Monday, September 24, 2012

Jenga Math, Robotics, and the List of Editions

I was not the first to describe Jenga as a NIM like game. Fellow Israeli Uri Zwick also describes Jenga this way in his paper analyzing the mathematics of the game [PDF] and how to win it.

Jason Ziglar analyzes the mechanics of the game [PDF], namely each of the various possible ways of extracting the blocks.

A bunch of guys built a mobile robot that plays the game, described in a research paper.

Tsuneo Yoshikawa and others also tackle the robotic challenge with a robot that has multi-articulated fingers [PDF].

Meanwhile, Matthew South write an 82 page Master's thesis [PDF] on how to simulate the physics of Jenga real-time on the computer.

Official editions of Jenga? 44 so far (not counting Jenga-branded other games and items).

  1. Standard
  2. Blast
  3. Book Lovers
  4. Boston Red Sox
  5. Chicago Bears
  6. Chicago Cubs
  7. Chicago White Sox
  8. Coca-Cola
  9. Dallas Cowboys
  10. Detroit Tigers
  11. Donkey Kong
  12. Extreme
  13. Girl Talk
  14. Halloween
  15. Harley-Davidson
  16. Hello Kitty
  17. Holiday
  18. Jacks
  19. John Deere
  20. Kit Kat
  21. Las Vegas Casino
  22. Love
  23. Mark II
  24. New England Patriots
  25. New York Yankees
  26. Nightmare Before Christmas, The
  27. Oakland Riaders
  28. Ohio State University
  29. Onyx
  30. Party
  31. Philadelphia Eagles
  32. Philadelphia Phillies
  33. Pittsburgh Steelers
  34. Scrooge McDuck
  35. Spider Man
  36. Tarzan
  37. Throw 'n Go
  38. Transformers: Revenge of the Fallen
  39. Truth or Dare
  40. Ultimate
  41. University of Michigan
  42. University of Texas
  43. Winnie-the-Pooh
  44. XXL

Sunday, September 23, 2012

Jenga Strategy First Thoughts; Amyitis

Jenga

I played Jenga a week or so ago, my first play since childhood. My adult gaming mind is curious to know if anyone has done a strategy analysis on the game.

Jenga is something like a NIM game + dexterity. The game starts with a number of layers (let's say X) of which X-1 are accessible for withdrawing a piece, each of which has three pieces. Withdraw a piece and place it on top. After three moves, there are now X+1 layers and the new second layer is now available.

Each time you withdraw a piece you have the following choices:

  • Withdraw the center piece from a complete row: no further withdrawals can be made from that row.
  • Withdrawn a side piece from a complete row: the other side piece may or may not still be withdrawable, depending on slight center of gravity changes in the layers.
  • Withdraw the other side piece from an incomplete row: no further withdrawals can be made from that row, with a caveat. The caveat is that the last and central piece MIGHT be withdrawn if the layers are highly stable and the player is very dexterous.
We will ignore the last case for the moment. In the first case, the number of available rows decreases by 2/3: one row becomes unusable, while 1/3 of a row becomes available. In the second case, the number of available rows decreases by 1/3 in some cases, or 2/3 in other cases.

If the reduction rate were perfectly consistent, a workable NIM strategy can be assessed from the start of the game, given X. You might also spend the first turn of the game poking every block a little to see which ones are loose; this is within the rules of the game, but liable to get the game thrown at your head, so perhaps not wise. Still, certainly by mid-game you should know how many regularly accessible blocks are available, count the remaining moves, and ensure that you end up with the last one. Assuming that you manage the shifting center of balance properly.

Needless to say, I lost the game.

Amyitis

In my last play, I solidified one problem with the game and proposed a fix, which we played with this game. Namely, that an infinite number of recruiting cards of all types are available for cost 3. This ensures that the highly undesirable, but all too often, occurrence where a resource card is not available for you as last player, but on the other turns was available to all players, can not wreck your entire game, so long as you have a little money set aside. The high cost ensures that it's a last recourse, but at least it's a recourse.

The fix worked perfectly, and was used three times during the game.

My other previous worry, about the overpowered nature of the last-level income card, I could see even before we started playing was overblown, and had rather more to do with our previous play style (and an error we made in the scoring of the other point cards) than an actual imbalance, and so the card was left as is.

Both Abraham and I obtained second level of income and both of us scored behind Sarah and Nadine, whom had no income. Not much behind, but still. The game ended very closely, with Sarah making up for last game by winning this game. Nadine was a few points behind, followed closely by me and then Abraham.

I really like the game, and so did everyone else. It has an emergent cooperation property, where you might do something that benefits someone else because their subsequent action then helps you. It has multiple paths to victory, but unlike games where this just means you can get six points here or half a dozen points there, the entire mechanics and play are different in the different areas.

Tuesday, September 18, 2012

Pathfinder (The Board Game, not the RPG)

I played an old Milton Bradley board game Pathfinder with one of the kids of a family that had invited me for dinner on Mon night.

Pathfinder is a game that looks like Battleship and plays a lot like Battleship, though it seems like it shouldn't. Each player has a hidden 6x6 grid. A player sets up a given number of walls between squares or along the left side and then sets a goal in one of the squares. So you start the game with a maze for your opponent to navigate and a target location for your opponent to reach. There must be at least one path from the left side of the board to the goal.

On your turn, if your hunting ship is off the board, you choose one of the squares on the left side to enter your opponent's grid. If you are already on the grid, you can choose one square orthogonal from your current position to which to travel (or one square orthogonal from any location along your current path). After any successful movement that does not hit a wall, you get to try to move again. First player to reach his opponent's goal wins.

It's cute, with about the same depth as Battleship, or perhaps a little closer to Stratego. However, it eventually comes down to a series of blind guessing with no real information (other than your opponent's placement style). Of course, it's long out of print, but you can pick up a copy at the above link.

I also played (at lunch) a game of Homesteaders with Laurie and Abraham. I was pretty confident that I was winning, and so was surprised that Abraham beat me by a few points. Usually, when I think I'm losing in Homesteaders I'm actually winning, and when I think I'm winning I'm winning. I'm still not sure where I went wrong. Laurie thinks it's because Abraham was pulling in more trade chips per round than I was (3 to 1). But Laurie wasn't pulling in any, and so her progress was quite hobbled.

Happy new year.

Sunday, August 26, 2012

Shabbat Games: Troyes, Kingdom of Solomon, Amyitis

A week ago shabbat I played Troyes and Kingdom of Solomon with Nadine, Eitan, and Emily. This week I played Amyitis with Abraham and Sarah.

Troyes: First plays for Eitan and Emily. Eitan won in the mid-60s, about 10 points over Emily. Nadine and I were tied with one point below Emily. Nadine's favorite level three yellow card, the Sculptor (15 cost, 6/5 points, 3 yellow = 1 point), came out yet again, but she only got to use it a few times.

I managed to grab a decent red card point generator, The Joust (5 cost, 3/2 points, 3 red = 2 points if you have the most red dice). Eitan won by fighting the most events and earning the 6 point bonus for Henry 1; Emily gained the 6 point influence bonus of Hughes de Paynes. Nadine and I didn't get much in the way of bonuses.

Kingdom of Solomon: First plays for me and Nadine.This is a new game from Philip duBarry and Minion Games.

This is a worker placement, building game. As you build buildings, you gain extra placement options from your buildings. You can also build in the temple, which gives you VP or a chip, your choice: the player with the most chips at end game gets 20 points (about 3-4 times the VP value of the usual placement).

The spaces give you goods to build the buildings. Some of the spaces give big bonuses, but you have to use all of your remaining workers to claim one, so it's a chicken game of who will spend his 2 or 3 workers to take one before someone else does. Since there are three of these spaces, it's probably not as much of a deal in a game with less than four players.

Lather rinse repeat. You can't build a building in the first round, because you don't have enough resources. You really HAVE to build a building every round after that, because not only are the buildings worth 14-18 points (nearly as much as the "most chips" bonus) but the buildings also give you minor benefits on the board. Nadine missed one building round, but she got the chips benefit of 20 points, and so won the game.

When we first started playing, everything looked like it was balanced ok except for the Thief action which allows you to steal a good from another player. That nearly brought the entire game crashing down to a halt for me. I HATE that mechanic, especially when the value of a good is critical, when multiple players can effectively gang up on one, and when anything you plan is subject to ruin on the whim of another player. I took the Thief every chance I could because I hated it; I didn't even like to play it, but better to play it than be subject to it. If the space's value had continued to be as annoying during the rest of the game as it was during the first several rounds, I would have quit mid-game.

As it happens, we began collecting a sufficient amount of goods during the game that the loss of one became relatively irrelevant, and so the game was redeemed. The redemption came from not only the amount of goods we collected but from the hidden cards with goods that we held, which made targeting a specific good that you think another player needs to be harder. Nadine and I believe that the problem caused by this mechanic can be solved by giving the victim some kind of compensation: you lose a good and possibly the chance to build a building in exchange for something (that might help you this round or the next).

The second problem was the absolute necessity of building every round (or taking one round to secure the temple bonus). That made the turn order combined with which cards get flipped up during the turn an overpowering luck factor. Turn order is fine when the board information is always available; it's a crap-shoot when you spend resources to go first only to reveal four cards of equal value, or don't spend the resources to go first only to reveal 1 powerful card (available only to the first player) and some bad cards. This can be solved by turning face up the upcoming cards in the deck.

Aside from those details, the game was ok, a medium worker control game. Even Nadine seemed to come around in the end.

Amyitis: First play for Abraham and Sarah, second (in a long time) for me. I bought this game after my first play; though I recalled that there was a card availability problem (like in Kingdom of Solomon above), I didn't recall what it was, and I remembered the game being fun.

In this game, you build the gardens on Babylon. Each round you take as many actions was you want:: either a) take one of the available 9 workers in four types, or b) spend some of your goods on the camel track.

The four types of workers let you a) take a camel, b) take a good, c) place an irrigation cube for 2 points, or d) place a cube in a temple. The camel track lets you a) bump up your income or VP or b) plant a garden space.

To move on the camel track requires camels, goods, and timing. Planting nets you VPs, bumps your income or VP, and gives a few VPs to the person who most irrigated the area. Temples pay out in some kind of resource or VP at the end of each round.

The game is filled with viable options and paths, which makes it intriguing and fun (for me). VPs and money are available everywhere; money is tight, but there are mitigating mechanics. There are usually a few camels to be had here are there, and you only need one camel to move on the track. However, you need one or more resources to do anything after moving, and that's where the gridlock comes in.

When you are first player, if you have first crack at the only resource giving worker, you're in great shape. If there are three resource giving workers in a three player game, then your turn advantage has basically given you nothing. And the reverse, of course: if you're last player and there are enough workers to let you get a resource, great. If not, you're screwed. Very, very rarely will someone not take a resource giving worker as first player, and that's only if there are enough of them that it will come back to him anyway (for slightly higher cost).

Once again, I have to shake my head a this mechanic and ask: didn't they see this as a problem during playtestiung? It wasn't just this play: the same thing happened last play, and all the plays by the guy who taught me the game.

Luckily, borrowing from some other games, I can once again fix it: The workers costs range from 0 to 2. It seems simple enough to just add an infinite supply of workers available of every type that cost 3. So if you run out of one kind, you are not locked out from a resource because of a bad card draw, so long as you stock up on some reserve cash.

Have to try it.

The only other potentially unbalanced effect was the third level income card, available to only one person that gives 2 VP per round. If gained early, and that's not too difficult without much sacrifice, the card will net you upwards of 16 or more VP during the game (not to mention the extra money), which is far better than any victory point gain anywhere else. And, once again, it's availability is subject to the whims of turn order.

Abraham took it from me; he still lost the game by around 14 points, but I had to concentrate on screwing him the entire game from that point on. And he forgot about the 10 point bonus for planting six regions.

Reducing the bonus to 1 point per round still makes it a desirable card without the potential unbalancing effect; of course, if the card is gained late in the game, it won't give too many VPs.

Yehuda

Thursday, August 23, 2012

Games Day in Jerusalem Oct 4

As a reminder, this blog is on slowdown, though I will still post from time to time. I post a little more frequently (like pictures from recent weddings) on Facebook.

I carry the games No Thanks and Parade with me as games to play with the children of families to which I am invited for a meal. I played a few rounds of each of them over the last few weekends. Game nights in Raanana continue as usual, even if the session reports are late.

We're planning a Games Day in Jerusalem for Thursday, Oct 4.

My book writing has slowed down as I'm reading more books and less articles.

Yehuda

Thursday, August 02, 2012

Olympics Badminton: A Study in Bad Game Design

Here's a game for you:

The game lasts eight rounds. In each of the last five rounds, if you lose against your opponents you are out of the game. In other words, you have to win each round in order to win the game.

In the first three rounds, if you lose against your opponents, the only result is that you will receive easier challenges in the last five rounds; there are no penalties for losing, because the rounds are not scored. If you win these rounds, you face harder challenges in the last five rounds, making it much harder to win the whole game.

And oh yeah: The only thing that counts is winning the whole game, for which you are massively rewarded.

Any idiot could tell you that a player's best move is to LOSE the first three rounds. These rounds don't count for anything other than to make your life more difficult in the last five rounds, which are the only ones that actually provide any payoff; and the payoff is the same whether the challenges in the last rounds are more or less difficult.

Sounds like a dumb game? That's Badminton in the London 2012 Olympics, where 4 pairs of players, including the most recent gold medal winner from the last Olympics, were tossed out of the Olympics for "match fixing". Did they toss the game because of shadowy gambling connections? No, they played the game as it was designed by losing the first games in order to face easier challenges in the last games, the last ones being the only ones that counted.

But to hear the Olympics officials, the media, the fans, and the news pundits talk about it, you would think that they cheated. A scandal! A shame on the Olympics, the game, and the world! Well, technically they violated two codes of sportsmanship that require players to play their best during all games and adhere to the spirit of the games. But some of what I've heard is just nonsense.

"The players are supposed to be providing an example to the young people of the world" (BBC). Uh, no they're not. They're supposed to win the gold medal.

People who paid money to watch the game don't expect to see lackluster performance. "Who wants to sit through something like that?" said the Olympic chief. So what? The players are there to win the gold medal, not to entertain the audience. How about we ask them to perform a tap dance while they play? That would be entertaining.

"It's not in the spirit of the games." Really? Trying to win a gold medal by conserving your resources during completely irrelevant rounds is not in the spirit of the games?

I don't know who made the decision to add these useless and silly preliminary rounds (apparently added to prolong the games so that the organizers make more money by selling more tickets), but whomever it was wasn't a game designer, or a good one at any rate. A good game designer knows that when you want players to perform a particular task, you have to offer a reward that motivates them. If the reward for throwing the game is higher than the reward for winning it, guess what is going to happen?

You can't just toss a meaningless game or fake competition or points (I'm looking at you, poorly designed gamification) into an activity and expect someone to play for them if you simultaneously punish them for doing so.

How about providing games that matter to the players, and not just the spectators and the sponsors?

Yehuda

Tuesday, July 31, 2012

Why I Hate the Olympics

Once upon a time I enjoyed watching some Olympics events like gymnastics. Now I don't care.

1. The IOC has turned what was once grassroots and heartfelt into a moneymaking sponsor-driven ad fest.

They security firms were unable to find enough security personnel needed to secure the games, but they managed to find almost 300 brand enforcers to walk around taping over faucets at local establishments bearing company names that haven't sponsored the event.

Their corporate money-driven greed prevents anyone except NBC, who signed an exclusive contract for over $1 billion, from broadcasting the event so many people didn't get to see it and it wasn't live streamed on the Internet (what was, was plagued with delays and problems). Live events should not HAVE exclusivity contracts; they should be unenforceable. NBC wouldn't have covered the games otherwise?

The IOC has tried to geoblock social media reporting about the event. My ONLY choice for seeing the Olympics is via illegal download (simple, but not interested). Update: Turns out I can see the Olympics on IBA (thanks Bassie).

You can't even mention the word Olympics, the date 2012 and the word games, or any symbology associated with the games without being hit with a lawsuit. A 30 year old Greek restaurant named Olympic Gyro was forced to change its name to "protect the rights" of the corporate sponsors. An 81 year old grandmother making little teddy bears to sell for $1 was shut down.

The IOC went so far as to try to prevent anyone from linking to their site if the link was in a context that wasn't positive (to universal scorn and derision).

Ticket prices range from a mere 15 GBP for cheap seats at events that last 30 minutes to over 700 GBP for good seats in some events. Most seats are 50 GBP or up. (To be fair, there were some 20 GBP seats at the opening ceremony, with other seats ranging as high as 2000 GBP.)

So much for the games of the people.

2. The competition brings out the worst.

Winning is far more important than competing. The World Doping Agency is now an integral part of the IOC, and several athletes have already failed doping tests. Bizarrely, even the players in the mind sports games are subject to doping tests, as if someone playing Chess is ever going to take steroids to win a game!

Never heard of the World Mind Sports Games? They're part of the Olympics, but they don't televise well so no one seems to care.

As for the former humans who now complete, don't even think about it unless you have a ton of money for the computers and science that can analyze your every twitch to sculpt your body and movement into robotic perfection.

Does the competition break down stereotypes and increase world peace? Apparently not, if you consider the recent spate of athletes tossed out of the game for racist tweets. The Lebanese team refused to train near the Israelis and the Iranian team won't compete against them.

Does the competition at least bring pride to their nations? I don't know, but it sure doesn't do anything of importance for them. Did you know that Syria has an Olympic team? Has that registered yet? Who in Syria is going to benefit right now if their team wins or loses?

Does the competition even inspire anyone to exercise? Or do we just live vicariously through those who do?

Countries don't benefit internally from having their players win or lose, and countries don't make peace as a result of the competition.

3. It costs too many resources.

The UK taxpayer has spent more than $14 billion (Sky News reportedly thinks it may end up at over 24 billion GBP) to host the games, and the only one benefiting from that is the IOC and its sponsors. They spent $500,000 just on 17 sandstone toadstools. The people of England could have used that money at this particular time (when they are cutting pensions, sick pay, or simply firing public sector workers). The people lost a vast amount of public space, either destroyed or permanently turned over to corporate ownership. Other countries have spent millions to billions of dollars to send their athletes.

The UK assigned more armed forces to protect the Olympics than they deployed to Afghanistan. Don't these people have anything better to do?

4. It takes up too much media time.

7 rockets aimed at civilians have hit Israel since the start of the Olympics. These were not in response to any activity on Israel's part, just the daily fun time of Islamic militants. Did your news cover that?

The only English language radio I receive here is the BBC, whose reporters appear to be in a continuous state of climax over the games and believe that all their listeners are too.

Around the world, real things are happening; other than a great monetary, privacy, and human rights loss to UK taxpayers and the imaginary importance of winning some games, nothing is happening in London.

Yehuda

P.S. And I didn't even mention the minute of silence controversy. The IOC said that the minute of silence for the Israeli victims of massacre 40 years ago at the Olympics was not appropriate for an Olympic opening ceremony, but the 4 hour ceremony managed to include a minute of silence for people killed in WW1 and WWII. Past Olympics ceremonies have included minutes of silence for those killed on 9/11 and in London on 7/7.

Read: we don't want Arab countries to boycott the Olympics. How about this: tell any country that threatens to boycott the games that they are violating the spirit of the games and then throw them out? Oh right: money.