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authorSébastien Dailly <sebastien@dailly.me>2024-03-07 10:54:37 +0100
committerSébastien Dailly <sebastien@dailly.me>2024-03-07 10:54:37 +0100
commit7ad4aedc49e97a2a62de08c89b47a877adf9e076 (patch)
treeb43233ffd74ffeedf05b2f62dd8031bf4eb5e703 /calculette_aoo
parentfe13ea5ce39b24b2d49b43c384ed01b013d683db (diff)
calculette_aoo: updated the way to evaluate the oddsHEADmaster
Diffstat (limited to 'calculette_aoo')
-rw-r--r--calculette_aoo/bin/dune4
-rw-r--r--calculette_aoo/bin/main.ml60
-rw-r--r--calculette_aoo/lib/build.ml2
-rw-r--r--calculette_aoo/lib/roll.ml85
4 files changed, 97 insertions, 54 deletions
diff --git a/calculette_aoo/bin/dune b/calculette_aoo/bin/dune
index 1177b56..3fee2aa 100644
--- a/calculette_aoo/bin/dune
+++ b/calculette_aoo/bin/dune
@@ -1,3 +1,5 @@
(executable
(name main)
- (libraries aoo))
+ (libraries
+ zarith
+ aoo))
diff --git a/calculette_aoo/bin/main.ml b/calculette_aoo/bin/main.ml
index c738cd7..37d015b 100644
--- a/calculette_aoo/bin/main.ml
+++ b/calculette_aoo/bin/main.ml
@@ -3,34 +3,33 @@ let cout_m = (110, 55, 35)
let cout_rm = (50, 40, 20)
let cout_pm = (5, 3, 1)
let cout_fm = (100, 50, 30)
-let fm_oponent = 10
+let fm_oponent = 1
+let n = 3
+let ratio = Float.(to_int (pow 3.0 (of_int n)))
+
+let print_arr arr =
+ Format.printf "@[<v>%a@]@." (Format.pp_print_array Format.pp_print_int) arr
+
+let () = print_arr (Aoo.Roll.build_frequencies n)
+
+(* Calcule les probabilités de toucher contre les 10 prochains niveaux *)
+let compare_result = Aoo.Roll.compare 9 1
+
+let () =
+ Format.printf "%.4f - %s\n"
+ (compare_result |> Q.to_float)
+ (compare_result |> Q.to_string)
let env : Aoo.Build.env =
{
cost_max = 1800
- ; max_tours = 5.0
+ ; max_tours = 5
; cout_sort = 8
; degat_sort = 6
; fm_oponent
; frequencies = Aoo.Build.buil_freq_table 9 fm_oponent
}
-(*
-let () = Random.self_init ()
-
-let roll_and_accumulate dices =
- Seq.repeat () |> Seq.take dices
- |> Seq.fold_left (fun res _ -> res + (1 + Random.int 6)) 0
-
-let delta_carac level =
- Seq.repeat () |> Seq.take 1000000
- |> Seq.fold_left
- (fun acc _ ->
- if roll_and_accumulate level > roll_and_accumulate (level - 2) then acc
- else acc + 1)
- 0
-*)
-
(* Définition des caractéristiques *)
let a = Aoo.Carac.create 2 cout_a
let m = Aoo.Carac.create 5 cout_m
@@ -38,12 +37,23 @@ let rm = Aoo.Carac.create 7 cout_rm
let pm = Aoo.Carac.create 40 cout_pm
let fm = Aoo.Carac.create 9 cout_fm
let default = Aoo.Build.{ a; m; rm; pm; fm }
+let score1 = Aoo.Build.score env default
+let cost1 = Aoo.Build.cost default
+let () = print_endline @@ Printf.sprintf "Score du build : %f" score1
+let build3 = { default with fm = Aoo.Carac.incr ~step:1 fm }
+let score3 = Aoo.Build.score env build3
+let cost3 = Aoo.Build.cost build3
+let () = print_endline @@ Printf.sprintf "Score du build : %f" score3
+let () = print_endline @@ Printf.sprintf "%b" (score1 = score3)
+let () = print_endline @@ Printf.sprintf "%b" (cost1 < cost3)
-let () =
- let build =
- Aoo.Build.traverse env
- (Aoo.Build.cost default, Aoo.Build.score env default)
- (Aoo.Build.upgrade env default)
- in
+(*
+ let () =
+ let build =
+ Aoo.Build.traverse env
+ (Aoo.Build.cost default, Aoo.Build.score env default)
+ (Aoo.Build.upgrade env default)
+ in
- Aoo.Build.repr env Format.std_formatter build
+ Aoo.Build.repr env Format.std_formatter build
+*)
diff --git a/calculette_aoo/lib/build.ml b/calculette_aoo/lib/build.ml
index 5c2ac0b..2119fb6 100644
--- a/calculette_aoo/lib/build.ml
+++ b/calculette_aoo/lib/build.ml
@@ -80,7 +80,7 @@ let repr : env -> Format.formatter -> build -> unit =
let score : env -> build -> float =
fun env build ->
- let d, v = eval build env in
+ let d, _ = eval build env in
d
(* Upgrade each caracteristic and keep only the values in range *)
diff --git a/calculette_aoo/lib/roll.ml b/calculette_aoo/lib/roll.ml
index 00d8465..14488e6 100644
--- a/calculette_aoo/lib/roll.ml
+++ b/calculette_aoo/lib/roll.ml
@@ -1,24 +1,52 @@
open StdLabels
-(** Evaluate the coefficient for the product of two polynamials *)
-let mul p1 p2 =
- let n1 = Array.length p1 and n2 = Array.length p2 in
- let n = n1 + n2 in
- let res = Array.make n 0 in
- for i = 0 to n1 - 1 do
- for j = 0 to n2 - 1 do
- res.(i + j + 1) <- res.(i + j + 1) + (p1.(i) * p2.(j))
- done
- done;
- res
+(** Build the frequencies table for the given number of dices to roll. The
+ function return a table with the number of occurences for the each index.
+
+ Example :
+ table[2] = 1
+ table[3] = 4
+
+ Tell us than there the probabily to get the value 3 is 4× higher to get the
+ value 2.
+ *)
+let build_frequencies n =
+ let length = n * 3 in
+
+ let arr_source = Array.init length ~f:(fun i -> if i < 3 then 1 else 0) in
+
+ (* Recursive function, evaluate the odd by adding a new dice to the previous
+ distribution.
+
+ The probabily to get the value V with N dice is equal to :
+ - The probabilyt to get the value V - 1 with N - 1 dices and having 1 with
+ the new dice
+ - The probabilyt to get the value V - 2 with N - 1 dices and having 2 with
+ the new dice
+ - The probabilyt to get the value V - 3 with N - 1 dices and having 3 with
+ the new dice
-(** Apply a power function over a polynomial *)
-let pow p1 n =
- let result = ref p1 in
- for _ = 1 to n - 1 do
- result := mul !result p1
- done;
- !result
+ As the dice is fair, the probability to get the new value is equal in each
+ case, and we can just ignore this part.
+
+ This give us this formula :
+
+ P(V)_N = P(V - 1)_(N-1) + P(V - 2)_(N-1) + P(V - 3)_(N-1)
+ *)
+ let rec apply level arr_source =
+ match level with
+ | 0 -> arr_source
+ | _ ->
+ let arr_target = Array.init length ~f:(fun _ -> 0) in
+ let depth = n - level + 1 in
+ for index = max 1 (depth - 1) to (3 * depth) - 1 do
+ for j = max 0 (index - 3) to index - 1 do
+ arr_target.(index) <- arr_target.(index) + arr_source.(j)
+ done
+ done;
+ apply (level - 1) arr_target
+ in
+ apply (n - 1) arr_source
(** Evaluate the odd to win agains a give difficulty *)
let against : int -> int array -> Q.t array =
@@ -26,18 +54,19 @@ let against : int -> int array -> Q.t array =
match n with
| 0 -> Array.map ~f:(fun _ -> Q.zero) difficulties
| _ ->
- (* Create the polynomial with the odd ratio for the given caracteristic *)
- let arr = Array.make 3 1 in
- let frequencies = pow arr n in
+ (* Create the polynomial with the odd ratio for the given
+ caracteristic *)
+ let frequencies = build_frequencies n in
let ratio = Z.(of_int 3 ** n) in
let get_chances difficulty =
(* Evaluate the ratio to win the roll *)
let chances = ref Z.zero in
for i = difficulty - 1 to Array.length frequencies - 1 do
- (* The index in the table is the odd to get exactly this value in the roll.
- Here, we just add every value in the array from the index strarting from
- the given difficulty. *)
+ (* The index in the table is the odd to get exactly this value in the
+ roll.
+ Here, we just add every value in the array from the index
+ strarting from the given difficulty. *)
chances := Z.(!chances + of_int frequencies.(i))
done;
Q.make !chances ratio
@@ -51,7 +80,6 @@ let against : int -> int array -> Q.t array =
In case of equality, the win is given to [v1] *)
let compare : int -> int -> Q.t =
fun carac1 carac2 ->
- let arr = Array.make 3 1 in
let z3 = Z.of_int 3 in
let ordinal1 = Z.(z3 ** carac1)
@@ -63,8 +91,11 @@ let compare : int -> int -> Q.t =
(* The number of iterations to do is elements1 × elements2. For every iteration of elements2, we have ordinal1 points to get. *)
let cases = Z.(ordinal1 * ordinal2) in
- let frequencies_1 = pow arr carac1 |> Array.map ~f:(fun v -> Z.(of_int v))
- and frequencies_2 = pow arr carac2 |> Array.map ~f:(fun v -> Z.(of_int v)) in
+ let frequencies_1 =
+ build_frequencies carac1 |> Array.map ~f:(fun v -> Z.(of_int v))
+ and frequencies_2 =
+ build_frequencies carac2 |> Array.map ~f:(fun v -> Z.(of_int v))
+ in
(* Now, compare for each values the probabily to win *)
let res = ref Z.zero in