# in the Hare and Hounds game, will Hare always win? **URL:** \ **Category:** Factual Questions\ **Created:** [January 29, 2011, 5:13am UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378 "2011-01-29T05:13:06Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![drhess](https://avatars.discourse-cdn.com/v4/letter/d/94ad74/32.png) [@drhess](https://boards.straightdope.com/u/drhess)\ **Post date:** [January 29, 2011, 5:13am UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/1 "2011-01-29T05:13:06Z")
Assuming perfect play by both sides in the Hare and Hounds game, will Hare always win? Several websites sponsor Java coded versions of the game and even after learning to win as hounds several times, the version that I paid (which “learned” as you went along) seemed able to eventually always win. Although, since repeated positions are a win for the hare, not a draw, I guess you could say that with one rule change (draws given if positions repeat without the hare passing the hounds or the hare being trapped), that with perfect play it’s always a draw. Is there a name for games where only one side always wins with correct play? ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [January 29, 2011, 3:15pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/2 "2011-01-29T15:15:46Z")
> [@drhess](#): > > Is there a name for games where only one side always wins with correct play? Deterministic. The hare and hounds is such a game. ---
**Author:** ![DCnDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dcndc/32/2842_2.png) [@DCnDC](https://boards.straightdope.com/u/DCnDC)\ **Post date:** [January 29, 2011, 3:19pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/3 "2011-01-29T15:19:03Z")
> [@drhess](#): > > Is there a name for games where only one side always wins with correct play? It’s called a [solved game](http://en.wikipedia.org/wiki/Solved_game). ---
**Author:** ![DCnDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dcndc/32/2842_2.png) [@DCnDC](https://boards.straightdope.com/u/DCnDC)\ **Post date:** [January 29, 2011, 3:43pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/4 "2011-01-29T15:43:44Z")
Correction, or rather, clarification: Hare and Hounds is a deterministic game, and a game that is always won by one side given perfect play is a solved game, however I don’t believe that Hare and Hounds is a solved game. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [January 29, 2011, 6:15pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/5 "2011-01-29T18:15:59Z")
Not quite. For a game to be solved, it’s also necessary that it be known what perfect play is. For instance, in the game of Hex, it’s known that player 1 will always win with perfect play, but (aside from very small game boards) it’s not known how to always do that, so it’s not solved. It’s widely suspected, but not proven, that the same is true of chess (it’s conceivable that black can always force a draw, but considered unlikely, and even less likely that black might be able to force a win). ---
**Author:** ![Dead\_Cat](https://avatars.discourse-cdn.com/v4/letter/d/9fc29f/32.png) [@Dead\_Cat](https://boards.straightdope.com/u/Dead_Cat)\ **Post date:** [January 30, 2011, 3:57pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/6 "2011-01-30T15:57:58Z")
> [@Chronos](#): > > It’s widely suspected, but not proven, that the same is true of chess (it’s conceivable that black can always force a draw, but considered unlikely, and even less likely that black might be able to force a win). Surely it is downright impossible for black to be able to force a win, since if such a sequence of moves is found, White can simply avoid it by mirroring Black’s moves (taking the first Black move as White’s first move), and forcing the win for White instead? Or is it theoretically possible that White is in fact in _zugzwang_ at move 1? I would find that hard to believe given the symmetrical position, though. ---
**Author:** ![Snarky\_Kong](https://avatars.discourse-cdn.com/v4/letter/s/a183cd/32.png) [@Snarky\_Kong](https://boards.straightdope.com/u/Snarky_Kong)\ **Post date:** [January 30, 2011, 5:46pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/7 "2011-01-30T17:46:09Z")
> [@Dead\_Cat](#): > > Surely it is downright impossible for black to be able to force a win, since if such a sequence of moves is found, White can simply avoid it by mirroring Black’s moves (taking the first Black move as White’s first move), and forcing the win for White instead? Or is it theoretically possible that White is in fact in _zugzwang_ at move 1? I would find that hard to believe given the symmetrical position, though. I don’t understand your logic. Lets take a more simple game, dueling. Perfect play by the person that goes first results in a win. It seems like you’re arguing that if the second (dead) person does the same thing as the first, then they’ll win? I guess you’re hoping for white to checkmate black one move after losing the game? Hell, this falls apart at the first check at the latest, probably much much sooner. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [January 30, 2011, 6:40pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/8 "2011-01-30T18:40:59Z")
> [@](#): > > Surely it is downright impossible for black to be able to force a win, since if such a sequence of moves is found, White can simply avoid it by mirroring Black’s moves (taking the first Black move as White’s first move), and forcing the win for White instead? Or is it theoretically possible that White is in fact in zugzwang at move 1? I would find that hard to believe given the symmetrical position, though. It’s hard to believe, like I said, but it’s never been rigorously _proven_ that white is not in zugzwang at the start of the game. In Hex, by contrast, there is no such thing as zugzwang: A move might not improve your position by very much, but it can never make your position worse. So the strategy-stealing argument (which is a little more sophisticated than just mirroring one’s opponent) is valid in Hex, and thus player 1 can always force a win. ---
**Author:** ![RealityChuck](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/realitychuck/32/195_2.png) [@RealityChuck](https://boards.straightdope.com/u/RealityChuck)\ **Post date:** [January 30, 2011, 8:26pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/9 "2011-01-30T20:26:58Z")
Even when it was played as a sport, not a game, the hares always won. It was actually quite popular in the US in the 1870s, with clubs established at many East Coast colleges. You can see a re-creation of it in the Orson Wells’s **The Stranger** ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [January 30, 2011, 9:25pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/10 "2011-01-30T21:25:20Z")
> [@Dead\_Cat](#): > > Surely it is downright impossible for black to be able to force a win, since if such a sequence of moves is found, White can simply avoid it by mirroring Black’s moves (taking the first Black move as White’s first move), and forcing the win for White instead? Or is it theoretically possible that White is in fact in _zugzwang_ at move 1? I would find that hard to believe given the symmetrical position, though. It’s possible. White cannot simply mirror Black’s moves, because whatever Black’s optimum response is to White’s first move, White can’t play it himself first since Black has not yet played any move at all. It’s perfectly possible for a symmetrical position to be _zugzwang_, although the evidence to date is that the array is not such a position and, indeed, seems statistically to favour White by a respectable margin. ---
**Author:** ![Dead\_Cat](https://avatars.discourse-cdn.com/v4/letter/d/9fc29f/32.png) [@Dead\_Cat](https://boards.straightdope.com/u/Dead_Cat)\ **Post date:** [January 30, 2011, 11:33pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/11 "2011-01-30T23:33:36Z")
> [@Snarky\_Kong](#): > > I don’t understand your logic. > > Lets take a more simple game, dueling. Perfect play by the person that goes first results in a win. It seems like you’re arguing that if the second (dead) person does the same thing as the first, then they’ll win? I guess you’re hoping for white to checkmate black one move after losing the game? Hell, this falls apart at the first check at the latest, probably much much sooner. This was not what I was meaning to argue - I meant that (to use the duelling analogy again) if it was found that a winning strategy for the second player in a duel was to shoot the first player in the head (and for some reason this was not known before), the first player can simply negate this by taking this strategy for themselves. See below for a further explanation of what I was attempting to convey. > [@Chronos](#): > > It’s hard to believe, like I said, but it’s never been rigorously _proven_ that white is not in zugzwang at the start of the game. In Hex, by contrast, there is no such thing as zugzwang: A move might not improve your position by very much, but it can never make your position worse. So the strategy-stealing argument (which is a little more sophisticated than just mirroring one’s opponent) is valid in Hex, and thus player 1 can always force a win. > [@Malacandra](#): > > It’s possible. White cannot simply mirror Black’s moves, because whatever Black’s optimum response is to White’s first move, White can’t play it himself first since Black has not yet played any move at all. It’s perfectly possible for a symmetrical position to be _zugzwang_, although the evidence to date is that the array is not such a position and, indeed, seems statistically to favour White by a respectable margin. Interesting, thanks. I am aware that it is possible for symmetrical position to be _zugzwang_ (king and pawn against king provides an obvious example), so I suppose it is possible, but unlikely, as you say. I am also aware that the “strategy-stealing argument” may not just involve mirroring your opponents moves - my point here was that if a winning line of play was found for Black in chess, from the start of the game, then you would think it possible that White could win in the same way by using Black’s first move in this line as White’s first move. But of course, it is theoretically possible that such a winning line by Black is possible only because White’s first move creates a weakness. I personally think that this should not be the case, particularly if White opens with a knight move, but I can see how it is not impossible. If chess computers and data processing power continues to improve at the rate we have seen in the last twenty years, we may not have to wait too long for the definitive answer. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [January 31, 2011, 12:44am UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/12 "2011-01-31T00:44:01Z")
> [@](#): > > If chess computers and data processing power continues to improve at the rate we have seen in the last twenty years, we may not have to wait too long for the definitive answer. Moore’s Law is fast, but not that fast. Even if computing power continues its current exponential growth, it’ll still take a very long time indeed before we have enough power to solve chess via brute force. What you need is a major leap in technology, like possibly practical quantum computing (though I don’t think anyone’s come up with a quantum algorithm for chess, nor even a rigorous proof that such is possible). ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [January 31, 2011, 12:59pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/13 "2011-01-31T12:59:14Z")
> [@DCnDC](#): > > … I don’t believe that Hare and Hounds is a solved game. I _strongly_ doubt the game has never been solved. To the contrary, the game is simple so, like tic-tac-toe, those who write playing software for it at all, usually focus on less trivial tasks like automatic learning. I enjoy solving games, and am not too proud to avoid it just because the game is trivial. 😃 Assuming I’ve understood the rules correctly, Hounds can force victory. I examined 4890 positions to reach this conclusion. The repetition-of-moves rule is the only complication; a simple workaround is to limit the number of vertical moves by Hounds; I discover that 5 is enough. (If Hounds are limited to a maximum of 4 vertical moves in the game, Hare wins.) > [@Chronos](#): > > It’s hard to believe, like I said, but it’s never been rigorously _proven_ that white is not in zugzwang at the start of the game. [Chess master Gyula Breyer wrote:](http://books.google.com/books?id=rWYK2rOi8dAC&pg=PA121) > [@](#): > > After 1 P-K4 White’s game is in its last throes. ---
**Author:** ![Steve\_MB](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/steve_mb/32/5339_2.png) [@Steve\_MB](https://boards.straightdope.com/u/Steve_MB)\ **Post date:** [January 31, 2011, 3:02pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/14 "2011-01-31T15:02:35Z")
**White:** P-K4 **Black:** (resigns) ---
**Author:** ![drhess](https://avatars.discourse-cdn.com/v4/letter/d/94ad74/32.png) [@drhess](https://boards.straightdope.com/u/drhess)\ **Post date:** [February 2, 2011, 3:21pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/15 "2011-02-02T15:21:33Z")
> [@Chronos](#): > > Not quite. For a game to be solved, it’s also necessary that it be known what perfect play is. For instance, in the game of Hex, it’s known that player 1 will always win with perfect play, but (aside from very small game boards) it’s not known how to always do that, so it’s not solved. It’s widely suspected, but not proven, that the same is true of chess (it’s conceivable that black can always force a draw, but considered unlikely, and even less likely that black might be able to force a win). Back to Hare and Hounds though: The board is fairly small, the pieces are few and the hounds can only move forward (straight or diag., but forward). After just a few moves it seems that the Hare only has a few choices to make and one will allow it to force a perpetual repition (win) or pass (win). No? ---
**Author:** ![SCSimmons](https://avatars.discourse-cdn.com/v4/letter/s/e495f1/32.png) [@SCSimmons](https://boards.straightdope.com/u/SCSimmons)\ **Post date:** [February 2, 2011, 3:49pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/16 "2011-02-02T15:49:17Z")
> [@septimus](#): > > I _strongly_ doubt the game has never been solved. To the contrary, the game is simple so, like tic-tac-toe, those who write playing software for it at all, usually focus on less trivial tasks like automatic learning. > > I enjoy solving games, and am not too proud to avoid it just because the game is trivial. 😃 Assuming I’ve understood the rules correctly, Hounds can force victory. Are you going to share your solution, or is this to be left as an exercise for the student? 🙂 ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [February 2, 2011, 5:21pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/17 "2011-02-02T17:21:45Z")
> [@SCSimmons](#): > > Are you going to share your solution, or is this to be left as an exercise for the student? 🙂 I’m afraid I’ve little of interest to share. ☹ I didn’t derive strategic principles of play (though Googling I notice a website with such). All I did was write a simple piece of software that explores the game, concludes that Hounds can force victory, then challenges human to play (insisting human takes the Hare 😃 ). Computer starts by moving his rearmost man; I didn’t check whether other first moves also win. The software isn’t Javascript (it’s just ordinary C), so I’ve no plan to place it on-line. (If you want the source, I’d be happy to e-mail it to you. PM me with your e-mail address.) ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 3, 2011, 4:58am UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/18 "2011-02-03T04:58:50Z")
> [@](#): > > Back to Hare and Hounds though: The board is fairly small, the pieces are few and the hounds can only move forward (straight or diag., but forward). After just a few moves it seems that the Hare only has a few choices to make and one will allow it to force a perpetual repition (win) or pass (win). No? Well, it’s certainly easier to solve than, say, chess (and probably also easier than checkers, but there’s probably been more effort expended on checkers). I just don’t know whether it actually has been solved, though, or is just solvable. ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [February 3, 2011, 8:17am UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/19 "2011-02-03T08:17:27Z")
> [@septimus](#): > > Assuming I’ve understood the rules correctly, Hounds can force victory. > [@Chronos](#): > > I just don’t know whether [Hounds and Hares] actually has been solved, though, or is just solvable. Same to you, buddy! 😃 ---
**Author:** ![SCSimmons](https://avatars.discourse-cdn.com/v4/letter/s/e495f1/32.png) [@SCSimmons](https://boards.straightdope.com/u/SCSimmons)\ **Post date:** [February 3, 2011, 10:49pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/20 "2011-02-03T22:49:08Z")
> [@septimus](#): > > Same to you, buddy! 😃 He’ll know it’s been solved when he sees a solution. 😉 I just PM’d you my e-mail address–I’d love to see the code. [Next page](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378.md?page=2)