Bobina is a game for two players, where each player tries to make a loop of stones on the board while preventing her opponent from doing the same.

Rules

Setup: place one grey stone on each of the 6 corners of the board, and place an additional 4 grey stones on non-adjacent but otherwise random spaces. One player takes ownership of the black stones, and the other takes the white stones.

The players take turns. On your turn you must either place 1 grey stone or 1 stone of your color on any empty space. The first player to form a loop of her own color, possibly including grey stones, wins. If the board fills without a loop of either color forming, the player who was the first to play a stone of her own color loses.

Design Background + Discussion

Bobina is the love child of two previous games: Coil (which pleases me) and Glorieta (which doesn’t). It combines elements of both in a form more elegant than both.

Bobina, Coil, and Glorieta are all part of a longstanding project to design games with a hex loop win condition (Havannah long ago convinced me it’s a worthy project).

Two things I like about loops, as a win condition:

They’re intuitive and easy to visualize, especially on hex boards. They have many degrees of freedom and come in many sizes. A loop can be a grand strategic objective, a local tactical objective, and anything in-between. With the right mechanics, this range of objectives can be balanced, and thus a single stone placement can have many consequences. It can: build toward local tactical loop threats, build toward big strategic loop threats, defend against local enemy loop threats, and defend against strategic enemy loop threats. Sometimes all of those at once!

In Bobina, the players bid for a tie-breaker by playing neutral stones that both players can use to make loops. But the more neutral stones are on the board, the less likely the game will end in a tie. The value of the tie-breaker falls as the bid for it rises.

The bidding comes from Coil (which was in turn inspired by Unlur), and as in that game, it balances the players’ chances and generates brinksmanshipy tension.

The neutral stones come from Glorieta. In Coil, after the bid is over, only one player can win by forming a loop. The other player wins by stopping him, making the game asymmetric after the bid. In Bobina, thanks to the neutral stones, both players can win by forming a loop, as in Glorieta. This makes Bobina more symmetrical than Coil after the bid ends and ensures a higher proportion of games end with loops, which is what I want.

You might wonder why 6 of the neutral set-up stones are not random, but placed in the corners. Two reasons:

The corners, by themselves, are low-value spaces on which players would rarely play their own stones. Putting neutrals in the corners increases their value and spreads out the game. Because the corners are so low-value, I believe skilled players would fill them with neutrals during the bid anyway. Starting with filled corners eliminates the rote part of the bid so the players get right to the fun stuff.

Open Questions

The key uncertainty for me is how many neutral stones to lay out randomly at the start. This random setup serves two purposes:

Prevents memorized openings – randomized opening layouts often don’t work in many luckless combinatorial games because they bias the game toward one player. There’s no such problem here because they’re neutral (as long as there aren’t too many). The more neutrals you randomly lay out, the shorter the bid will be – I don’t know what the right bidding length is for maximum fun.

Another uncertainty is the best board-size. On one hand, the board should be large enough so the winning loops come in a variety of sizes and shapes. On the other hand, the board shouldn’t be too large, because, between highly-skilled players, I believe the board will end mostly full (the nature of the bidding pushes the game in this direction), and I don’t want the game to be too long. The board pictured above seems pretty good for now.

Finally, I’d like to know, for high-level play, what fraction of games end with completed loops and what fraction end with a full, loop-less board. In games where the bid-winner wins the game, there will always be a loop, by definition. Since the bid winner will win the game about half the time, we know a loop will form no less than half the time overall.

But what happens in games where the bid-winner loses? In some instances, she’ll lose because no loop forms. In others, she’ll lose because her opponent forms a loop first. What are the relative frequencies of those two outcomes? It’s a hard question.

I can tell you what I want the answer to be: I want the bid-loser to win the game by forming a loop at least as often as she wins by stymie. The more often the bid-loser wins by stymie, the more like my game Coil Bobina will be, and the less interest the neutral stones will add. I think it’s more fun and exciting when the game ends in a loop than when it doesn’t. That’s the whole reason the neutral stones exist here. If they’re not doing their job, they’re pointless.

If they did turn out pointless, it occurs to me a modified turn rule would likely address the issue:

The players take turns. On your turn you must either place 1 grey stone or 1 stone of your color on any empty space. After either player has placed a stone of her color for the first time, each must thereafter place 2 stones of her color on her turn.

We shall see…