a matter of how close you're willing to get to your opponent's goal before you decide to spike it on them. Either you take a long shot, which is easy to block, or you get up close and then it turns into a struggle for who can get a lucky hit on the ball in one direction or another.

Adding another person to each side introduces a whole new level of strategy, though. When you're playing doubles, you still have the same options as with singles hall pong — namely, keep the entire team back on defense, or send both team members up to the opposite end of the court to play offense — but there's also the fairly logical choice of splitting the team, one person back defending the goal and one person forward to shoot on the other goal. This is a nice way to set up some pass-action plays. For instance, if the "goalie" has the ball, usually one of the other team's players will come forward to try to knock it away from them, but then that leaves your team's offensive player wide open. Your goalie can easily hit the ball around the other team's offense, and then your offensive player has most of the hall space available to set up a shot, without worrying about an open goal behind him (or her, whenever we can get some women into the sport).

As one might expect, playing doubles invites a few modifications to some of the original "rules," or guidelines really (the actual rules 1-3 are fortunately unchanged):

  • You can safely get away with a slightly longer hallway
  • It's kind of silly to have all players retreat to their respective ends of the hallway when starting play. The goalies can be at their goals, but the two offensive players will probably want to both move to the end of the court away from the server.
  • A nice effect of doubles play is that the offsides guideline seems wholly unnecessary. It was introduced to prevent a player from getting so close to the other goal that their shot would be effectively impossible to block, but with two defenders, it's a lot harder to score, even when you are right up at the end of the court. Plus if you take the typical strategy of leaving a goalie back to play defense, you wind up with a 1-on-2 matchup, which seems fairly balanced in our experience.

Although it took a little while to work out the kinks, 2v2 hall pong seems really promising and I'm sure we're going to have a lot of fun with it this season. Hopefully you can say the same!


Hall Pong: Now with tougher balls

One of the things you'll notice if you ever play hall pong is that ping pong balls will break, and fairly easily, too. (Especially the tournament quality 3-star balls) The logical way to get around that is of course to use harder balls, like whiffle-style practice golf balls. They're made of much tougher plastic, so you can use just one for a long time.

But using a different ball also changes the dynamics of the game significantly. For one thing, they're more massive, so they don't slow down as much while flying. A hall pong court is just long enough that you can hit a ping pong ball from one end to the other and have it arrive at a reasonably slow speed, but these practice golf balls can seem to come at you like bullets. It makes defense a lot harder and really tests your reflexes.

The other thing about the heavier balls is that they don't seem to bounce as well. Or rather, they bounce and keep going just about as fast as they were going before. So on defense, you'll have a tendency to be jabbing your paddle at the ground a lot, increasing the risk of breaking it. Of course, the sport of hall pong is no stranger to breaking equipment, but paddles are a little more expensive than balls and it'd be nice to keep them around. If you want to play this faster variant with practice golf balls, I'd recommend investing in some extra-sturdy plastic ping-pong paddles so you don't have to keep replacing them.


Hall Pong: The sport of grad students

I couldn't let a new fall semester roll around without loudly proclaiming the greatest thing to come out of my second year of grad school: hall pong. Born out of a combination of ping-pong, racquetball, hockey, and sheer boredom, hall pong is a perfect way to procrastinate (and pretend to get some exercise) when you're stuck in a basement office.

Classic hall pong is a two-player sport. It's played in a hallway, with a goal line of some sort on the floor at each end (it could be a change in the floor tile pattern, or the base of a doorway, or you could just mark it with tape), using a ping-pong ball and two paddles (one per player). The Official Rules are simple:

  1. You score a point when the ball hits the floor behind your opponent's line.
  2. Whenever anyone other than the players enters the hallway, play stops until they have passed through. (This is a safety issue)
  3. Don't be a dick.

That's it. Well, actually rule #3 is more of a guideline. But if you routinely do things like carrying the ball up to your opponent's end of the hallway and spiking it behind their goal line (which is technically legal), the sport loses its appeal pretty fast. Hall pong is supposed to be fun.

If that's not enough for you, here are some conventions and clarifications that have developed to supplement the Official Rules.

  • The ideal playing court is a hallway about 15 meters long, or about as far as you can hit a ping-pong ball before it bounces.
  • At the beginning of the game, both players retreat to a starting position just in front of their goal lines. The player with the ball starts the game with a serve. That generally entails either throwing the ball up or bouncing it on the floor, and then hitting it as hard as you can, but anything goes.
  • The ball has to travel past the middle of the court for a serve to count.
  • There's no penalty for missing a serve; you get to try as many times as you want.
  • You can use your paddle or any part of your body to keep the ball from going behind your goal line.
  • Try to avoid actively hitting the ball with a part of your body. The paddle is for offense; body parts are for defense.
  • Catching the ball is acceptable but generally discouraged, except when necessary for defense. After you catch it, both players return to their starting positions, as at the beginning of the game. Then you restart play by serving the ball.
  • If the ball is rolling on the floor, you can just pick it up and proceed as with a catch.
  • Whenever a point is scored, play immediately stops until the ball is served by the player who was scored on.
  • The offsides guideline: stay at least a quarter of the hall length away from your opponent's goal line, unless your opponent is further away from the line than you are. This definitely falls under Official Guideline #3, so it's subject to being broken whenever necessary to make a really cool play.
  • Games are played to 5 points, or until the ball breaks.

That last point bears mentioning again: the ball will break. As in, literally crack in half (or smaller pieces, if you're good). Evidently ping-pong balls don't stand up to a lot of high-velocity impacts, so you'll want to have plenty of extras on hand.

Of course, hall pong is subject to many possible variations. You can play in a hallway with closed ends, in which case rule #1 is modified to say that you score a point when the ball hits the door or wall behind your opponent. Using a shorter hallway gives you a faster paced game (and better reflex training); alternatively, this may be good for players who have weaker swings. There are endless ways to formulate the offsides rule — I mean guideline — you may want to make it more or less restrictive depending on who's playing, and you can even make it asymmetric to handicap one player. Or dispense with it entirely.

What I'd really like to do is play in a hallway with air vents in the floor, like a high-powered air hockey table, so the ping-pong ball effectively floats. Or even better, play in a zero-gravity environment. I bet this game could fit perfectly in some of the cramped spaces on the space shuttle or ISS ;-) Wishful thinking, sure, but it sounds more fun than getting a Ph.D. Anyway, until then, happy playing!