## 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• Withdrawn a side piece from a complete row: the other side piece may or may not still be withdrawable, depending on slight center of gravity changes in the layers.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 The caveat is that the last and central piece MIGHT be withdrawn if the layers are highly stable and the player is very dexterous.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.