Trusted97 · September 12, 2025 10:05 · Sep 12, 2025
diff --git a/gistfile1.txt b/gistfile1.txt
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+# Monte Carlo method
+# Goal:
+# 1) Find best opening hands
+# 2) Estimate combo-read hands
+
+import random, collections, itertools, textwrap, pandas as pd
+
+deck_list = [
+"1 Abrade","1 Ad Nauseam","1 Agatha's Soul Cauldron","1 All Will Be One","1 Arcane Signet","1 Barbarian Ring","1 Beseech the Mirror","1 Birgi, God of Storytelling",
+"1 Blackcleave Cliffs","1 Blazemire Verge","1 Blightstep Pathway","1 Blood Crypt","1 Bloodstained Mire","1 Cabal Ritual","1 Cavern of Souls","1 Command Tower",
+"1 Coruscation Mage","1 Dark Ritual","1 Dauthi Voidwalker","1 Deadly Rollick","1 Defense Grid","1 Deflecting Swat","1 Demonic Tutor","1 Desperate Ritual","1 Diabolic Intent",
+"1 Dismember","1 Dragonskull Summit","1 Dualcaster Mage","1 Emergence Zone","1 Exotic Orchard","1 Fellwar Stone","1 Final Fortune","1 Fire Covenant","1 Firebrand Archer",
+"1 Flare of Duplication","1 Gamble","1 Gemstone Caverns","1 Go for the Throat","1 Goblin Engineer","1 Grapeshot","1 Grinding Station","1 Imperial Recruiter","1 Jeska's Will",
+"1 Kederekt Parasite","1 Kessig Flamebreather","1 Lightning Bolt","1 Lotus Petal","1 Luxury Suite","1 Mana Vault","1 Marionette Apprentice","1 Marsh Flats","1 Mayhem Devil",
+"1 Molten Duplication","1 Mount Doom","3 Mountain","1 Mox Amber","1 Necropotence","1 Opposition Agent","1 Orcish Bowmasters","1 Party Thrasher","1 Praetor's Grasp","1 Prosper, Tome-Bound",
+"1 Pyretic Ritual","1 Ragavan, Nimble Pilferer","1 Raucous Theater","1 Razorkin Needlehead","1 Red Elemental Blast","1 Reflecting Pool","1 Rite of Flame","1 Roiling Vortex",
+"1 Sensei's Divining Top","1 Shizo, Death's Storehouse","1 Simian Spirit Guide","1 Slaughter Pact","1 Smoldering Marsh","1 Snuff Out","1 Sokenzan, Crucible of Defiance","1 Sol Ring",
+"1 Sulfurous Springs","5 Swamp","1 Tainted Peak","1 Takenuma, Abandoned Mire","1 Talisman of Indulgence","1 Underworld Breach","1 Unstable Amulet","1 Untimely Malfunction",
+"1 Urza's Saga","1 Vampiric Tutor","1 Vexing Bauble","1 Volrath's Stronghold","1 Walking Ballista","1 Wheel of Fortune","1 Wooded Foothills","1 Ob Nixilis, Captive Kingpin"
+]
+
+expanded = []
+for entry in deck_list:
+    parts = entry.split(" ",1)
+    count = int(parts[0])
+    name = parts[1].strip()
+    for _ in range(count):
+        expanded.append(name)
+deck = expanded[:]
+len(deck)
+# Define sets
+fast_mana = set(["Mana Vault","Sol Ring","Mox Amber","Lotus Petal","Gemstone Caverns","Fellwar Stone","Talisman of Indulgence","Unstable Amulet","Arcane Signet","Simian Spirit Guide"])
+rituals = set(["Dark Ritual","Cabal Ritual","Desperate Ritual","Pyretic Ritual","Rite of Flame","Jeska's Will"])
+tutors = set(["Vampiric Tutor","Demonic Tutor","Diabolic Intent","Gamble","Beseech the Mirror","Praetor's Grasp","Imperial Recruiter"])
+combo_pieces = set(["Underworld Breach","Grinding Station","All Will Be One","Walking Ballista","Ad Nauseam"])
+
+# Simulation
+import math
+N=100000
+random.seed(42)
+counts = collections.Counter()
+top_hands = collections.Counter()
+
+for _ in range(N):
+    d = deck[:]
+    random.shuffle(d)
+    hand = tuple(sorted(d[:7]))
+    handset = set(hand)
+    has_fast = len([c for c in hand if c in fast_mana]) + len([c for c in hand if c in rituals])
+    # Criteria A: Breach + Grinding Station + at least one mana source (land or fast mana/ritual)
+    has_land = any(name in hand for name in ["Swamp","Mountain","Blood Crypt","Dragonskull Summit","Smoldering Marsh","Tainted Peak","Takenuma, Abandoned Mire","Blackcleave Cliffs","Sokenzan, Crucible of Defiance","Gemstone Caverns","Blightstep Pathway","Reflecting Pool","Exotic Orchard","Command Tower","Luxury Suite","Mount Doom","Wooded Foothills","Marsh Flats"])
+    criteria_A = ("Underworld Breach" in handset) and ("Grinding Station" in handset) and (has_land or any(c in fast_mana or c in rituals for c in hand))
+    # Criteria B: All Will + Ballista + mana
+    criteria_B = ("All Will Be One" in handset) and ("Walking Ballista" in handset) and (has_land or any(c in fast_mana or c in rituals for c in hand))
+    # Criteria C: Ad Nauseam + at least 2 fast mana/rituali
+    fastcount = sum(1 for c in hand if c in fast_mana or c in rituals)
+    criteria_C = ("Ad Nauseam" in handset) and (fastcount >= 2)
+    # Criteria D: tutor + at least 1 fast mana or land
+    criteria_D = any(c in handset for c in tutors) and (has_land or fastcount>=1)
+    combo_ready = criteria_A or criteria_B or criteria_C or criteria_D
+    if combo_ready:
+        counts['combo_ready'] += 1
+        top_hands[hand] += 1
+    else:
+        counts['not_ready'] += 1
+
+# Compute percentages
+combo_pct = counts['combo_ready']/N*100.0
+not_pct = counts['not_ready']/N*100.0
+
+# Top 10 most frequent combo-ready opening hands observed
+top_combo_hands = [(hand, cnt) for hand,cnt in top_hands.most_common(30)]
+top_combo_hands = top_combo_hands[:10]
+
+# Prepare output table for top hands (show only card names and frequency)
+rows = []
+for hand, cnt in top_combo_hands:
+    rows.append({"hand": ", ".join(hand), "count": cnt, "percent_of_sim": cnt/N*100.0})
+
+df = pd.DataFrame(rows)
+from caas_jupyter_tools import display_dataframe_to_user
+display_dataframe_to_user("Top combo-ready opening hands (sampled)", df)
+
+# Print summary stats
+print(f"Simulation: {N}")
+print(f"Openings combo-ready: {counts['combo_ready']} ({combo_pct:.2f}%)")
+print(f"Openings not combo-ready: {counts['not_ready']} ({not_pct:.2f}%)")
+
+# Breakdown of which criteria were hit (approximate) - re-run to count each criterion individually
+criteria_counts = collections.Counter()
+random.seed(42)
+for _ in range(N):
+    d = deck[:]; random.shuffle(d); hand = d[:7]; handset=set(hand)
+    has_land = any(name in hand for name in ["Swamp","Mountain","Blood Crypt","Dragonskull Summit","Smoldering Marsh","Tainted Peak","Takenuma, Abandoned Mire","Blackcleave Cliffs","Sokenzan, Crucible of Defiance","Gemstone Caverns","Blightstep Pathway","Reflecting Pool","Exotic Orchard","Command Tower","Luxury Suite","Mount Doom","Wooded Foothills","Marsh Flats"])
+    fastcount = sum(1 for c in hand if c in fast_mana or c in rituals)
+    if ("Underworld Breach" in handset) and ("Grinding Station" in handset) and (has_land or any(c in fast_mana or c in rituals for c in hand)):
+        criteria_counts['Breach_line'] += 1
+    if ("All Will Be One" in handset) and ("Walking Ballista" in handset) and (has_land or any(c in fast_mana or c in rituals for c in hand)):
+        criteria_counts['AllWill_Ballista'] += 1
+    if ("Ad Nauseam" in handset) and (fastcount >= 2):
+        criteria_counts['AdNauseam'] += 1
+    if any(c in handset for c in tutors) and (has_land or fastcount>=1):
+        criteria_counts['Tutor_plus_accel'] += 1
+
+print("Breakdown (hits per criterion):")
+for k,v in criteria_counts.items():
+    print(f"  {k}: {v} ({v/N*100:.2f}%)")
+