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Monte Carlo versus "The Math"
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<blockquote data-quote="Truename" data-source="post: 4983486" data-attributes="member: 78255"><p><strong>A Hard Day's Night</strong></p><p></p><p>As I've mentioned, I don't think "the math" is so much about rounds per combat or damage per round as it is about resource consumption. Now that the dwarf actually has daily resources (healing surges and his level 1 daily power), I was able to simulate it. I had the poor creature fight until he died, and then I recorded how many rounds he survived.</p><p></p><p>This is where I'm planning on going with the rest of the simulations: looking at how long a particular build can survive. I think this is the most accurate and holistic metric we can use, although I'm happy to try something else if I'm wrong.</p><p></p><p>I went ahead and ran this for the complete range of DMG-recommended encounters, from level +0 to level +5. Enjoy... future posts will be less frequent--this is as far as I've gotten with the program, so far.</p><p></p><p>(Oh, I also changed the short rest AI to spend a surge even if half of it would be lost. This led to better survivability.)</p><p></p><p><strong>Edit: As Elric mentions below, the monster to-hit probability is way too low in these simulations. The correct results are in a post below.</strong></p><p></p><p>[code]</p><p>Avg rounds: 3.1</p><p> 1 (8.0%): ================</p><p> 2 (40.5%): ===================================================================</p><p> 3 (64.0%): ================================================</p><p> 4 (82.9%): =======================================</p><p> 5 (93.1%): =====================</p><p> 6 (98.3%): ==========</p><p> 7 (99.5%): ==</p><p></p><p>Avg fights survived: 6.8</p><p> 0 (3.1%): =================</p><p> 1 (8.2%): ============================</p><p> 2 (14.0%): ================================</p><p> 3 (19.9%): =================================</p><p> 4 (26.6%): =====================================</p><p> 5 (34.9%): ==============================================</p><p> 6 (45.1%): =========================================================</p><p> 7 (57.0%): ===================================================================</p><p> 8 (67.9%): =============================================================</p><p> 9 (77.2%): ====================================================</p><p> 10 (84.9%): ===========================================</p><p> 11 (90.4%): ===============================</p><p> 12 (94.6%): =======================</p><p> 13 (97.0%): =============</p><p> 14 (98.4%): =======</p><p> 15 (99.1%): ===</p><p> 16 (99.6%): ==</p><p> 17 (99.8%): =</p><p></p><p>Daily used: 86.6%</p><p>[/code][code]</p><p>LEVEL 2 SOLDIER VS. DWARF GREATWEAPON FIGHTER</p><p>Days simulated: 10000</p><p></p><p>Avg rounds: 4.0</p><p> 1 (1.8%): ====</p><p> 2 (17.5%): ==========================================</p><p> 3 (42.4%): ===================================================================</p><p> 4 (63.3%): ========================================================</p><p> 5 (82.3%): ==================================================</p><p> 6 (93.2%): =============================</p><p> 7 (97.5%): ===========</p><p> 8 (99.3%): =====</p><p> 9 (99.8%): =</p><p></p><p>Avg fights survived: 3.8</p><p> 0 (8.9%): ==========================================</p><p> 1 (21.5%): ============================================================</p><p> 2 (34.4%): ==============================================================</p><p> 3 (46.7%): ==========================================================</p><p> 4 (59.4%): =============================================================</p><p> 5 (73.2%): ===================================================================</p><p> 6 (84.5%): ======================================================</p><p> 7 (92.0%): ===================================</p><p> 8 (96.7%): ======================</p><p> 9 (98.6%): =========</p><p> 10 (99.4%): ===</p><p> 11 (99.8%): =</p><p></p><p>Daily used: 82.0%</p><p>[/code][code]</p><p>LEVEL 3 SOLDIER VS. DWARF GREATWEAPON FIGHTER</p><p>Days simulated: 10000</p><p></p><p>Avg rounds: 5.0</p><p> 1 (1.3%): ====</p><p> 2 (4.6%): ==========</p><p> 3 (21.0%): ==================================================</p><p> 4 (42.8%): ===================================================================</p><p> 5 (63.4%): ===============================================================</p><p> 6 (79.6%): =================================================</p><p> 7 (91.0%): ===================================</p><p> 8 (96.5%): ================</p><p> 9 (98.6%): ======</p><p> 10 (99.5%): ==</p><p></p><p>Avg fights survived: 2.5</p><p> 0 (16.5%): ===================================================</p><p> 1 (38.2%): ===================================================================</p><p> 2 (57.1%): ==========================================================</p><p> 3 (71.0%): ==========================================</p><p> 4 (82.9%): ====================================</p><p> 5 (91.6%): ==========================</p><p> 6 (97.0%): ================</p><p> 7 (99.0%): ======</p><p> 8 (99.8%): ==</p><p></p><p>Daily used: 78.2%</p><p>[/code][code]</p><p>LEVEL 4 SOLDIER VS. DWARF GREATWEAPON FIGHTER</p><p>Days simulated: 10000</p><p></p><p>Avg rounds: 5.6</p><p> 1 (0.4%): =</p><p> 2 (2.5%): ======</p><p> 3 (12.5%): ===============================</p><p> 4 (30.9%): =========================================================</p><p> 5 (52.2%): ===================================================================</p><p> 6 (70.8%): ==========================================================</p><p> 7 (84.3%): ==========================================</p><p> 8 (92.4%): =========================</p><p> 9 (97.1%): ==============</p><p> 10 (99.0%): =====</p><p> 11 (99.6%): ==</p><p></p><p>Avg fights survived: 1.1</p><p> 0 (38.5%): ===================================================================</p><p> 1 (72.6%): ===========================================================</p><p> 2 (88.1%): ==========================</p><p> 3 (95.5%): ============</p><p> 4 (98.8%): =====</p><p> 5 (99.8%): =</p><p></p><p>Daily used: 70.9%</p><p>[/code][code]</p><p>LEVEL 5 SOLDIER VS. DWARF GREATWEAPON FIGHTER</p><p>Days simulated: 10000</p><p></p><p>Avg rounds: 6.3</p><p> 2 (1.2%): ===</p><p> 3 (7.8%): ========================</p><p> 4 (20.6%): ==============================================</p><p> 5 (38.3%): ================================================================</p><p> 6 (56.8%): ===================================================================</p><p> 7 (72.7%): =========================================================</p><p> 8 (84.9%): ============================================</p><p> 9 (92.1%): ==========================</p><p> 10 (96.3%): ===============</p><p> 11 (98.5%): ========</p><p> 12 (99.5%): ===</p><p> 13 (99.8%): =</p><p></p><p>Avg fights survived: 0.7</p><p> 0 (52.2%): ===================================================================</p><p> 1 (85.2%): ==========================================</p><p> 2 (95.8%): =============</p><p> 3 (98.9%): ===</p><p> 4 (99.8%): =</p><p></p><p>Daily used: 65.6%</p><p>[/code][code]</p><p>LEVEL 6 SOLDIER VS. DWARF GREATWEAPON FIGHTER</p><p>Days simulated: 10000</p><p></p><p>Avg rounds: 6.6</p><p> 2 (0.8%): ===</p><p> 3 (6.8%): =======================</p><p> 4 (18.9%): ===============================================</p><p> 5 (35.6%): =================================================================</p><p> 6 (52.8%): ===================================================================</p><p> 7 (68.0%): ===========================================================</p><p> 8 (80.3%): ================================================</p><p> 9 (88.6%): ================================</p><p> 10 (94.1%): =====================</p><p> 11 (97.2%): ===========</p><p> 12 (98.7%): =====</p><p> 13 (99.6%): ===</p><p> 14 (99.8%): =</p><p></p><p>Avg fights survived: 0.3</p><p> 0 (73.3%): ===================================================================</p><p> 1 (96.0%): ====================</p><p> 2 (99.6%): ===</p><p></p><p>Daily used: 58.0%</p><p>[/code]One of the notable things about these results is that the daily usage goes down as the level of the opponent goes up, but as I said in my lost post, that's skewed because it's a reliable power. The "Daily Used" line only checks to see if the power was <em>consumed</em>, not if it was tried. Presumably, the poor dwarf is trying it but missing a lot.</p><p></p><p>(Source code to follow. I've got to run now and won't be able to post for a while.)</p></blockquote><p></p>
[QUOTE="Truename, post: 4983486, member: 78255"] [b]A Hard Day's Night[/b] As I've mentioned, I don't think "the math" is so much about rounds per combat or damage per round as it is about resource consumption. Now that the dwarf actually has daily resources (healing surges and his level 1 daily power), I was able to simulate it. I had the poor creature fight until he died, and then I recorded how many rounds he survived. This is where I'm planning on going with the rest of the simulations: looking at how long a particular build can survive. I think this is the most accurate and holistic metric we can use, although I'm happy to try something else if I'm wrong. I went ahead and ran this for the complete range of DMG-recommended encounters, from level +0 to level +5. Enjoy... future posts will be less frequent--this is as far as I've gotten with the program, so far. (Oh, I also changed the short rest AI to spend a surge even if half of it would be lost. This led to better survivability.) [b]Edit: As Elric mentions below, the monster to-hit probability is way too low in these simulations. The correct results are in a post below.[/b] [code] Avg rounds: 3.1 1 (8.0%): ================ 2 (40.5%): =================================================================== 3 (64.0%): ================================================ 4 (82.9%): ======================================= 5 (93.1%): ===================== 6 (98.3%): ========== 7 (99.5%): == Avg fights survived: 6.8 0 (3.1%): ================= 1 (8.2%): ============================ 2 (14.0%): ================================ 3 (19.9%): ================================= 4 (26.6%): ===================================== 5 (34.9%): ============================================== 6 (45.1%): ========================================================= 7 (57.0%): =================================================================== 8 (67.9%): ============================================================= 9 (77.2%): ==================================================== 10 (84.9%): =========================================== 11 (90.4%): =============================== 12 (94.6%): ======================= 13 (97.0%): ============= 14 (98.4%): ======= 15 (99.1%): === 16 (99.6%): == 17 (99.8%): = Daily used: 86.6% [/code][code] LEVEL 2 SOLDIER VS. DWARF GREATWEAPON FIGHTER Days simulated: 10000 Avg rounds: 4.0 1 (1.8%): ==== 2 (17.5%): ========================================== 3 (42.4%): =================================================================== 4 (63.3%): ======================================================== 5 (82.3%): ================================================== 6 (93.2%): ============================= 7 (97.5%): =========== 8 (99.3%): ===== 9 (99.8%): = Avg fights survived: 3.8 0 (8.9%): ========================================== 1 (21.5%): ============================================================ 2 (34.4%): ============================================================== 3 (46.7%): ========================================================== 4 (59.4%): ============================================================= 5 (73.2%): =================================================================== 6 (84.5%): ====================================================== 7 (92.0%): =================================== 8 (96.7%): ====================== 9 (98.6%): ========= 10 (99.4%): === 11 (99.8%): = Daily used: 82.0% [/code][code] LEVEL 3 SOLDIER VS. DWARF GREATWEAPON FIGHTER Days simulated: 10000 Avg rounds: 5.0 1 (1.3%): ==== 2 (4.6%): ========== 3 (21.0%): ================================================== 4 (42.8%): =================================================================== 5 (63.4%): =============================================================== 6 (79.6%): ================================================= 7 (91.0%): =================================== 8 (96.5%): ================ 9 (98.6%): ====== 10 (99.5%): == Avg fights survived: 2.5 0 (16.5%): =================================================== 1 (38.2%): =================================================================== 2 (57.1%): ========================================================== 3 (71.0%): ========================================== 4 (82.9%): ==================================== 5 (91.6%): ========================== 6 (97.0%): ================ 7 (99.0%): ====== 8 (99.8%): == Daily used: 78.2% [/code][code] LEVEL 4 SOLDIER VS. DWARF GREATWEAPON FIGHTER Days simulated: 10000 Avg rounds: 5.6 1 (0.4%): = 2 (2.5%): ====== 3 (12.5%): =============================== 4 (30.9%): ========================================================= 5 (52.2%): =================================================================== 6 (70.8%): ========================================================== 7 (84.3%): ========================================== 8 (92.4%): ========================= 9 (97.1%): ============== 10 (99.0%): ===== 11 (99.6%): == Avg fights survived: 1.1 0 (38.5%): =================================================================== 1 (72.6%): =========================================================== 2 (88.1%): ========================== 3 (95.5%): ============ 4 (98.8%): ===== 5 (99.8%): = Daily used: 70.9% [/code][code] LEVEL 5 SOLDIER VS. DWARF GREATWEAPON FIGHTER Days simulated: 10000 Avg rounds: 6.3 2 (1.2%): === 3 (7.8%): ======================== 4 (20.6%): ============================================== 5 (38.3%): ================================================================ 6 (56.8%): =================================================================== 7 (72.7%): ========================================================= 8 (84.9%): ============================================ 9 (92.1%): ========================== 10 (96.3%): =============== 11 (98.5%): ======== 12 (99.5%): === 13 (99.8%): = Avg fights survived: 0.7 0 (52.2%): =================================================================== 1 (85.2%): ========================================== 2 (95.8%): ============= 3 (98.9%): === 4 (99.8%): = Daily used: 65.6% [/code][code] LEVEL 6 SOLDIER VS. DWARF GREATWEAPON FIGHTER Days simulated: 10000 Avg rounds: 6.6 2 (0.8%): === 3 (6.8%): ======================= 4 (18.9%): =============================================== 5 (35.6%): ================================================================= 6 (52.8%): =================================================================== 7 (68.0%): =========================================================== 8 (80.3%): ================================================ 9 (88.6%): ================================ 10 (94.1%): ===================== 11 (97.2%): =========== 12 (98.7%): ===== 13 (99.6%): === 14 (99.8%): = Avg fights survived: 0.3 0 (73.3%): =================================================================== 1 (96.0%): ==================== 2 (99.6%): === Daily used: 58.0% [/code]One of the notable things about these results is that the daily usage goes down as the level of the opponent goes up, but as I said in my lost post, that's skewed because it's a reliable power. The "Daily Used" line only checks to see if the power was [I]consumed[/I], not if it was tried. Presumably, the poor dwarf is trying it but missing a lot. (Source code to follow. I've got to run now and won't be able to post for a while.) [/QUOTE]
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