## 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
28. Ohio State University
29. Onyx
30. Party
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• Withdrawn a side piece from a complete row: the other side piece may or may not still be withdrawable, depending on slight center of gravity changes in the layers.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.