Disaster Area
formerly Piexplode
I'm going to look at a specific scenario (one that comes up frequently in my matches) and do some mathematical analysis of it, to deduce some probabilities.
Scenario: Tauros - Paralyzed, Snorlax - on turn of using rest, reflect is up. Simplification: Ignore Blizzard (for now)
Calculations:
Tauros Body Slam vs. Snorlax through Reflect: 61-72 (11.6 - 13.7%)
Tauros Hyper Beam vs. Snorlax through Reflect: 105-124 (20 - 23.7%)
Tauros Body Slam vs. Snorlax on a critical hit: 232-273 (44.3 - 52.1%) -- 15.8% chance to 2HKO
Tauros Hyper Beam vs. Snorlax on a critical hit: 409-481 (78.2 - 91.9%)
Chance of a critical hit for Tauros: 21.484% (3dp)
Probability of Tauros crit HBeam+non-crit Body Slam KOs = 0.34122 (5dp)
The question is what's the probability that Snorlax is KOed, and what's the probability that Snorlax reaches a healthy state where it's not immediately forced to Rest [I consider this the point where you can't be KOed by a bslam crit - this is an assumption that this is a sensible point].
In this model, I am treating Body Slam's accuracy as exactly 100%, and Hyper Beam's as exactly 90%.
For simplicity, we can look at these different scenarios when Tauros uses Body Slam on the turn I rest:
[1] Bslam x3 (this is what everyone seems to do to me)
[2] Bslam, HB, BSlam if HBfail
[3] Bslam, HB, HB if HBfail
[4] Bslam, Bslam, HB
[1]
Probability I'm KOd: (a)Probability of hitting all 3, 3 critical hits + (b)Probability of hitting all 3, 2 critical hits, + (c)Probability of hitting 2 of 3, all critical hits x 0.158.
(a)=(0.75*0.21484)^3=0.00418 (5dp) +
(b)=(0.75*0.21484)^2 * (0.75*0.78516) * 3 = 0.04566 (5dp) +
(c)=0.158 * 3 * 0.25 * (0.75*0.21484)^2 = 0.00308 =
0.05292 = ~5.3% I'm KOed by this strategy whilst resting.
Probability I survive healthily: (a) 3 full paralyses, (b) 2 full paralyses + 1 non-crit body slam, (c) 1 full para + 2 non-crit body slams, (d) 3 non-crit body slams
(a)=0.25^3=0.01564
(b)=3 * 0.25^2 * 0.75*0.78516 = 0.10991
(c)=3 * 0.25 * (0.75*0.78516)^2 = 0.25770
(d)=(0.75*0.78516)^3=0.20141
total = 0.56902 = ~56.9% chance I come out healthily without being forced to rest.
Probability I am KOed before I can awaken without need of rest = 0.05292/(0.05292+0.56902)=0.08509=~8.5% chance, or about 1 in 12.
[2]
Probability I'm KOd: (a) Body Slam Crit + Hyper Beam crit, (b), Body Slam non-crit + Hyper Beam crit, (c) Body Slam double crit
(a)=0.21484^2 * 0.75^2 * 0.9 = 0.02337
(b)=0.78516 * 0.21484 * 0.75^2 * 0.34122 = 0.03238
(c)=0.21484^2 * 0.75^2 * 0.25 * 0.158 = 0.00103
total = 0.05678 = ~5.7% chance to KO me with this strategy in one attempt.
Probability I survive healthily enough to not require a rest again: (a) 3 full paralysis [or hbeam miss + 2 fp], (b) Body Slam no crit + 2 full para (either bslam at start or end) or 1 fp + hbeam miss, (c) 2 bslam no crit + a full para/hb miss, (d) hbeam hits, doesn't crit + no bslam crit
(a)=0.25^2 * (1-0.75*0.9) = 0.25^2 * 0.325 = 0.02031
(b)=2 * 0.78516 * 0.75 * 0.25 * 0.325 = 0.09569
(c)=0.78516^2 * 0.75^2 * 0.325 = 0.11270
(d)=0.75 * 0.9 * (1-0.21484*0.75) = 0.56624
total = 0.79494 = ~79.4%.
Probability I am KOed before I can awaken without need of rest = 0.05678/(0.05678+0.79494)=0.06667=~6.6% chance, or about 1 in 15.
[3]Bslam, HB, HB if HBfail
Probability I'm KOed: (a) BSlam Crit + first Hbeam crit, (b) BSlam crit+2nd hbeam crit, (c) Bslam+first hbeam, (d) Bslam + 2nd hbeam
(a)=0.21484^2 * 0.75^2 * 0.9 = 0.02337
(b)=0.21484^2 * 0.75^2 * 0.9 * 0.325 = 0.00759
(c)=0.21484 * 0.78516 * 0.75^2 * 0.9 * 0.34122 = 0.02914
(d)=0.21484 * 0.78516 * 0.75^2 * 0.9 * 0.34122 * 0.325 = 0.00947
total = 0.06957 = 7.0% I'm KOed by this strategy whilst resting.
Probability I survive: (a) FP or BSlam doesn't crit, 1st HB doesn't crit, (b) FP or BSlam doesn't crit, 2nd HB doesn't crit or doesn't hit
(a)=(1-0.75*0.21484)*0.75*0.9*0.78516=0.44255
(b)=(1-0.75*0.21484)*(1-0.75*0.9)^2*0.78516=0.06957
total = 0.51212 = ~51.2%
Probability I am KOed before I can awaken without need of rest = 0.06957/(0.06957+0.51212)=0.11960=~12.0% chance, or about 1 in 8.
[4]BS, BS, HB
Probability I'm KOed: (a) BSlam Crit x2, (b) BSlam Crit x2 + HB [this is clearly non-sensical - in this scenario you would always body slam], (c) BSlam Crit + BSlam No-Crit + HB Crit, (d) 2 BSlam hit no crit + HB crit
(a)=0.75^2 * 0.21484^2 * 0.158 = 0.00410
(b)=0.75^3 * 0.21484^2 * 0.842 * 0.9 = 0.01476
(c)=0.75^3 * 0.21484^2 * 0.78516 * 0.9 = 0.01376
(d)=0.75^3 * 0.21484 * 0.78516^2 * 0.9 = 0.05029
total = 0.08291 = ~8.3% I'm KOed by this strategy whilst resting in one trial.
Probability I survive healthily: (a) All full para, (b) All bslam fp, hbeam miss, (c) All bslam fp, hbeam fail to crit, (d) 1 Bslam hit and no crit, 2 FP, (e) 2 bslam hit and no crit, FP, (f) 1 bslam and 1 hb hit, 1 fp, no crits, (g), 1 bslam and 1 hb miss, 1 fp, no crits, (h) 2 bslam hit, fp, (i) 2 bslam hit, hbeam miss, (j) 2 bslam hit, hbeam hit, no crits
(a)=0.25^3 = 0.01563
(b)=0.25^2 * 0.75 * 0.1 = 0.00469
(c)=0.25^2 * 0.75 * 0.9 * 0.78516 = 0.03312
(d)=0.25^2 * 0.75 * 2 * 0.78516 = 0.07361
(e)=0.25 * 0.75^2 * 0.78516^2 = 0.08669
(f)=0.25 * 0.75^2 * 0.78516^2 * 0.9 * 2 = 0.15605
(g)=0.25 * 0.75^2 * 0.78516 * 0.1 * 2 = 0.02208
(h)=0.25 * 0.75^2 * 0.78516^2 = 0.08669
(i)=0.75^3 * 0.78516^2 * 0.1 = 0.02601
(j)=0.75^3 * 0.78516^3 * 0.9 = 0.18378
Total = 0.68835 = ~68.8% that I survive healthily.
Probability I am KOed before I can awaken without need of rest = 0.08291/(0.08291+0.68835)=0.10750=~10.8% chance, or about 1 in 9.
This is as far as I've gotten so far.
To-do:
Consider when Hyper beaming on Rest turn.
Consider Blizzard and Freeze chance.
Consider Chance of KO with Bslam, and with Bslam+Hbeam.
Consider different approaches (there's certianly some flaws and illogicalities in this approach)
Scenario: Tauros - Paralyzed, Snorlax - on turn of using rest, reflect is up. Simplification: Ignore Blizzard (for now)
Calculations:
Tauros Body Slam vs. Snorlax through Reflect: 61-72 (11.6 - 13.7%)
Tauros Hyper Beam vs. Snorlax through Reflect: 105-124 (20 - 23.7%)
Tauros Body Slam vs. Snorlax on a critical hit: 232-273 (44.3 - 52.1%) -- 15.8% chance to 2HKO
Tauros Hyper Beam vs. Snorlax on a critical hit: 409-481 (78.2 - 91.9%)
Chance of a critical hit for Tauros: 21.484% (3dp)
Probability of Tauros crit HBeam+non-crit Body Slam KOs = 0.34122 (5dp)
The question is what's the probability that Snorlax is KOed, and what's the probability that Snorlax reaches a healthy state where it's not immediately forced to Rest [I consider this the point where you can't be KOed by a bslam crit - this is an assumption that this is a sensible point].
In this model, I am treating Body Slam's accuracy as exactly 100%, and Hyper Beam's as exactly 90%.
For simplicity, we can look at these different scenarios when Tauros uses Body Slam on the turn I rest:
[1] Bslam x3 (this is what everyone seems to do to me)
[2] Bslam, HB, BSlam if HBfail
[3] Bslam, HB, HB if HBfail
[4] Bslam, Bslam, HB
[1]
Probability I'm KOd: (a)Probability of hitting all 3, 3 critical hits + (b)Probability of hitting all 3, 2 critical hits, + (c)Probability of hitting 2 of 3, all critical hits x 0.158.
(a)=(0.75*0.21484)^3=0.00418 (5dp) +
(b)=(0.75*0.21484)^2 * (0.75*0.78516) * 3 = 0.04566 (5dp) +
(c)=0.158 * 3 * 0.25 * (0.75*0.21484)^2 = 0.00308 =
0.05292 = ~5.3% I'm KOed by this strategy whilst resting.
Probability I survive healthily: (a) 3 full paralyses, (b) 2 full paralyses + 1 non-crit body slam, (c) 1 full para + 2 non-crit body slams, (d) 3 non-crit body slams
(a)=0.25^3=0.01564
(b)=3 * 0.25^2 * 0.75*0.78516 = 0.10991
(c)=3 * 0.25 * (0.75*0.78516)^2 = 0.25770
(d)=(0.75*0.78516)^3=0.20141
total = 0.56902 = ~56.9% chance I come out healthily without being forced to rest.
Probability I am KOed before I can awaken without need of rest = 0.05292/(0.05292+0.56902)=0.08509=~8.5% chance, or about 1 in 12.
[2]
Probability I'm KOd: (a) Body Slam Crit + Hyper Beam crit, (b), Body Slam non-crit + Hyper Beam crit, (c) Body Slam double crit
(a)=0.21484^2 * 0.75^2 * 0.9 = 0.02337
(b)=0.78516 * 0.21484 * 0.75^2 * 0.34122 = 0.03238
(c)=0.21484^2 * 0.75^2 * 0.25 * 0.158 = 0.00103
total = 0.05678 = ~5.7% chance to KO me with this strategy in one attempt.
Probability I survive healthily enough to not require a rest again: (a) 3 full paralysis [or hbeam miss + 2 fp], (b) Body Slam no crit + 2 full para (either bslam at start or end) or 1 fp + hbeam miss, (c) 2 bslam no crit + a full para/hb miss, (d) hbeam hits, doesn't crit + no bslam crit
(a)=0.25^2 * (1-0.75*0.9) = 0.25^2 * 0.325 = 0.02031
(b)=2 * 0.78516 * 0.75 * 0.25 * 0.325 = 0.09569
(c)=0.78516^2 * 0.75^2 * 0.325 = 0.11270
(d)=0.75 * 0.9 * (1-0.21484*0.75) = 0.56624
total = 0.79494 = ~79.4%.
Probability I am KOed before I can awaken without need of rest = 0.05678/(0.05678+0.79494)=0.06667=~6.6% chance, or about 1 in 15.
[3]Bslam, HB, HB if HBfail
Probability I'm KOed: (a) BSlam Crit + first Hbeam crit, (b) BSlam crit+2nd hbeam crit, (c) Bslam+first hbeam, (d) Bslam + 2nd hbeam
(a)=0.21484^2 * 0.75^2 * 0.9 = 0.02337
(b)=0.21484^2 * 0.75^2 * 0.9 * 0.325 = 0.00759
(c)=0.21484 * 0.78516 * 0.75^2 * 0.9 * 0.34122 = 0.02914
(d)=0.21484 * 0.78516 * 0.75^2 * 0.9 * 0.34122 * 0.325 = 0.00947
total = 0.06957 = 7.0% I'm KOed by this strategy whilst resting.
Probability I survive: (a) FP or BSlam doesn't crit, 1st HB doesn't crit, (b) FP or BSlam doesn't crit, 2nd HB doesn't crit or doesn't hit
(a)=(1-0.75*0.21484)*0.75*0.9*0.78516=0.44255
(b)=(1-0.75*0.21484)*(1-0.75*0.9)^2*0.78516=0.06957
total = 0.51212 = ~51.2%
Probability I am KOed before I can awaken without need of rest = 0.06957/(0.06957+0.51212)=0.11960=~12.0% chance, or about 1 in 8.
[4]BS, BS, HB
Probability I'm KOed: (a) BSlam Crit x2, (b) BSlam Crit x2 + HB [this is clearly non-sensical - in this scenario you would always body slam], (c) BSlam Crit + BSlam No-Crit + HB Crit, (d) 2 BSlam hit no crit + HB crit
(a)=0.75^2 * 0.21484^2 * 0.158 = 0.00410
(b)=0.75^3 * 0.21484^2 * 0.842 * 0.9 = 0.01476
(c)=0.75^3 * 0.21484^2 * 0.78516 * 0.9 = 0.01376
(d)=0.75^3 * 0.21484 * 0.78516^2 * 0.9 = 0.05029
total = 0.08291 = ~8.3% I'm KOed by this strategy whilst resting in one trial.
Probability I survive healthily: (a) All full para, (b) All bslam fp, hbeam miss, (c) All bslam fp, hbeam fail to crit, (d) 1 Bslam hit and no crit, 2 FP, (e) 2 bslam hit and no crit, FP, (f) 1 bslam and 1 hb hit, 1 fp, no crits, (g), 1 bslam and 1 hb miss, 1 fp, no crits, (h) 2 bslam hit, fp, (i) 2 bslam hit, hbeam miss, (j) 2 bslam hit, hbeam hit, no crits
(a)=0.25^3 = 0.01563
(b)=0.25^2 * 0.75 * 0.1 = 0.00469
(c)=0.25^2 * 0.75 * 0.9 * 0.78516 = 0.03312
(d)=0.25^2 * 0.75 * 2 * 0.78516 = 0.07361
(e)=0.25 * 0.75^2 * 0.78516^2 = 0.08669
(f)=0.25 * 0.75^2 * 0.78516^2 * 0.9 * 2 = 0.15605
(g)=0.25 * 0.75^2 * 0.78516 * 0.1 * 2 = 0.02208
(h)=0.25 * 0.75^2 * 0.78516^2 = 0.08669
(i)=0.75^3 * 0.78516^2 * 0.1 = 0.02601
(j)=0.75^3 * 0.78516^3 * 0.9 = 0.18378
Total = 0.68835 = ~68.8% that I survive healthily.
Probability I am KOed before I can awaken without need of rest = 0.08291/(0.08291+0.68835)=0.10750=~10.8% chance, or about 1 in 9.
This is as far as I've gotten so far.
To-do:
Consider when Hyper beaming on Rest turn.
Consider Blizzard and Freeze chance.
Consider Chance of KO with Bslam, and with Bslam+Hbeam.
Consider different approaches (there's certianly some flaws and illogicalities in this approach)