diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..496ee2c
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1 @@
+.DS_Store
\ No newline at end of file
diff --git a/go/.gitignore b/go/.gitignore
new file mode 100644
index 0000000..eaaedcd
--- /dev/null
+++ b/go/.gitignore
@@ -0,0 +1,6 @@
+
+*.out
+
+*.sublime-project
+
+*.sublime-workspace
diff --git a/go/.travis.yml b/go/.travis.yml
new file mode 100644
index 0000000..745f061
--- /dev/null
+++ b/go/.travis.yml
@@ -0,0 +1,11 @@
+language: go
+
+install:
+ - go get -t ./...
+ - go get golang.org/x/tools/cmd/cover
+ - go get github.com/mattn/goveralls
+
+script:
+ - PATH="$HOME/gopath/bin:$PATH"
+ - go test ./... -v -covermode=count -coverprofile=cover.out
+ - goveralls -coverprofile cover.out -service=travis-ci -repotoken $TOKEN
diff --git a/go/LICENSE.md b/go/LICENSE.md
new file mode 100644
index 0000000..5dc6b42
--- /dev/null
+++ b/go/LICENSE.md
@@ -0,0 +1,675 @@
+
+ GNU GENERAL PUBLIC LICENSE
+ Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc.
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
+
+ The GNU General Public License is a free, copyleft license for
+software and other kinds of works.
+
+ The licenses for most software and other practical works are designed
+to take away your freedom to share and change the works. By contrast,
+the GNU General Public License is intended to guarantee your freedom to
+share and change all versions of a program--to make sure it remains free
+software for all its users. We, the Free Software Foundation, use the
+GNU General Public License for most of our software; it applies also to
+any other work released this way by its authors. You can apply it to
+your programs, too.
+
+ When we speak of free software, we are referring to freedom, not
+price. Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
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+want it, that you can change the software or use pieces of it in new
+free programs, and that you know you can do these things.
+
+ To protect your rights, we need to prevent others from denying you
+these rights or asking you to surrender the rights. Therefore, you have
+certain responsibilities if you distribute copies of the software, or if
+you modify it: responsibilities to respect the freedom of others.
+
+ For example, if you distribute copies of such a program, whether
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+freedoms that you received. You must make sure that they, too, receive
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+know their rights.
+
+ Developers that use the GNU GPL protect your rights with two steps:
+(1) assert copyright on the software, and (2) offer you this License
+giving you legal permission to copy, distribute and/or modify it.
+
+ For the developers' and authors' protection, the GPL clearly explains
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+authors' sake, the GPL requires that modified versions be marked as
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+
+ Some devices are designed to deny users access to install or run
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+
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+ "This License" refers to version 3 of the GNU General Public License.
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+ To "propagate" a work means to do anything with it that, without
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+ 3. Protecting Users' Legal Rights From Anti-Circumvention Law.
+
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+similar laws prohibiting or restricting circumvention of such
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+
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+circumvention of technological measures to the extent such circumvention
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+modification of the work as a means of enforcing, against the work's
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+ 4. Conveying Verbatim Copies.
+
+ You may convey verbatim copies of the Program's source code as you
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+
+ a) The work must carry prominent notices stating that you modified
+ it, and giving a relevant date.
+
+ b) The work must carry prominent notices stating that it is
+ released under this License and any conditions added under section
+ 7. This requirement modifies the requirement in section 4 to
+ "keep intact all notices".
+
+ c) You must license the entire work, as a whole, under this
+ License to anyone who comes into possession of a copy. This
+ License will therefore apply, along with any applicable section 7
+ additional terms, to the whole of the work, and all its parts,
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+ permission to license the work in any other way, but it does not
+ invalidate such permission if you have separately received it.
+
+ d) If the work has interactive user interfaces, each must display
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+ d) Convey the object code by offering access from a designated
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+
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+your receipt of the notice.
+
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+ 9. Acceptance Not Required for Having Copies.
+
+ You are not required to accept this License in order to receive or
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+
+ 10. Automatic Licensing of Downstream Recipients.
+
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+propagate that work, subject to this License. You are not responsible
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+any patent claim is infringed by making, using, selling, offering for
+sale, or importing the Program or any portion of it.
+
+ 11. Patents.
+
+ A "contributor" is a copyright holder who authorizes use under this
+License of the Program or a work on which the Program is based. The
+work thus licensed is called the contributor's "contributor version".
+
+ A contributor's "essential patent claims" are all patent claims
+owned or controlled by the contributor, whether already acquired or
+hereafter acquired, that would be infringed by some manner, permitted
+by this License, of making, using, or selling its contributor version,
+but do not include claims that would be infringed only as a
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+patent sublicenses in a manner consistent with the requirements of
+this License.
+
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+patent license under the contributor's essential patent claims, to
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+sue for patent infringement). To "grant" such a patent license to a
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+patent against the party.
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+ If you convey a covered work, knowingly relying on a patent license,
+and the Corresponding Source of the work is not available for anyone
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+publicly available network server or other readily accessible means,
+then you must either (1) cause the Corresponding Source to be so
+available, or (2) arrange to deprive yourself of the benefit of the
+patent license for this particular work, or (3) arrange, in a manner
+consistent with the requirements of this License, to extend the patent
+license to downstream recipients. "Knowingly relying" means you have
+actual knowledge that, but for the patent license, your conveying the
+covered work in a country, or your recipient's use of the covered work
+in a country, would infringe one or more identifiable patents in that
+country that you have reason to believe are valid.
+
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+arrangement, you convey, or propagate by procuring conveyance of, a
+covered work, and grant a patent license to some of the parties
+receiving the covered work authorizing them to use, propagate, modify
+or convey a specific copy of the covered work, then the patent license
+you grant is automatically extended to all recipients of the covered
+work and works based on it.
+
+ A patent license is "discriminatory" if it does not include within
+the scope of its coverage, prohibits the exercise of, or is
+conditioned on the non-exercise of one or more of the rights that are
+specifically granted under this License. You may not convey a covered
+work if you are a party to an arrangement with a third party that is
+in the business of distributing software, under which you make payment
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+contain the covered work, unless you entered into that arrangement,
+or that patent license was granted, prior to 28 March 2007.
+
+ Nothing in this License shall be construed as excluding or limiting
+any implied license or other defenses to infringement that may
+otherwise be available to you under applicable patent law.
+
+ 12. No Surrender of Others' Freedom.
+
+ If conditions are imposed on you (whether by court order, agreement or
+otherwise) that contradict the conditions of this License, they do not
+excuse you from the conditions of this License. If you cannot convey a
+covered work so as to satisfy simultaneously your obligations under this
+License and any other pertinent obligations, then as a consequence you may
+not convey it at all. For example, if you agree to terms that obligate you
+to collect a royalty for further conveying from those to whom you convey
+the Program, the only way you could satisfy both those terms and this
+License would be to refrain entirely from conveying the Program.
+
+ 13. Use with the GNU Affero General Public License.
+
+ Notwithstanding any other provision of this License, you have
+permission to link or combine any covered work with a work licensed
+under version 3 of the GNU Affero General Public License into a single
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+License will continue to apply to the part which is the covered work,
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+section 13, concerning interaction through a network will apply to the
+combination as such.
+
+ 14. Revised Versions of this License.
+
+ The Free Software Foundation may publish revised and/or new versions of
+the GNU General Public License from time to time. Such new versions will
+be similar in spirit to the present version, but may differ in detail to
+address new problems or concerns.
+
+ Each version is given a distinguishing version number. If the
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+version or of any later version published by the Free Software
+Foundation. If the Program does not specify a version number of the
+GNU General Public License, you may choose any version ever published
+by the Free Software Foundation.
+
+ If the Program specifies that a proxy can decide which future
+versions of the GNU General Public License can be used, that proxy's
+public statement of acceptance of a version permanently authorizes you
+to choose that version for the Program.
+
+ Later license versions may give you additional or different
+permissions. However, no additional obligations are imposed on any
+author or copyright holder as a result of your choosing to follow a
+later version.
+
+ 15. Disclaimer of Warranty.
+
+ THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
+APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
+HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
+OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
+THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
+IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
+ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
+
+ 16. Limitation of Liability.
+
+ IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
+THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
+GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
+USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
+DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
+PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+ 17. Interpretation of Sections 15 and 16.
+
+ If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+ END OF TERMS AND CONDITIONS
+
+ How to Apply These Terms to Your New Programs
+
+ If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+ To do so, attach the following notices to the program. It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+
+ Copyright (C)
+
+ This program is free software: you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program. If not, see .
+
+Also add information on how to contact you by electronic and paper mail.
+
+ If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+ {project} Copyright (C) {year} {fullname}
+ This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+ This is free software, and you are welcome to redistribute it
+ under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License. Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+ You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+.
+
+ The GNU General Public License does not permit incorporating your program
+into proprietary programs. If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library. If this is what you want to do, use the GNU Lesser General
+Public License instead of this License. But first, please read
+.
diff --git a/go/README.md b/go/README.md
new file mode 100644
index 0000000..33c9156
--- /dev/null
+++ b/go/README.md
@@ -0,0 +1,3 @@
+[](https://godoc.org/github.com/sbrow/risk) [](https://travis-ci.org/sbrow/risk) [](https://coveralls.io/github/sbrow/risk?branch=master) [](https://goreportcard.com/report/github.com/sbrow/risk)
+
+# Risk
diff --git a/go/go.mod b/go/go.mod
new file mode 100644
index 0000000..3062065
--- /dev/null
+++ b/go/go.mod
@@ -0,0 +1,3 @@
+module github.com/sbrow/risk
+
+require github.com/sbrow/prob v1.0.1
diff --git a/go/math.go b/go/math.go
new file mode 100644
index 0000000..5d69fc2
--- /dev/null
+++ b/go/math.go
@@ -0,0 +1,15 @@
+package risk
+
+func min(a, b int) int {
+ if a < b {
+ return a
+ }
+ return b
+}
+
+func max(a, b int) int {
+ if a > b {
+ return a
+ }
+ return b
+}
diff --git a/go/risk.go b/go/risk.go
new file mode 100644
index 0000000..f7cee13
--- /dev/null
+++ b/go/risk.go
@@ -0,0 +1,130 @@
+package risk
+
+import (
+ "fmt"
+ "sort"
+ "strconv"
+ "strings"
+
+ "github.com/sbrow/prob/dice"
+)
+
+const Delim = ","
+
+// loadRolls loads a roll table from path
+func loadRolls(n int) []string {
+ d := make([]dice.Die, n)
+ for i := 0; i < n; i++ {
+ d[i] = dice.D6()
+ }
+ rolls, err := dice.NewTable(d)
+ if err != nil {
+ panic(err) // TODO(sbrow): Fix
+ }
+ var out []string
+ for _, s := range rolls.Data {
+ out = append(out, s[0])
+ }
+ return out
+}
+
+func sortRoll(s string) string {
+ i := strToInt(s)
+ sort.Sort(sort.Reverse(sort.IntSlice(i)))
+ s = fmt.Sprint(i[0], s[1:])
+ for j := 2; j <= len(s)-1; j += 2 {
+ s = fmt.Sprint(s[:j], i[j/2], s[j+1:])
+ }
+ s = fmt.Sprint(s[:len(s)-1], i[len(i)-1])
+ return s
+}
+
+// Compare enumerates the results of a combat.
+//
+// TODO(sbrow): Rename
+func Compare(atk, def int, mods ...string) (win, tie, loss float64) {
+ if atk < 1 || def < 1 {
+ return
+ }
+ sum := 0.0
+ for _, atkRoll := range loadRolls(min(atk, 3)) {
+ atkRoll = sortRoll(atkRoll)
+ for _, defRoll := range loadRolls(min(def, 2)) {
+ defRoll = sortRoll(defRoll)
+ lost := Combat(atkRoll, defRoll, mods...)
+ switch {
+ case lost == 0:
+ win++
+ case lost == 1:
+ if atk > 1 && def > 1 {
+ tie++
+ } else {
+ loss++
+ }
+ case lost == 2:
+ loss++
+ }
+ sum++
+ }
+ }
+
+ return win / sum, tie / sum, loss / sum
+}
+
+// strToInt converts a string value to a list of ints,
+// using rolltable.Delim as the delimiter.
+func strToInt(s string) []int {
+ i := []int{}
+ for _, t := range strings.Split(s, dice.Delim) {
+ n, err := strconv.Atoi(t)
+ if err != nil {
+ panic(err)
+ }
+ i = append(i, n)
+ }
+ return i
+}
+
+// Combat determines the winner of a dice clash.
+func Combat(atk, def string, mod ...string) int {
+ a, d := strToInt(atk), strToInt(def)
+ addModifiers(&a, &d, mod...)
+
+ short := min(len(a), len(d))
+
+ lost := 0
+ for i := 0; i < short; i++ {
+ if d[i] >= a[i] {
+ lost++
+ }
+ }
+ return lost
+}
+
+// addModifiers adds modifiers to the dice roll
+func addModifiers(atk, def *[]int, mod ...string) {
+ sort.Ints(*atk)
+ sort.Ints(*def)
+ if len(*atk) > len(*def) {
+ *atk = (*atk)[len(*def)-1:]
+ }
+ for _, m := range mod {
+ switch m {
+ case "fortification":
+ if len(*def) == 2 {
+ (*def)[1] = min((*def)[1]+1, 6)
+ }
+ fallthrough
+ case "bunker":
+ (*def)[0] = min((*def)[0]+1, 6)
+ case "ammo shortage":
+ i := 0
+ if len(*def) == 2 {
+ i = 1
+ }
+ (*def)[i] = max((*def)[1]-1, 0)
+ }
+ }
+ sort.Sort(sort.Reverse(sort.IntSlice(*atk)))
+ sort.Sort(sort.Reverse(sort.IntSlice(*def)))
+}
diff --git a/go/risk_test.go b/go/risk_test.go
new file mode 100644
index 0000000..6b8f623
--- /dev/null
+++ b/go/risk_test.go
@@ -0,0 +1,87 @@
+package risk
+
+import (
+ "fmt"
+ "math/rand"
+ "sort"
+ "testing"
+ "time"
+
+ "github.com/sbrow/prob/dice"
+)
+
+func init() {
+ _, _ = dice.NewTable(dice.New(dice.D6()))
+ _, _ = dice.NewTable(dice.New(dice.D6(), dice.D6(), dice.D6()))
+ _, _ = dice.NewTable(dice.New(dice.D6(), dice.D6()))
+}
+
+var comparetests = []struct {
+ att int
+ def int
+ want string
+}{
+ {2, 1, "0.5787 0.0000 0.4213"},
+ {3, 1, "0.6597 0.0000 0.3403"},
+ {2, 2, "0.2276 0.3241 0.4483"},
+}
+
+func TestCompare(t *testing.T) {
+ for i, tt := range comparetests {
+ t.Run(fmt.Sprint(i), func(t *testing.T) {
+ win, loss, tie := Compare(tt.att, tt.def)
+ s := fmt.Sprintf("%.4f %.4f %.4f", win, loss, tie)
+ if s != tt.want {
+ t.Errorf("got %q, want %q", s, tt.want)
+ }
+ })
+ }
+}
+
+var walktests = []struct {
+ att int
+ def int
+ oneDef bool
+ mods []string
+ want string
+}{
+ {1, 1, false, []string{}, "0.4167 0.5833"},
+ {1, 1, true, []string{}, "0.4167 0.5833"},
+ {2, 1, false, []string{}, "0.5787 0.1755 0.2458"},
+ {2, 1, true, []string{}, "0.5787 0.1755 0.2458"},
+ {3, 1, false, []string{}, "0.6597 0.1969 0.0597 0.0836"},
+ {3, 1, true, []string{}, "0.6597 0.1969 0.0597 0.0836"},
+ {2, 2, false, []string{}, "0.2276 0.1350 0.6373"},
+ // {2, 2, true, []string{}, "0.2276 0.1350 0.6373"},
+ {2, 2, true, []string{"bunker", "bunker", "bunker", "bunker", "bunker"},
+ "0.0000 0.0000 1.0000"},
+}
+
+func TestCompleteWalk(t *testing.T) {
+ for i, tt := range walktests {
+ t.Run(fmt.Sprint(i), func(t *testing.T) {
+ node := new(tt.att, tt.def, tt.oneDef, tt.mods...)
+ s := fmt.Sprint(node.Report(true))
+ if s != tt.want {
+ t.Errorf("got %q, want %q", s, tt.want)
+ }
+ })
+ }
+}
+
+func TestThings(t *testing.T) {
+ rand.Seed(time.Now().UnixNano())
+ sum := 0
+ n := 100000
+ for i := 0; i < n; i++ {
+ atk := []int{rand.Intn(6) + 1, rand.Intn(6) + 1}
+ def := []int{rand.Intn(6) + 1} //, rand.Intn(6) + 1}
+ sort.Ints(atk)
+ sort.Ints(def)
+ if def[0] < atk[0] { // && def[1] < atk[1] {
+ sum++
+ }
+
+ }
+ fmt.Println(float64(sum) / float64(n))
+}
diff --git a/go/tree.go b/go/tree.go
new file mode 100644
index 0000000..b3fc79c
--- /dev/null
+++ b/go/tree.go
@@ -0,0 +1,107 @@
+package risk
+
+import (
+ "fmt"
+)
+
+type node struct {
+ att int // Number of attackers.
+ def int // Number of defenders.
+ edges []*edge
+}
+
+func (n *node) Report(short bool) string {
+ s := ""
+ if !short {
+ s += fmt.Sprintf("Projected Losses: %dv%d\n", n.att, n.def)
+ }
+ for i, odds := range n.walk() {
+ if short {
+ s += fmt.Sprintf("%.4f ", odds)
+ } else {
+ s += fmt.Sprintf("%-2d casualties - %.4f%%\n", i, 100*odds)
+ }
+ }
+ return s[:len(s)-1]
+}
+
+func (n *node) walk() []float64 {
+ // TODO(sbrow): Fix
+ var ch = make(chan []int, 1000)
+ for i, node := range n.edges {
+ if node != nil {
+ walker(ch, node.node, []int{i})
+ }
+ }
+ close(ch)
+ sorted := make([]float64, n.att+1)
+ for r := range ch {
+ lost, path := n.Walk(r...)
+ sorted[lost] += path
+ }
+ return sorted
+}
+
+func walker(ch chan []int, curr *node, path []int) {
+ if curr == nil {
+ return
+ }
+ for i, node := range curr.edges {
+ if node != nil {
+ walker(ch, node.node, append(path, i))
+ } else {
+ if i+1 == len(curr.edges) {
+ cpy := make([]int, len(path))
+ copy(cpy, path)
+ ch <- cpy
+ }
+ }
+ }
+}
+
+func (n *node) Walk(path ...int) (att int, p float64) {
+ curr := n.edges[path[0]].node
+ p = n.edges[path[0]].p
+ for _, n := range path[1:] {
+ p *= curr.edges[n].p
+ curr = curr.edges[n].node
+ }
+ return n.att - curr.att, p
+}
+
+type edge struct {
+ node *node
+ p float64
+}
+
+func new(att, def int, oneDef bool, mods ...string) *node {
+ n := &node{
+ att: att,
+ def: def,
+ }
+ if att < 1 || def < 1 {
+ n.edges = []*edge{nil}
+ return n
+ }
+ d := def
+ if oneDef {
+ d = 1
+ }
+ win, tie, loss := Compare(att, d, mods...)
+
+ switch {
+ case att >= 2 && def >= 2 && !oneDef:
+ n.edges = []*edge{
+ {node: new(att, def-2, oneDef, mods...), p: win},
+ {node: new(att-1, def-1, oneDef, mods...), p: tie},
+ {node: new(att-2, def, oneDef, mods...), p: loss},
+ }
+ default:
+ n.edges = []*edge{nil, nil}
+ if win > 0 {
+ n.edges[0] = &edge{node: new(att, def-1, oneDef, mods...), p: win}
+ }
+ n.edges[1] = &edge{node: new(att-1, def, oneDef, mods...), p: loss}
+ }
+ return n
+}
diff --git a/go/tree.gv b/go/tree.gv
new file mode 100644
index 0000000..93dbf03
--- /dev/null
+++ b/go/tree.gv
@@ -0,0 +1,58 @@
+digraph {
+ // graph [splines=line]
+ graph [outputorder="edgesfirst"]
+ node [shape=record]
+
+ SixZero [label="6v0"]
+ FiveOne [label="5v1"]
+ FourTwo [label="4v2"]
+ ThreeThree [label="3v3"]
+ TwoFour [label="2v4"]
+ OneFive [label="1v5"]
+ ZeroSix [label="0v6"]
+ FiveOne -> FiveZero, FourOne
+ FourTwo -> FourZero, ThreeOne, TwoTwo
+ ThreeThree -> ThreeOne, TwoTwo, OneThree
+ TwoFour -> ZeroFour, TwoTwo, OneThree
+ OneFive -> OneFour, ZeroFive
+ {ordering=out; FiveOne, FourTwo}
+ {rank=same; FiveOne; FourTwo; ThreeThree; TwoFour}//ThreeThree}
+
+
+ FiveZero [label="5v0"]
+ FourOne [label="4v1"]
+ ThreeTwo [label="3v2"]
+ TwoThree [label="2v3"]
+ OneFour [label="1v4"]
+ ZeroFive [label="0v5"]
+ FourOne -> FourZero, ThreeOne
+ ThreeTwo -> OneTwo, TwoOne, ThreeZero
+ TwoThree -> ZeroThree, OneTwo, TwoOne
+ OneFour -> OneThree, ZeroFour
+ {rank=same; FourOne; ThreeTwo; TwoThree}
+
+ FourZero [label="4v0"]
+ ThreeOne [label="3v1"]
+ TwoTwo [label="2v2"]
+ OneThree [label="1v3"]
+ ZeroFour [label="0v4"]
+ ThreeOne -> ThreeZero, TwoOne
+ TwoTwo -> TwoZero, OneOne, ZeroTwo
+ OneThree -> OneTwo, ZeroThree
+ {rank=same; ThreeOne; TwoTwo; OneThree}
+
+ ThreeZero [label="3v0"]
+ TwoOne [label="2v1"]
+ OneTwo [label="1v2"]
+ ZeroThree [label="0v3"]
+ OneTwo -> OneOne, ZeroTwo
+ TwoOne -> TwoZero, OneOne
+
+ TwoZero [label="2v0"]
+ OneOne [label="1v1"]
+ ZeroTwo [label="0v2"]
+ OneOne -> OneZero, ZeroOne
+
+ OneZero [label="1v0"]
+ ZeroOne [label="0v1"]
+}
\ No newline at end of file
diff --git a/go/tree.png b/go/tree.png
new file mode 100644
index 0000000..cecfe08
Binary files /dev/null and b/go/tree.png differ
diff --git a/haskell/CHANGELOG.md b/haskell/CHANGELOG.md
new file mode 100644
index 0000000..801383c
--- /dev/null
+++ b/haskell/CHANGELOG.md
@@ -0,0 +1,5 @@
+# Revision history for risk
+
+## 0.1.0.0 -- YYYY-mm-dd
+
+* First version. Released on an unsuspecting world.
diff --git a/haskell/app/Main.hs b/haskell/app/Main.hs
new file mode 100644
index 0000000..fa26f4f
--- /dev/null
+++ b/haskell/app/Main.hs
@@ -0,0 +1,19 @@
+#!/usr/bin/env stack
+-- stack runghc
+
+import Risk
+
+maximum' :: Ord a => [a] -> a
+maximum' = foldr1 (\x y ->if x >= y then x else y)
+
+maximum'' :: Ord a => [a] -> a
+maximum'' [x] = x
+maximum'' (x:x':xs) = maximum' ((if x >= x' then x else x'):xs)
+
+a :: [Int]
+a = [3,5,8,6]
+
+main :: IO ()
+main = print $ maximum'' a
+-- main = print $ possibleOutcomes 3 3
+-- main = print $ Result(3, 5) + Result(1, 2)
diff --git a/haskell/cabal.project.local b/haskell/cabal.project.local
new file mode 100644
index 0000000..0432756
--- /dev/null
+++ b/haskell/cabal.project.local
@@ -0,0 +1,2 @@
+ignore-project: False
+tests: True
diff --git a/haskell/risk.cabal b/haskell/risk.cabal
new file mode 100644
index 0000000..d1ab5e8
--- /dev/null
+++ b/haskell/risk.cabal
@@ -0,0 +1,46 @@
+cabal-version: 2.4
+name: risk
+version: 0.1.0.0
+
+-- A short (one-line) description of the package.
+-- synopsis:
+
+-- A longer description of the package.
+-- description:
+
+-- A URL where users can report bugs.
+-- bug-reports:
+
+-- The license under which the package is released.
+-- license:
+author: spencer
+maintainer: brower.spencer@gmail.com
+
+-- A copyright notice.
+-- copyright:
+-- category:
+extra-source-files: CHANGELOG.md
+
+executable risk
+ main-is: Main.hs
+
+ -- Modules included in this executable, other than Main.
+ other-modules: Dice, Risk
+
+ -- LANGUAGE extensions used by modules in this package.
+ -- other-extensions:
+ build-depends: base ^>=4.14.1.0, containers, combinat
+ hs-source-dirs: app, src
+ default-language: Haskell2010
+
+Test-Suite test
+ type: exitcode-stdio-1.0
+ main-is: Spec.hs
+ hs-source-dirs: test
+ default-language: Haskell2010
+ build-depends:
+ base >= 4 && < 5,
+ tasty >= 1.4.1,
+ tasty-hunit,
+ tasty-quickcheck,
+ tasty-smallcheck
\ No newline at end of file
diff --git a/haskell/src/Dice.hs b/haskell/src/Dice.hs
new file mode 100644
index 0000000..f32de7b
--- /dev/null
+++ b/haskell/src/Dice.hs
@@ -0,0 +1,21 @@
+module Dice (d, dice, total) where
+
+infixl 5 `d`
+d :: Integer -> Integer -> [[Integer]]
+n `d` s = dice n s
+
+-- Returns the entire possibility space of rolling d dice with sides sides.
+dice :: Integer -> Integer -> [[Integer]]
+dice d sides
+ | d == 1 = [ [d] | d<-[1..sides]]
+ | otherwise = combine (dice (d-1) sides) (dice 1 sides)
+
+-- Returns the total possible dice combinations
+total :: Integer -> Integer -> Integer
+total d sides
+ | d == 1 = sides
+ | otherwise = (total (d-1) sides) * sides
+
+-- Get the union of all combinations of set a with set b
+combine :: [[Integer]] -> [[Integer]] -> [[Integer]]
+combine a b = [ x ++ y | x<-a, y<-b ]
\ No newline at end of file
diff --git a/haskell/src/Risk.hs b/haskell/src/Risk.hs
new file mode 100755
index 0000000..41a131f
--- /dev/null
+++ b/haskell/src/Risk.hs
@@ -0,0 +1,128 @@
+-- | Functions for exploring the possibility space of the board game Risk.
+module Risk (Result (Result), Possibility (Possibility), battle, fight, odds, possibleOutcomes) where
+
+import Data.List
+import Data.Ord
+import Data.Tree
+import Dice
+
+-- | Represents A number of attackers and defenders respectively.
+data Result = Result (Integer, Integer) deriving (Eq, Ord, Show)
+
+instance Num Result where
+ Result (x, y) + Result (x', y') = Result (x + x', y + y')
+ Result (x, y) - Result (x', y') = Result (x - x', y - y')
+ Result (x, y) * Result (x', y') = Result (x * x', y * y')
+ abs (Result (x, y)) = Result (abs x, abs y)
+ signum (Result (x, y)) = Result (signum x, signum y)
+
+-- | A Particular result, and the Probability of arriving at it.
+-- The Probability should be a number between 0 and 1, inclusive.
+data Possibility = Possibility (Result, Float) deriving (Ord, Show)
+
+instance Num Possibility where
+ Possibility (a, b) + Possibility (a', b') = Possibility (a, b + b')
+ Possibility (a, b) - Possibility (a', b') = Possibility (a, b - b')
+ abs pos = pos
+ signum pos = 1
+
+instance Eq Possibility where
+ Possibility (a, b) == Possibility (a', b') = a == a'
+
+-- | Compares two dice and returns the casualties as a 'Result'.
+-- The 'Result' returned is relative e.g.
+-- @
+-- Result(0, 1)
+-- @
+-- . You must add the 'Result' to Your starting numbers.
+battle :: Integer -> Integer -> Result
+battle att def
+ | att == 0 = Result (0, 0)
+ | def == 0 = Result (0, 0)
+ | att <= def = Result (-1, 0)
+ | att > def = Result (0, -1)
+
+-- | Returns the losses of a battle given the attacking and defending dice rolls.
+-- Requires pre-sorted arguments
+fight :: ((Integer, Integer, Integer), (Integer, Integer)) -> Result
+fight ((attHigh, attMid, attLow), (defHigh, defLow)) = battle attHigh defHigh + battle attMid defLow
+
+-- | Returns a Tree of all the possible results of fighting,
+-- including intermediate (non-terminal) results.
+odds :: Integer -> Integer -> Tree Possibility
+odds att def = unfoldTree buildNode $ Possibility (Result (att, def), 1.0)
+ where
+ buildNode :: Possibility -> (Possibility, [Possibility])
+ buildNode node
+ | def == 0 || att == 0 = (node, [])
+ | def == 1 && att == 1 = (node, oneVoneLosses node)
+ | def == 1 && att == 2 = (node, twoVoneLosses node)
+ | def == 1 && att >= 3 = (node, threeVoneLosses node)
+ | def >= 2 && att == 1 = (node, oneVtwoLosses node)
+ | def >= 2 && att == 2 = (node, twoVtwoLosses node)
+ | def >= 2 && att >= 3 = (node, threeVtwoLosses node)
+ where
+ Possibility (Result (att, def), p) = node
+
+-- | Returrns a linked list of all the possible terminal outcomes of fighting.
+-- Assumes attackers and defenders will always roll as many dice as possible,
+-- And will contiune fighting until one side is dead.
+possibleOutcomes :: Integer -> Integer -> [Possibility]
+possibleOutcomes att def = outcomes
+ where
+ outcomes = [sumProbabilities p | p <- groupedResults]
+ sumProbabilities = foldr (+) (Possibility (Result (0, 0), 0))
+ groupedResults = (group . reverse . sort . removeStems . flatten) results
+ removeStems = filter onlyLeaves
+ onlyLeaves (Possibility (Result (att, def), p)) = att == 0 || def == 0
+ results = odds att def
+
+-- Converts a list of dice rolls into tuples that can be fed to fight.
+toRolls :: [[Integer]] -> [((Integer, Integer, Integer), (Integer, Integer))]
+toRolls dice = [toTuple . sortArgs . splitArgs $ x | x <- dice]
+ where
+ -- Split args int attackers and defenders
+ splitArgs = splitAt 3
+ sortArgs (att, def) = (sortOn Down att, sortOn Down def)
+ toTuple (x, y) = ((x !! 0, x !! 1, x !! 2), (y !! 0, y !! 1))
+
+groupRolls :: [((Integer, Integer, Integer), (Integer, Integer))] -> [[Result]]
+groupRolls rolls = (group . reverse . sort) [fight roll | roll <- rolls]
+
+rollsByProbability :: [((Integer, Integer, Integer), (Integer, Integer))] -> Integer -> Possibility -> [Possibility]
+rollsByProbability rolls tot (Possibility (units, p)) = [Possibility (units + head loss, p * (fromIntegral (length loss) / fromIntegral tot)) | loss <- groupRolls rolls]
+
+oneVoneLosses :: Possibility -> [Possibility]
+oneVoneLosses = rollsByProbability rolls (total 2 6)
+ where
+ rolls = toRolls . fill $ 2 `d` 6
+ fill rolls = [[roll !! 0, 0, 0, roll !! 1, 0] | roll <- rolls]
+
+twoVoneLosses :: Possibility -> [Possibility]
+twoVoneLosses = rollsByProbability rolls (total 3 6)
+ where
+ rolls = toRolls . fill $ 3 `d` 6
+ fill rolls = [[roll !! 0, roll !! 1, 0, roll !! 2, 0] | roll <- rolls]
+
+oneVtwoLosses :: Possibility -> [Possibility]
+oneVtwoLosses = rollsByProbability rolls (total 3 6)
+ where
+ rolls = toRolls . fill $ 3 `d` 6
+ fill rolls = [[roll !! 0, 0, 0, roll !! 1, roll !! 2] | roll <- rolls]
+
+twoVtwoLosses :: Possibility -> [Possibility]
+twoVtwoLosses = rollsByProbability rolls (total 4 6)
+ where
+ rolls = toRolls . fill $ 4 `d` 6
+ fill rolls = [[roll !! 0, roll !! 1, 0, roll !! 2, roll !! 3] | roll <- rolls]
+
+threeVtwoLosses :: Possibility -> [Possibility]
+threeVtwoLosses = rollsByProbability rolls (total 5 6)
+ where
+ rolls = toRolls $ 5 `d` 6
+
+threeVoneLosses :: Possibility -> [Possibility]
+threeVoneLosses = rollsByProbability rolls (total 4 6)
+ where
+ rolls = toRolls . fill $ 4 `d` 6
+ fill rolls = [[roll !! 0, roll !! 1, roll !! 2, roll !! 3, 0] | roll <- rolls]
diff --git a/haskell/test/Spec.hs b/haskell/test/Spec.hs
new file mode 100644
index 0000000..48c285d
--- /dev/null
+++ b/haskell/test/Spec.hs
@@ -0,0 +1,29 @@
+import Test.Tasty
+import Test.Tasty.HUnit
+import Test.Tasty.QuickCheck
+import qualified Test.Tasty.SmallCheck as SC
+
+arith :: Integer -> Integer -> Property
+arith x y = (x > 0) && (y > 0) ==> (x+y)^2 > x^2 + y^2
+
+negation :: Integer -> Bool
+negation x = abs (x^2) >= x
+
+suite :: TestTree
+suite = testGroup "Test Suite" [
+ testGroup "Units"
+ [ testCase "Equality" $ True @=? True
+ , testCase "Assertion" $ assert $ (length [1,2,3]) == 3
+ ],
+
+ testGroup "QuickCheck tests"
+ [ testProperty "Quickcheck test" arith
+ ],
+
+ testGroup "SmallCheck tests"
+ [ SC.testProperty "Negation" negation
+ ]
+ ]
+
+main :: IO ()
+main = defaultMain suite
\ No newline at end of file