# 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:** 4
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [February 7, 2011, 9:55pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/61 "2011-02-07T21:55:00Z")
> [@SCSimmons](#): > > A program _can_ be a proof, if it’s clear enough and well-documented. No. A program can be part of a proof, but there also needs to be an argument that the program is complete and correct. That part can’t be done in code. ---
**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 7, 2011, 10:27pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/62 "2011-02-07T22:27:19Z")
> [@](#): > > No. A program can be part of a proof, but there also needs to be an argument that the program is complete and correct. That part can’t be done in code. On the other hand, there’s not all that great a difference between computer code and a symbolic formal system of the sort used to write a proof. One could just as well claim that you can’t write a proof in a symbolic formal system, because you need both the formal derivation and an argument that the derivation is complete and correct. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [February 7, 2011, 11:04pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/63 "2011-02-07T23:04:55Z")
> [@Chronos](#): > > On the other hand, there’s not all that great a difference between computer code and a symbolic formal system of the sort used to write a proof. One could just as well claim that you can’t write a proof in a symbolic formal system, because you need both the formal derivation and an argument that the derivation is complete and correct. This is a little bit of a hijack, but if you’re dealing with C or most other imperative languages, the difference between proofs and programs is a vast chasm. There are other languages where the difference is a bit smaller, [to say the least](https://secure.wikimedia.org/wikipedia/en/wiki/Curry-Howard_correspondence), but that’s not what almost anyone is thinking about here. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [February 8, 2011, 2:06am UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/64 "2011-02-08T02:06:28Z")
> [@Chronos](#): > > > [@drhess](#): > > > > Assuming the “traditional rules” with a draw (repititions) as a win for Hare. Can a smart, experienced Hare player always (assuming no flaws in play) wins against the best Hounds can do? Is anybody debating that the answer to this is yes, Hare always wins? (Or should the question be reworded?) > > You seem to be asking “If the Hare can always win, can the Hare always win?”. The answer to that question is clearly “yes”, though it looks like it’s a true conditional by virtue of a false premise. I’m not sure how you’re getting this, although it is a bit hard to parse. But I think **drhess** ’s question could be rephrased as: “Under the traditional rules where a draw (meaning too many repetitions) is a win for Hare, can the Hare, using best play, always win against the Hounds?” I do think the answer is “no, the hounds can force a win”, although I’m not as certain as **septimus** is. ---
**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 8, 2011, 2:14am UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/65 "2011-02-08T02:14:17Z")
On re-reading what **drhess** said, and then re-reading it again because I still had the wrong reading stuck in my head, I realize that I was completely mis-parsing the question, and gave an answer that wasn’t asked for. Ignore my post 62. ---
**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 8, 2011, 7:02am UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/66 "2011-02-08T07:02:04Z")
> [@ultrafilter](#): > > … the difference between proofs and programs is a vast chasm. A listing of all possible Hare moves and winning Hounds’ responses would constitute a rather rigorous proof, I think, at least if English phrases like “if Hare plays … Hounds play …” were inserted. My program can be modified to produce such a listing by adding one print statement. As my brain power has deteriorated with age, I’ve tried to make my C codings more simple and transparent. I think **SCSimmons** can attest, however, that my brain needs to deteriorate much more before my code has acceptable readability. :smack: ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [February 8, 2011, 11:02pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/67 "2011-02-08T23:02:20Z")
In the game room thread, the dogs immediately occupied the center position, and it was shown that if after the hare’s second move it goes back to the far right position, the hounds can force a win. There are only three other possibilities for the Hare’s location after its second move, due to symmetry. Those other three possibilities could be examined in the same manner fairly easily using the code. That’s assuming a win for the Hare isn’t found from that position, so you didn’t have to back up a move. ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [February 9, 2011, 1:02am UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/68 "2011-02-09T01:02:56Z")
So I finally found time to take a crack at solving this game. My approach… The number of game states is small. There are 11 spaces to be occupied; it is someone’s turn; and the hounds have accumulated some number 0 through 9 of vertical moves. In this enumeration, the number of game states is: 11 \* 10 \* 9 \* 8 \* 2 \* 10 / 6 = 26400 where the 6 in the denominator accounts for the indistinguishable hounds. Many of these board states are only accessible after passing through a “win” state, so we can cull those. Many others are simply inaccessible, _i.e._, they have no valid parent state, such as this one: ```auto Not accessible, since it's the hounds turn. The hare couldn't have come from anywhere... + + D + + + D R T=D VM=0 + + D ``` In the above notation, D=hound(dog), R=hare(rabbit), T=whose turn, VM=number of accumulated vertical hound moves. After culling post-win and inaccessible states, there are 23742 states left. Previous to this (to facilitate the culling and the later steps), I set up a multiply-linked list of the available game states. Each node of the network corresponds to a state and carries with it a list of all possible daughter states and all possible parent states. **Step 1:** Simply loop through the list of 23742 states, tagging all win-states. **Step 2:** Loop through again, looking for any state which is tagged as a win for one team but it is the other team’s turn. That is, if Team A wins in this state but it is Team B’s turn, then Team A is able to force this win by moving to this state on the previous turn. So, tag all parents of these states as wins for Team A. **Step 3:** Loop through again, looking for any state which is not yet tagged for either team. If all daughter states for this state are tagged for the same team, then this state is a lock for that team. Tag it as such. I repeat Steps 2 and 3 until the number of undetermined states no longer decreases. It so happens that when this condition is met, all states have been tagged for one team or the other. \*Result: \*there are 861 game states in which hounds can force a win. The starting state is not one of them. That is, **hare can force a win.** Of the 861 states from which hounds can force a win, only 95 distinct layouts exist when you remove the vertical-move-count multiplicity. Thus, I can list all 95 layouts from which a hound force is possible. The VM notation used below indicates the range of accumulated vertical moves that are okay if the hounds are to force. ```auto D D R + + + + + T=D VM=0-9 + + D D D + + + + + R T=D VM=0-7 + + D D R D + D + + + T=D VM=0-9 + + + D R D + + D + + T=R VM=0-9 + + + D + D + + D + R T=D VM=0-8 + + + D + D + + + D R T=D VM=0-7 + + + D R D + + + + + T=D VM=0-9 D + + D R D + + + + + T=D VM=0-8 + D + D + D + + + + R T=D VM=0-9 + D + D + D + + + R + T=D VM=0-8 + + D D + D + + + + R T=D VM=0-9 + + D D + D + + + + R T=R VM=0-8 + + D D + + D + + + R T=D VM=0-9 + + D D R + + D + + + T=D VM=0-9 + + D D + R + D + + + T=D VM=0-9 + + D D R + + + D D + T=D VM=0-8 + + + D R + + + D + + T=R VM=0-9 + + D D + R + + D + + T=D VM=0-9 + + D D + + + + D R + T=R VM=0-7 + + D D + + + + D + R T=D VM=0-7 + + D D + + + + + D R T=D VM=0-7 + + D D + + + + + + + T=D VM=0-9 D R D + D D + + + D R T=D VM=0-7 + + + + D D + + + R + T=D VM=0-6 D + + + D D + + + + + T=D VM=0-6 D R + + D D + + + + R T=D VM=0-8 + D + + D D + + + + + T=D VM=0-6 + D R + D D + + + R + T=D VM=0-8 + + D + D D + + + + R T=R VM=0-8 + + D + D R D + + + + T=D VM=0-8 + + D + D + D + + + R T=D VM=0-8 + + D + D R + D + + + T=D VM=0-7 + + D + D + + D + + R T=D VM=0-9 + + D + D + + + D R + T=D VM=0-9 D + + + D + + + D + + T=D VM=0-9 D R + + D + + + D + + T=D VM=0-9 + D R + D R + + D + + T=R VM=0-9 + + D + D + + + D R + T=D VM=0-9 + + D + D + + + D + R T=D VM=0-9 + + D + D + + + + D R T=D VM=0-9 + + D + D + + + + + R T=D VM=0-9 D + D + D + + + + + + T=D VM=0-8 D R D + D R + + + + + T=D VM=0-8 + D D + D + + + + + R T=D VM=0-9 + D D + R D D + D + + T=D VM=0-9 + + + + + D D + D R + T=D VM=0-9 + + + + + D D + + + R T=D VM=0-9 + + D + R D + D D + + T=D VM=0-8 + + + + + D + D D + R T=D VM=0-7 + + + + + D + D + D R T=D VM=0-7 + + + + + D + D + + R T=D VM=0-7 + D + + + D + D + R + T=D VM=0-9 + + D + + D + D + + R T=D VM=0-7 + + D + + D + D + + R T=R VM=0-9 + + D + + D + + D D R T=D VM=0-9 + + + + + D + + D R + T=R VM=0-7 D + + + + D + + D + R T=D VM=0-7 D + + + + D + + D + + T=R VM=0-7 D R + + + D + + D + + T=D VM=0-7 D + R + + D + + D R + T=D VM=0-9 + D + + + D + + D + R T=D VM=0-7 + D + + + D + + D + + T=R VM=0-7 + D R + + D + + D R + T=R VM=0-9 + + D + + D + + D + R T=D VM=0-9 + + D + + D + + + D R T=D VM=0-8 D + + + + D + + + D R T=D VM=0-9 + D + + + D + + + D R T=R VM=0-0 + + D + + D + + + + R T=D VM=0-8 D D + + + D + + + R + T=D VM=0-9 D + D + + D + + + + R T=D VM=0-8 D + D + + D + + + + R T=R VM=0-9 D + D + + D + + + R + T=D VM=0-8 + D D + + D + + + + R T=R VM=0-8 + D D + + R D + D D + T=D VM=0-8 + + + + + R D + D + + T=D VM=0-9 + D + + R + D + D + + T=D VM=0-9 + + D + + R D + D + + T=D VM=0-9 + + D + + R D + D + + T=R VM=0-9 + + D + + + D + D R + T=D VM=0-9 + + D + + + D + D + R T=R VM=0-9 + + D + + + D + D + + T=D VM=0-9 + R D + + R + D D D + T=D VM=0-4 + + + + R + + D D + + T=D VM=0-8 + + D + + R + D D + + T=R VM=0-6 + + D + + + + D D R + T=D VM=0-6 + + D + + + + D D + R T=D VM=0-8 + + D + + + + D D + + T=D VM=0-8 + R D + + + + D + + + T=D VM=0-9 D R D + + + + + D D + T=D VM=0-8 D R + + + + + + D D R T=D VM=0-9 + + D + + + + + D + R T=D VM=0-9 D + D + + + + + D + + T=R VM=0-9 D R D + + + + + D + R T=D VM=0-9 + D D + + + + + + D R T=D VM=0-8 D + D + + + + + + D R T=D VM=0 + D D ``` I haven’t seen anything so far that looks out-of-sorts, but I haven’t read the other thread yet. If anyone wants to give me an unlisted state that they think should be a hound-lock, I can do an analysis of that state (either to show why it isn’t a hound-lock or to uncover a bug in my code 🙂 ) I also haven’t chewed over these results much at all; hopefully someone finds something interesting in them… ---
**Author:** ![mr.jp](https://avatars.discourse-cdn.com/v4/letter/m/48db29/32.png) [@mr.jp](https://boards.straightdope.com/u/mr.jp)\ **Post date:** [February 9, 2011, 1:16am UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/69 "2011-02-09T01:16:04Z")
So can’t your program play against Septimus’? ---
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [February 9, 2011, 1:16am UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/70 "2011-02-09T01:16:33Z")
> [@septimus](#): > > A listing of all possible Hare moves and winning Hounds’ responses would constitute a rather rigorous proof, I think, at least if English phrases like “if Hare plays … Hounds play …” were inserted. My program can be modified to produce such a listing by adding one print statement. Or make up a system of algebraic notation, and print out the moves in algebraic notation. So what are you waiting for? Hop to it! ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [February 9, 2011, 1:24am UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/71 "2011-02-09T01:24:39Z")
> [@mr.jp](#): > > So can’t your program play against Septimus’? Yes. I haven’t had a chance to parse the history of this thread, so: is the conclusion still from **septimus** that hounds can force from the starting configuration? If so, then I’d be happy to play against **septimus** ’s program with mine, if only to find a fault with mine. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [February 9, 2011, 2:52am UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/72 "2011-02-09T02:52:35Z")
> [@Pasta](#): > > If anyone wants to give me an unlisted state that they think should be a hound-lock, I can do an analysis of that state I don’t see the position in [post 18](http://boards.straightdope.com/sdmb/showpost.php?p=13434778&postcount=18) shown as a win for the hounds, but we played that one out, and it seemed to be a forced win for the hounds. I’d like to see that one checked. I believed the plays I didn’t make as the hare always led to a loss for the hare, and eventually I could see the hare would lose no matter the move. ETA: the hounds just moved to reach that position. ETA2: I reference post 9 as losing for the hare a couple times and you _do_ have that as a win for the hounds. ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [February 9, 2011, 3:35am UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/73 "2011-02-09T03:35:31Z")
> [@ZenBeam](#): > > I don’t see the position in [post 18](http://boards.straightdope.com/sdmb/showpost.php?p=13434778&postcount=18) shown as a win for the hounds, but we played that one out, and it seemed to be a forced win for the hounds. I’d like to see that one checked. I believed the plays I didn’t make as the hare always led to a loss for the hare, and eventually I could see the hare would lose no matter the move. > > ETA: the hounds just moved to reach that position. > ETA2: I reference post 9 as losing for the hare a couple times and you _do_ have that as a win for the hounds. Beautiful… This is exactly the sort of test I wanted! Upon tracing this state’s tagging sequence, I found a mistake… (misplaced curly brace!). New results coming in next post… ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [February 9, 2011, 3:52am UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/74 "2011-02-09T03:52:43Z")
Updated result after bugfix (thanks, **ZenBeam**!) There are 4122 states from which hounds can force a win, and the starting configuration is one of them. That is, **hounds can force a win**. Eliminating the vertical-move-count multiplicity leaves 438 layouts, which I will attempt to paste into this message if the hamsters let me… Okay they won’t, but I’m only over by 2000 characters. I’ll break the list in two. Here are 219 of the hound-lock layouts: ```auto D D D + + + R + T=D VM=0-6 + + + D D R D + + + + T=D VM=0-9 + + + D D + D R + + + T=D VM=0-6 + + + D D + D + + R + T=D VM=0-9 + + + D D + D + + + R T=D VM=0-9 + + + D D + D + + + R T=R VM=0-8 + + + D D + D + + + + T=D VM=0-6 + R + D D + D + + + + T=D VM=0-8 + + R D D R + D + + + T=D VM=0-9 + + + D D + + D + + R T=D VM=0-9 + + + D D + + D + + + T=D VM=0-7 + + R D D R + + D + + T=R VM=0-9 + + + D D + + + D R + T=D VM=0-9 + + + D D + + + D + R T=D VM=0-9 + + + D D R + + + D + T=D VM=0-5 + + + D D + + + + D R T=D VM=0-7 + + + D D R + + + + + T=D VM=0-9 D + + D D + + + + R + T=D VM=0-8 D + + D D + + + + + R T=R VM=0-8 D + + D D + + + + + + T=D VM=0-8 D R + D D + + + + + + T=D VM=0-9 D + R D D R + + + + + T=D VM=0-8 + D + D D + + + + + R T=D VM=0-9 + D + D D + + + + + + T=D VM=0-8 + D R D D R + + + + + T=D VM=0-9 + + D D D + + + + R + T=D VM=0-8 + + D D D + + + + + R T=D VM=0-9 + + D D D + + + + + R T=R VM=0-8 + + D D + D D + + R + T=D VM=0-9 + + + D + D D + + + R T=D VM=0-9 + + + D + D D + + + R T=R VM=0-9 + + + D + D D + + + + T=D VM=0-9 + + R D R D + D + + + T=D VM=0-9 + + + D + D + D + R + T=D VM=0-9 + + + D + D + D + + R T=R VM=0-9 + + + D + D + D + + + T=D VM=0-9 + + R D R D + + D + + T=R VM=0-9 + + + D + D + + D R + T=R VM=0-7 + + + D + D + + D + R T=D VM=0-9 + + + D + D + + D + + T=D VM=0-7 + + R D + D + + + D R T=D VM=0-8 + + + D R D + + + + + T=D VM=0-9 D + + D + D + + + R + T=D VM=0-9 D + + D + D + + + + R T=D VM=0-9 D + + D + D + + + + + T=D VM=0-9 D R + D R D + + + + + T=D VM=0-8 + D + D + D + + + R + T=D VM=0-6 + D + D + D + + + + R T=D VM=0-9 + D + D + D + + + + R T=R VM=0-6 + D + D + D + + + + + T=D VM=0-9 + D R D + D + + + R + T=D VM=0-9 + + D D + D + + + + R T=D VM=0-9 + + D D + D + + + + R T=R VM=0-9 + + D D R + D D + + + T=D VM=0-9 + + + D R + D D + + + T=R VM=0-9 + + + D + R D D + + + T=D VM=0-9 + + + D + R D D + + + T=R VM=0-9 + + + D + + D D R + + T=D VM=0-9 + + + D + + D D R + + T=R VM=0-9 + + + D + + D D + R + T=D VM=0-9 + + + D + + D D + R + T=R VM=0-9 + + + D + + D D + + R T=D VM=0-9 + + + D + + D D + + R T=R VM=0-9 + + + D + + D D + + + T=D VM=0-9 R + + D + + D D + + + T=R VM=0-9 R + + D + + D D + + + T=D VM=0-9 + R + D + + D D + + + T=R VM=0-9 + R + D + + D D + + + T=D VM=0-9 + + R D + + D D + + + T=R VM=0-9 + + R D R + D + D + + T=D VM=0-9 + + + D R + D + D + + T=R VM=0-9 + + + D + R D + D + + T=D VM=0-9 + + + D + R D + D + + T=R VM=0-9 + + + D + + D R D + + T=R VM=0-7 + + + D + + D + D R + T=D VM=0-9 + + + D + + D + D R + T=R VM=0-9 + + + D + + D + D + R T=D VM=0-9 + + + D + + D + D + R T=R VM=0-9 + + + D + + D + D + + T=D VM=0-7 R + + D + + D + D + + T=D VM=0-9 + R + D + + D + D + + T=R VM=0-7 + R + D + + D + D + + T=D VM=0-9 + + R D + + D + D + + T=R VM=0-9 + + R D + + D + + D R T=D VM=0-9 + + + D R + D + + + + T=D VM=0-9 D + + D R + D + + + + T=R VM=0-9 D + + D + R D + + + + T=D VM=0-9 D + + D + R D + + + + T=R VM=0-9 D + + D + + D R + + + T=D VM=0-9 D + + D + + D R + + + T=R VM=0-9 D + + D + + D + R + + T=D VM=0-9 D + + D + + D + R + + T=R VM=0-9 D + + D + + D + + R + T=D VM=0-9 D + + D + + D + + R + T=R VM=0-9 D + + D + + D + + + R T=D VM=0-9 D + + D + + D + + + R T=R VM=0-9 D + + D + + D + + + + T=D VM=0-9 D R + D + + D + + + + T=R VM=0-9 D R + D + + D + + + + T=D VM=0-9 D + R D + + D + + + + T=R VM=0-9 D + R D R + D + + + + T=D VM=0-8 + D + D + R D + + + + T=D VM=0-8 + D + D + + D R + + + T=D VM=0-6 + D + D + + D + + R + T=D VM=0-9 + D + D + + D + + + R T=D VM=0-9 + D + D + + D + + + R T=R VM=0-8 + D + D + + D + + + + T=D VM=0-9 + D R D + R D + + + + T=D VM=0-9 + + D D + + D + + R + T=D VM=0-9 + + D D + + D + + + R T=D VM=0-9 + + D D + + D + + + R T=R VM=0-9 + + D D R + + D D + + T=D VM=0-8 + + + D + R + D D + + T=R VM=0-8 + + + D + + + D D R + T=D VM=0-8 + + + D + + + D D + R T=D VM=0-9 + + + D + + + D D + + T=D VM=0-8 + R + D + + + D D + + T=R VM=0-8 + + R D + R + D + D + T=D VM=0-9 + + + D + + + D + D R T=D VM=0-9 + + + D R + + D + + + T=D VM=0-9 D + + D + R + D + + + T=D VM=0-9 D + + D + + + D R + + T=R VM=0-9 D + + D + + + D + R + T=D VM=0-9 D + + D + + + D + + R T=R VM=0-9 D + + D + + + D + + + T=D VM=0-9 D R + D + + + D + + + T=D VM=0-9 D + R D + R + D + + + T=D VM=0-9 + D + D + + + D + + R T=D VM=0-9 + D + D + + + D + + + T=D VM=0-9 + D R D R + + D + + + T=D VM=0-9 + + D D + R + D + + + T=D VM=0-9 + + D D + + + D + R + T=D VM=0-9 + + D D + + + D + + R T=R VM=0-9 + + D D R + + + D D + T=D VM=0-8 + + + D + R + + D D + T=R VM=0-6 + + + D + + + + D D R T=D VM=0-6 + + + D R + + + D + + T=R VM=0-9 D + + D + R + + D + + T=D VM=0-9 D + + D + + + + D R + T=R VM=0-9 D + + D + + + + D + R T=D VM=0-9 D + + D + + + + D + + T=R VM=0-9 D R + D + + + + D + + T=D VM=0-9 D + R D R + + + D + + T=D VM=0-9 + D + D + R + + D + + T=R VM=0-9 + D + D + + + + D R + T=D VM=0-9 + D + D + + + + D + R T=D VM=0-9 + D + D + + + + D + + T=R VM=0-9 + D R D R + + + D + + T=R VM=0-9 + + D D + R + + D + + T=D VM=0-9 + + D D + + + + D R + T=R VM=0-9 + + D D + + + + D + R T=D VM=0-9 + + D D + R + + + D + T=D VM=0-9 D + + D + + + + + D R T=R VM=0-9 D + + D + + + + + D + T=D VM=0-9 D + R D + R + + + D + T=D VM=0-5 + D + D + + + + + D R T=D VM=0-5 + D + D + + + + + D R T=D VM=0-8 + + D D R + + + + + + T=D VM=0-8 D D + D + R + + + + + T=D VM=0-9 D D + D + + + + + R + T=D VM=0-8 D D + D + + + + + + R T=R VM=0-8 D D + D + + + + + + + T=D VM=0-9 D D R D R + + + + + + T=D VM=0-9 D + D D + + + + + R + T=D VM=0-9 D + D D + + + + + + R T=D VM=0-9 D + D D + + + + + + + T=D VM=0-9 D R D D R + + + + + + T=D VM=0-8 + D D D + + + + + R + T=D VM=0-8 + D D + D D D + + R + T=D VM=0-7 + + + + D D D + + + R T=D VM=0-8 + + + + D D D + + + R T=R VM=0-7 + + + + D D D + + + + T=D VM=0-7 + + R + D D + D + + + T=D VM=0-7 + + R + D D + + D + R T=D VM=0-9 + + + + D D + + + D R T=D VM=0-7 + + + + D D + + + R + T=D VM=0-8 D + + + D D + + + + + T=D VM=0-8 D R + + D D + + + + R T=D VM=0-9 + D + + D D + + + + + T=D VM=0-8 + D R + D D + + + R + T=D VM=0-8 + + D + D D + + + + R T=R VM=0-8 + + D R D + D D + + + T=D VM=0-7 + + + + D R D D + + + T=D VM=0-9 + + + + D + D D + R + T=D VM=0-9 + + + + D + D D + + R T=D VM=0-9 + + + + D + D D + + R T=R VM=0-7 + + + + D + D D + + + T=D VM=0-7 R + + + D + D D + + + T=D VM=0-7 + + R + D R D + D + + T=D VM=0-9 + + + + D R D + D + + T=R VM=0-9 + + + + D + D + D R + T=D VM=0-9 + + + + D + D + D R + T=R VM=0-9 + + + + D + D + D + R T=D VM=0-9 + + + + D + D + D + R T=R VM=0-9 + + + + D + D + D + + T=D VM=0-9 + + R + D + D + + D R T=D VM=0-8 + + + + D R D + + + + T=D VM=0-9 D + + + D + D R + + + T=D VM=0-6 D + + + D + D + + R + T=D VM=0-9 D + + + D + D + + + R T=D VM=0-9 D + + + D + D + + + R T=R VM=0-8 D + + + D + D + + + + T=D VM=0-8 D R + + D + D + + + + T=D VM=0-8 D + R + D R D + + + + T=D VM=0-8 + D + + D + D + + R + T=D VM=0-8 + D + + D + D + + + R T=D VM=0-9 + D + + D + D + + + R T=R VM=0-8 + D + + D + D + + + + T=D VM=0-8 + D R + D R D + + + + T=D VM=0-7 + + D + D + D + + R + T=D VM=0-7 + + D + D + D + + + R T=D VM=0-9 + + D + D + D + + + R T=R VM=0-7 + + D + D R + D D + + T=D VM=0-8 + + + + D + + D D + + T=D VM=0-9 + + R + D + + D + D R T=D VM=0-6 + + + + D R + D + + + T=D VM=0-9 D + + + D + + D + + R T=D VM=0-9 D + + + D + + D + + + T=D VM=0-9 D + R + D R + D + + + T=D VM=0-9 + + D ``` ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [February 9, 2011, 3:54am UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/75 "2011-02-09T03:54:41Z")
And here are the other 219: ```auto + D + + D + + R T=D VM=0-9 + + D + D R + + D D + T=D VM=0-8 + + + + D R + + D + + T=R VM=0-9 D + + + D + + + D R + T=D VM=0-9 D + + + D + + + D + R T=D VM=0-9 D + + + D + + + D + + T=D VM=0-9 D R + + D + + + D + + T=R VM=0-9 D + R + D R + + D + + T=D VM=0-9 + D + + D + + + D + + T=D VM=0-9 + D R + D R + + D + + T=R VM=0-9 + + D + D + + + D R + T=D VM=0-9 + + D + D + + + D + R T=D VM=0-9 + + D + D + + + + D R T=D VM=0-5 D + + + D + + + + D + T=D VM=0-5 D + R + D + + + + D R T=D VM=0-9 + + D + D R + + + + + T=D VM=0-8 D D + + D + + + + + R T=D VM=0-9 D D + + D + + + + + + T=D VM=0-8 D D R + D R + + + + + T=D VM=0-9 D + D + D + + + + R + T=D VM=0-6 D + D + D + + + + + R T=D VM=0-9 D + D + D + + + + + R T=R VM=0-6 D + D + D + + + + + + T=D VM=0-8 D R D + D R + + + + + T=D VM=0-8 + D D + D + + + + + R T=D VM=0-9 + D D + + D D D + R + T=D VM=0-9 + + + + + D D D + + R T=D VM=0-9 + + + + + D D D + + R T=R VM=0-9 + + + + + D D D + + + T=D VM=0-9 + + R + R D D + D + + T=D VM=0-9 + + + + + D D + D R + T=D VM=0-9 + + + + + D D + D R + T=R VM=0-8 + + + + + D D + D + R T=D VM=0-8 + + + + + D D + D + R T=R VM=0-9 + + + + + D D + D + + T=D VM=0-9 + R + + + D D + D + + T=D VM=0-9 + + R + + D D + D + + T=R VM=0-8 + + R + + D D + + R + T=D VM=0-9 D + + + + D D + + + R T=D VM=0-9 D + + + + D D + + + R T=R VM=0-9 D + + + + D D + + + + T=D VM=0-9 D + R + + D D + + R + T=D VM=0-7 + D + + + D D + + + R T=D VM=0-9 + D + + + D D + + + R T=R VM=0-7 + D + + + D D + + + + T=D VM=0-7 + D R + + D D + + + R T=D VM=0-9 + + D + R D + D D + + T=D VM=0-8 + + + + + D + D D R + T=D VM=0-8 + + + + + D + D D + R T=D VM=0-9 + + + + + D + D D + + T=D VM=0-8 + R + + + D + D D + + T=R VM=0-8 + + R + + D + D + D R T=D VM=0-8 + + + + + D + D + R + T=D VM=0-9 D + + + + D + D + + R T=R VM=0-9 D + + + + D + D + + + T=D VM=0-9 D R + + + D + D + + + T=D VM=0-9 D + R + + D + D + + R T=D VM=0-9 + D + + + D + D + + + T=D VM=0-9 + D R + + D + D + R + T=D VM=0-9 + + D + + D + D + + R T=D VM=0-8 + + D + + D + D + + R T=R VM=0-9 + + D + + D + + D D R T=D VM=0-9 + + + + + D + + D R + T=R VM=0-9 D + + + + D + + D + R T=D VM=0-9 D + + + + D + + D + + T=R VM=0-9 D R + + + D + + D + + T=D VM=0-9 D + R + + D + + D R + T=D VM=0-9 + D + + + D + + D + R T=D VM=0-9 + D + + + D + + D + + T=R VM=0-9 + D R + + D + + D R + T=R VM=0-9 + + D + + D + + D + R T=D VM=0-9 + + D + + D + + + D R T=D VM=0-8 D + + + + D + + + D R T=D VM=0-9 + D + + + D + + + D R T=R VM=0-0 + + D + + D + + + R + T=D VM=0-8 D D + + + D + + + + R T=D VM=0-9 D D + + + D + + + + R T=R VM=0-8 D D + + + D + + + + + T=D VM=0-9 D D R + + D + + + R + T=D VM=0-9 D + D + + D + + + + R T=D VM=0-9 D + D + + D + + + + R T=R VM=0-9 D + D + + D + + + R + T=D VM=0-8 + D D + + D + + + + R T=R VM=0-8 + D D R + + D D D + + T=R VM=0-8 + + + + R + D D D + + T=D VM=0-8 + + + + + R D D D + + T=D VM=0-9 + + + + + R D D D + + T=R VM=0-8 + + + + + + D D D R + T=D VM=0-8 + + + + + + D D D R + T=R VM=0-9 + + + + + + D D D + R T=D VM=0-9 + + + + + + D D D + R T=R VM=0-8 + + + + + + D D D + + T=R VM=0-8 R + + + + + D D D + + T=D VM=0-8 + R + + + + D D D + + T=D VM=0-9 + + R + + + D D D + + T=R VM=0-8 + + R + + + D D + D R T=D VM=0-9 + + + R + + D D + + + T=D VM=0-9 D + + R + + D D + + + T=R VM=0-9 D + + + R + D D + + + T=D VM=0-9 D + + + R + D D + + + T=R VM=0-9 D + + + + R D D + + + T=D VM=0-9 D + + + + R D D + + + T=R VM=0-9 D + + + + + D D R + + T=D VM=0-9 D + + + + + D D R + + T=R VM=0-9 D + + + + + D D + R + T=D VM=0-9 D + + + + + D D + R + T=R VM=0-9 D + + + + + D D + + R T=D VM=0-9 D + + + + + D D + + R T=R VM=0-9 D + + + + + D D + + + T=D VM=0-9 D R + + + + D D + + + T=R VM=0-9 D R + + + + D D + + + T=D VM=0-9 D + R + + + D D + + + T=R VM=0-9 D + R R + + D D + + + T=D VM=0-7 + D + + + R D D + + + T=D VM=0-7 + D + + + + D D + R + T=D VM=0-9 + D + + + + D D + + R T=D VM=0-9 + D + + + + D D + + R T=R VM=0-7 + D + + + + D D + + + T=D VM=0-7 R D + + + + D D + + + T=D VM=0-9 + D R + + R D D + + + T=D VM=0-9 + + D + + + D D + R + T=D VM=0-9 + + D + + + D D + + R T=D VM=0-9 + + D + + + D D + + R T=R VM=0-9 + + D + + R D + D D + T=D VM=0-9 + + + + + + D + D D R T=D VM=0-9 + + + + + + D + D D R T=R VM=0-9 + + + + + + D + D D + T=D VM=0-9 + + R R + + D + D + + T=D VM=0-7 D + + + R + D + D + + T=D VM=0-9 D + + + R + D + D + + T=R VM=0-7 D + + + + R D + D + + T=D VM=0-9 D + + + + R D + D + + T=R VM=0-9 D + + + + + D R D + + T=R VM=0-7 D + + + + + D + D R + T=D VM=0-9 D + + + + + D + D R + T=R VM=0-9 D + + + + + D + D + R T=D VM=0-9 D + + + + + D + D + R T=R VM=0-9 D + + + + + D + D + + T=D VM=0-9 D R + + + + D + D + + T=R VM=0-9 D R + + + + D + D + + T=D VM=0-9 D + R + + + D + D + + T=R VM=0-9 D + R + + R D + D + + T=D VM=0-9 + D + + + + D + D R + T=D VM=0-9 + D + + + + D + D R + T=R VM=0-9 + D + + + + D + D + R T=D VM=0-9 + D + + + + D + D + R T=R VM=0-9 + D + + + + D + D + + T=D VM=0-9 + D R + + + D + D + + T=R VM=0-9 + D R + R + D + D + + T=D VM=0-9 + + D + + R D + D + + T=D VM=0-9 + + D + + R D + D + + T=R VM=0-8 + + D + + + D + D R + T=D VM=0-9 + + D + + + D + D R + T=R VM=0-8 + + D + + + D + D + R T=D VM=0-8 + + D + + + D + D + R T=R VM=0-9 + + D + + + D + D + + T=D VM=0-9 + R D + + + D + + D R T=D VM=0-9 D + + + + + D + + D R T=D VM=0-8 + D + + R + D + + + + T=D VM=0-6 D D + + + R D + + + + T=D VM=0-8 D D + + + + D R + + + T=D VM=0-6 D D + + + + D + + R + T=D VM=0-9 D D + + + + D + + + R T=D VM=0-9 D D + + + + D + + + R T=R VM=0-8 D D + + + + D + + + + T=D VM=0-9 D D R + + R D + + + + T=D VM=0-9 D + D + + + D + + R + T=D VM=0-9 D + D + + + D + + + R T=D VM=0-9 D + D + + + D + + + R T=R VM=0-9 D + D + + R D + + + + T=D VM=0-7 + D D + + + D + + R + T=D VM=0-7 + D D + + + D + + + R T=D VM=0-8 + D D + + + D + + + R T=R VM=0-7 + D D + + R + D D D + T=D VM=0-7 + + + + + + + D D D R T=R VM=0-7 + + + + + + + D D D + T=D VM=0-7 + + R + R + + D D + + T=D VM=0-8 D + + + + R + D D + + T=R VM=0-8 D + + + + + + D D R + T=D VM=0-8 D + + + + + + D D + R T=D VM=0-9 D + + + + + + D D + + T=D VM=0-8 D R + + + + + D D + + T=R VM=0-8 D + R + + R + D D + + T=D VM=0-9 + D + + + + + D D + + T=D VM=0-8 + D R + R + + D D + + T=D VM=0-8 + + D + + R + D D + + T=R VM=0-8 + + D + + + + D D R + T=D VM=0-8 + + D + + + + D D + R T=D VM=0-9 + + D + + + + D D + + T=D VM=0-8 + R D + + + + D + D R T=D VM=0-9 D + + + + + + D + D + T=D VM=0-9 D + R + + + + D + D R T=D VM=0-6 + D + + + + + D + D R T=D VM=0-8 + + D + + R + D + + + T=D VM=0-7 D D + + + + + D + + R T=D VM=0-9 D D + + + + + D + + + T=D VM=0-9 D D R + + R + D + + + T=D VM=0-9 D + D + + + + D + R + T=D VM=0-9 D + D + + + + D + + R T=R VM=0-9 D + D + + + + D + + + T=D VM=0-9 D R D + + R + D + + + T=D VM=0-7 + D D + + + + + D D R T=D VM=0-6 D + + + + + + + D D + T=D VM=0-8 D R + + + + + + D D + T=R VM=0-6 D + R + + + + + D D + T=D VM=0-8 + D R + + + + + D D R T=D VM=0-9 + + D + + + + + D R + T=D VM=0-9 D D + + + + + + D + R T=D VM=0-9 D D + + + + + + D + + T=R VM=0-9 D D R + + R + + D + + T=D VM=0-7 D + D + + + + + D R + T=R VM=0-7 D + D + + + + + D + R T=D VM=0-9 D + D + + + + + D + + T=R VM=0-9 D R D + + + + + D + R T=D VM=0-9 + D D + + + + + + D R T=D VM=0-7 D D + + + + + + + D + T=D VM=0-5 D D R + + + + + + D R T=D VM=0-8 D + D + + + + + + D R T=D VM=0-7 + D D + + + + + + R + T=D VM=0-6 D D D ``` Further reduction (_e.g._, due to a layout’s symmetry) is probably warranted. Perhaps later tonight… ---
**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 9, 2011, 5:40pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/76 "2011-02-09T17:40:03Z")
Out of curiosity, what was the bug? ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [February 9, 2011, 5:47pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/77 "2011-02-09T17:47:05Z")
> [@Chronos](#): > > Out of curiosity, what was the bug? It was really stupid. I was writing in C++. I had a line like this: ```auto for () { if (condition) set_some_flag; } ``` A second later I realized that the loop could break, too, if the condition was met, so I added a break: ```auto for () { if (condition) set_some_flag; break; } ``` Oops! That should have read: ```auto for () { if (condition) { set_some_flag; break; } } ``` That was the bug. (When I write more formal code, I never use the bracket-less syntax so as to prevent such mistakes. But, when I write code for something like the SDMB, I’m looking to be fast, and that bit me here.) ---
**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 9, 2011, 5:57pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/78 "2011-02-09T17:57:19Z")
Ah, that’d do it. Usually when I’m going bracketless, I keep it all on one line, to prevent that. There is one program I wrote, though, where I have a whole slew of ifs one after the other, with no brackets (I could of course rewrite it to a single if with a bunch of logical ands, but this way it’s easier to add or remove conditions one at a time). ---
**Author:** ![Rysto](https://avatars.discourse-cdn.com/v4/letter/r/ecccb3/32.png) [@Rysto](https://boards.straightdope.com/u/Rysto)\ **Post date:** [February 9, 2011, 6:09pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/79 "2011-02-09T18:09:34Z")
[hijack]The coding standard that I have to follow requires the braces to be omitted if possible. I hate it for exactly that reason.[/hijack] ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [February 9, 2011, 6:11pm UTC](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378/80 "2011-02-09T18:11:20Z")
> [@Chronos](#): > > Ah, that’d do it. Usually when I’m going bracketless, I keep it all on one line, to prevent that. There is one program I wrote, though, where I have a whole slew of ifs one after the other, with no brackets (I could of course rewrite it to a single if with a bunch of logical ands, but this way it’s easier to add or remove conditions one at a time). Yeah, I usually do the one-line thing in these cases, too, and it actually might have been all on one line initially, unlike what I wrote above. In that case, I might have put in the hard-return first, got distracted for a split second, and then mindlessly added the ‘break’… [Previous page](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378.md?page=3) [Next page](https://boards.straightdope.com/t/in-the-hare-and-hounds-game-will-hare-always-win/569378.md?page=5)