Resource The Official ‘Hax’ Compendium Guide

Sage

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approved by Hogg and Kink
Special thanks to cb jose altuve corvettes for his valuable assistance


The Official ‘Hax’ Compendium Guide
by Sage of the 6 and Kink
Banner coming soon

Introduction: Hello there battler, welcome to the official guide to all things Hax! In this guide you’ll be able to locate exact probabilities of in-game scenarios. We’ve detailed nearly every possible outcome you could find in a battle, all in neat categories for you to find quickly in the heat of a game. Never again will you not know the odds with this trusty manual at your side.

Use this guide to help you make optimal decisions in battle or to conduct extensive post-game analyses to see what your best option could have been. This guide is not intended to tell you your odds of things happening on a turn-by-turn basis; rather, it is intended to help you calculate odds from a turn-zero position or a chain-of-events perspective. In other words, when we look at multiple turns we assume we look at these turns as a single event.

For example, if we are trying to calculate the odds of Draco Meteor hitting twice in a row, we calculate based on the initial turn before we click the first Draco Meteor, not the second. This is due to how probabilities work, and this extends to a probability-based game like Pokemon. Moves like Draco Meteor may have a 90% chance to hit in a single turn, but going for two Draco Meteors does not mean you are calculating two 90% turns separately. Instead, you treat them as a chain of events, and through our formula calculate that the odds of hitting two Draco Meteors back-to-back is 81%.

This logic applies to all elements of the game, including status moves. For example, the chance of thawing from a Freeze Status Condition is 20% on any single turn, but what if we're trying to calculate our odds of thawing it 3-4 turns in advance? See below:

Freeze Scenarios in Gen 7
Chance of thawing within one turns up is 20%
Chance of thawing within two turns is 36% assuming we begin on turn 0
Chance of thawing within three turns is 48.8% assuming we begin on turn 0**

** the reason we assume we begin on turn 0 is because of the gambler's fallacy. Two turns of unthaws does not equate to a 48.8% chance of being thawed turn three. Rather, before you test your luck you can calculate that with 20% chances to unthaw each turn, three total turn chances will give you a 48.8% chance to unthaw before you take your first chance to unthaw. To continue these chains of calculation beyond three turns, plug in 1-(1-y)^x in your scientific calculator, where x is the amount of turns and y is the percentage chance of hax. For example, the chance of a thawing within four turns would be 1-(1-0.2)^4 = 59%

This guide will include the following:
  1. The chance for a move without 100% accuracy to hit and miss more than once assuming we look at these turns as a single event.
  2. The chance for a move with a secondary effect to activate after two or three turns of use assuming we look at these turns as a single event.
  3. The chance for a move with a secondary effect without 100% accuracy to activate after one, two or three turns of use, assuming we look at these turns as a single event.
  4. The chance for a move to critical hit in after x amount of consecutive turns, including increased critical hit ratio, assuming we look at these turns as a single event.
  5. The chance for successful consecutive uses of moves such as Protect, Endure and Destiny Bond, assuming we look at these turns as a single event.
  6. A breakdown of sleep, paralysis mechanics, and freeze mechanics.
  7. Other miscellaneous mechanics, to be included.
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Basic Battle Tactics: Open up the correct toggle below that corresponds to your move. For example, if your move is Draco Meteor, you are looking for 90% accuracy moves. If you are looking for Ice Beam freeze chances after two turns, you are looking for 10% secondary effect moves. Once you open the correct toggle simply look at the percentages to find out the chance of your hax occurring from a purely statistical viewpoint. We do our best to include information from prior to USUM. Please post below if you have any suggestions to include vital information. For more comprehensive percentages that include miss chances on Secondary moves (For example, Fire Blast), see Advanced Battle Tactics below.

Chance of 95% moves missing twice in a row, then thrice in a row: 0.25%, 0.0125%
Chance of 95% moves hitting twice in a row, then thrice in a row: 90.25%, 85.74%

95% moves (miss): Aeroblast, Air Slash, Diamond Storm, Drill Run, Fire Fang, High Horsepower, Ice Fang, Icy Wind, Jump Kick, Pin Missile, Razor Leaf, Razor Shell, Rock Tomb, Sacred Fire, Spacial Rend, Steam Eruption, Thunder Fang

Chance of 90% moves missing twice in a row, then thrice in a row: 1%, 0.1%
Chance of 90% moves hitting twice in a row, then thrice in a row: 81%, 72.9%

90% moves (miss): Aqua Tail, Blaze Kick, Blizzard (Gen 1), Bonemerang, Charge Beam, Circle Throw, Crabhammer, Draco Meteor, Dragon Tail, Fleur Cannon, Giga Impact, Hyper Beam, Hammer Arm, Heat Wave, High Jump Kick, Ice Hammer, Icicle Crash, Leaf Storm, Leech Seed, Meteor Mash, Overheat, Play Rough, Psycho Boost, Rock Blast, Rock Slide, Rock Tomb, Rollout, Sky Attack, Sky Uppercut, Steel Wing, Super Fang, Thunder Wave, Toxic, Zen Headbutt


Chance of 10% secondary effects activating after two hits, then three hits: 19%, 27.1%
Chance of 10% secondary effects activating twice in a row, then thrice in a row: 1%, 0.1%

10% moves (secondary effect): Ancient Power, Blaze Kick, Blizzard, Bug Buzz, Earth Power, Energy Ball, Extrasensory, Fire Blast, Fire Fang, Flamethrower, Flare Blitz, Flash Cannon, Focus Blast, Freeze Dry, Heat Wave, Ice Beam, Ice Fang, Ice Punch, Meteor Mash, Play Rough, Psychic (Gen 2+), Signal Beam, Silver Wind, Sludge Wave, Steel Wing, Thunder Bolt, Thunder Fang

Chance of 85% moves missing twice in a row, then thrice in a row: 2.25%, 0.3375%
Chance of 85% moves hitting twice in a row, then thrice in a row: 72.75%, 61.41%

85% moves (miss): Bind, Blue Flare, Bolt Strike, Bounce, Fire Blast, Gear Grind, Megahorn, Metal Sound, Muddy Water, Origin Pulse, Power Whip, Precipice Blades, Rock Climb, Sand Tomb, Screech, Seed Flare, Tail Slap, Whirlpool, Will O Wisp, Wrap

Chance of 80% moves missing twice in a row, then thrice in a row: 4%, 0.8%
Chance of 80% moves hitting twice in a row, then thrice in a row: 64%, 51.2%

80% moves (miss): Cross Chop, Gunk Shot, Head Smash, Hydro Pump, Stone Edge, Submission


Chance of 20% secondary effects activating after two hits, then three hits: 36%, 48.8%
Chance of 20% secondary effects activating twice in a row, then thrice in a row: 4%, 0.8

20% moves (secondary effect): Bolt Strike, Crunch, Dark Pulse, Dragon Rush, Hurricane, Liquidation, Relic Song, Rock Climb, Shadow Ball, Tri Attack, Water Pulse, Waterfall, Zen Headbutt

Chance of 75% moves missing twice in a row, then thrice in a row: 6.25%, 1.56%
Chance of 75% moves hitting twice in a row, then thrice in a row: 56.25%, 42.19%

75% moves (miss): Clamp, Dragon Rush, Egg Bomb, Iron Tail, Lovely Kiss, Magma Storm, Poison Powder, Sleep Powder, Stun Spore, Sweet Kiss (Chance of Paralysis hitting twice and three times in a row also applies here)


Chance of 25% secondary effects activating after two hits, then three hits: 43.75%, 57.81%
Only Paralysis applies here. Chance of Paralysis hitting twice and three times in a row is 6.26% and 1.56% respectively. This does not apply to the move Thunder Wave hitting.

Chance of 70% moves missing twice in a row, then thrice in a row: 9%, 2.7%
Chance of 70% moves hitting twice in a row, then thrice in a row: 49%, 34.3%

70% moves (miss): Blizzard, Focus Blast, Hurricane, Thunder


Chance of 30% secondary effects activating after two hits, then three hits: 51%, 65.7%
30% moves (secondary effect): Air Slash, Body Slam, Bounce, Discharge, Dragonbreath, Gunk Shot, Icicle Crash, Iron Head, Iron Tail, Lava Plume, Moonblast, Muddy Water, Poison Jab, Psychic (Gen 1), Rock Slide, Scald, Sludge Bomb, Steam Eruption, Thunder

Chance of 60% moves missing twice in a row, then thrice in a row: 16%, 6.4%
Chance of 60% moves hitting twice in a row, then thrice in a row: 36%, 21.6%

60% moves (miss): Hypnosis

Chance of 40% secondary effects activating after two hits, then three hits: 64%, 78.4%
40% moves (secondary effect): Seed Flare

Chance of 55% moves missing twice in a row, then thrice in a row: 20.25%, 9.11%
Chance of 55% moves hitting twice in a row, then thrice in a row: 30.25%, 16.64%

55% moves (miss): Grasswhistle, Poison Gas (Gen 1-4), Sing

Chance of 50% moves missing twice in a row, then thrice in a row: 25%, 12.5%
Chance of 50% moves hitting twice in a row, then thrice in a row: 25%, 12.5%

50% moves (miss): Dynamic Punch, Zap Cannon


Chance of 50% secondary effects activating after two hits, then three hits: 25%, 12.5%
Chance of 50% secondary effects activating twice in a row, then thrice in a row: 25%, 12.5%

50% moves (secondary effect): Diamond Storm, Fiery Dance, Razor Shell

Chance of 60% (serene grace Air Slash + Iron Head) twice, then thrice: 36%, 21.6%
60% moves (Serene Grace Flinch): **Air Slash, Iron Head

** does not include miss chance - see advanced battle tactics for more information

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Critical Hits, Utility, and Status Tactics: Open up the correct toggle below that corresponds to your desired effect. For example, if you are looking for Critical Hit calculations, open up the Critical Hits toggle. Once you open the correct toggle simply look at the percentages to find out the chance of your hax occurring from a purely statistical viewpoint.
Gen 7 chance of Critical Hit:
Turn 1: 4.167%
Turn 2: 8.32%,
Turn 3: 12.22%


Gen 1-6 chance of Critical Hit
Turn 1: 6.25%
Turn 2: 12.11%
Turn 3: 17.60%


Increase Chance of Critical Hit after a single turn, two hits, then three hits: 12.5%, 23.44%, 33.01%

Increased Critical Hit Moves: Aeroblast, Blaze Kick, Crabhammer, Cross Chop, Drill Run, Leaf Blade, Night Slash, Psycho Cut, Razor Leaf, Shadow Claw, Slash, Stone Edge

In RBY (Gen 1), Critical Hit ratios are based on the Speed stat of the Pokemon using an attack. Pokemon such as Jolteon have a 25% chance of landing a critical hit based on the Gen 1 formula for calculating Critical Hits. Moves like Slash and Razor Leaf bolster this value even higher to extremely reliable levels. Even the slowest Pokemon with access to Slash, such as a Parasect, will still crit 50% of the time due to this formula. Faster Pokemon will have Critical Hit values well beyond 70-80% when using Slash or Razor Leaf. Keep this information in mind when attempting to land a Critical Hit in RBY.

Gen 1-5 Chance for successful consecutive Protect, Detect, Endure (and similar moves):
Turn 1: 100% *
Turn 2: 50%
Turn 3: 25%,
Turn 4: 12.5%**


* in gen 3, the move has a 1/65536 chance of missing on the first use.
** in gen 4, this value caps at 12.5%. In generation 5, there is no cap and it will continue to divide if used successfully in succession.

Gen 6 & 7 Chance for successful consecutive Protect, Detect, Destiny Bond, Endure (and similar moves):
Turn 1: 100%
Turn 2: 33.3%
Turn 3: 16.67%
Turn 4: 8.33%

Sleep Mechanics:
Chance of wake up on sleep turn is 0%
Chance of first turn wake up is 33.33%.
Chance of second turn wake up is 55.56%
Chance of third turn wake up is 100%


Paralysis Scenarios
Your chance of being fully paralyzed twice and three times in a row is 6.26% and 1.56% respectively. This does not apply to the move Thunder Wave hitting, which can be found in 90% move accuracy.

The chance of Thunder Wave hitting AND causing full paralysis on the same turn is 22.5%

If you are Paralyzed, your chance avoiding full paralysis on turn one is 75%. If you do not assume you were not paralyzed on turn 1 and see the two turns as a single event, on turn two your chance is 56.25% to avoid full paralysis, and, if we see three turns as a single event, on turn three your chance to avoid paralysis is 42.19%. This means that the odds are against you in getting fully paralyzed at least once in the three times you proceed to make a move.

There is a difference between using Thunder Wave with Iron Head or Air Slash (with Serene Grace):
1) Thunder Wave + Air Slash Calculations:

- Turn 1: 67.75% of gaining a turn
- Turn 2: 45.9% of gaining 2 turns, assuming we look at these turns as a single event
- Turn 3: 31.1% chance of gaining 3 turns, assuming we look at these turns as a single event

2) Thunder Wave + Iron Head Calculations:
- Turn 1: 70% chance of gaining a turn
- Turn 2: 49% chance of gaining 2 turns, assuming we look at these turns as a single event
- Turn 3: 34.3% chance of gaining 3 turns, assuming we look at these turns as a single event


Freeze Scenarios in Gen 7
Chance of thawing within one turns up is 20%
Chance of thawing within two turns is 36% assuming we begin on turn 0
Chance of thawing within three turns is 48.8% assuming we begin on turn 0**


** the reason we assume we begin on turn 0 is because of the gambler's fallacy. Two turns of unthaws does not equate to a 48.8% chance of being thawed turn three. Rather, before you test your luck you can calculate that with 20% chances to unthaw each turn, three total turn chances will give you a 48.8% chance to unthaw before you take your first chance to unthaw. To continue these chains of calculation beyond three turns, plug in 1-(1-y)^x in your scientific calculator, where x is the amount of turns and y is the percentage chance of hax. For example, the chance of a thawing within four turns would be 1-(1-0.2)^4 = 59%

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Advanced Battle Tactics: Below is a list of calculations of moves that combine accuracy variables with their secondary effects. For example, Fire Blast has 85% accuracy and a 10% chance of a burn, so the chance of a burn when accounting for accuracy on turn one is 8.5%. Subsequently, on turn two, because we're accounting for the miss probability, the chance of a burn is 16.28% and after three turns it is 23.39%. For more basic information about percentages, such as the simple odds of a Draco Meteor hitting twice in a row or your chance to freeze with Ice Beam after two turns, see Basic Battle Tactics.

Chance of 95% accuracy move with 10% secondary effect activating:
- one hit: 9.5%
- two hits: 18.1%,
- three hits: 25.9%
List of moves: Fire Fang, Ice Fang, Thunder Fang

Chance of 95% accuracy move with 30% secondary effect activating
- one hit: 28.5%
- two hits: 48.9%
- three hits: 63.5%
List of moves: Air Slash, Steam Eruption

Chance of 95% accuracy move with 50% secondary effect activating
- one hit: 47.5%
- two hits: 72.4%
- three hits: 85.5%
List of moves: Diamond Storm, Razor Shell, Sacred Fire

Chance of 90% accuracy move with 10% secondary effect activating
- one hit: 9%
- two hits: 17.2%
- three hits: 24.6%
List of moves: Blaze Kick, Blizzard (Gen 1), Heat Wave, Play Rough, Steel Wing

Chance of 90% accuracy move with 20% secondary effect activating
- one hit: 18%
- two hits: 32.76%
- three hits: 44.9%
List of moves: Meteor Mash, Zen Headbutt

Chance of 90% accuracy move with 30% secondary effect activating
- one hit: 27%
- two hits: 46.7%
- three hits: 61.1%
List of moves: Icicle Crash, Rock Slide

Chance of 90% accuracy move with 70% secondary effect activating
- one hit: 63%
- two hits: 86.3%
- three hits: 94.9%
List of moves: Charge Beam

Chance of 85% accuracy move with 10% secondary effect activating
- after one hit, 8.5%
- two hits, 16.3%
- three hits: 23.4%
List of moves: Fire Blast

Chance of 85% accuracy move with 20% secondary effect activating:
- one hit: 17%
- two hits: 31.1%
- three hits: 42.8%
List of moves: Blue Flare, Bolt Strike, Rock Climb

Chance of 85% accuracy move with 30% secondary effect activating:
- one hit: 25.5%
- two hits: 44.5%
- three hits: 58.7%
List of moves: Bounce, Muddy Water

Chance of 85% accuracy move with 40% secondary effect activating:
- one hit: 34%
- two hits: 56.5%
- three hits: 71.3%
List of moves: Seed Flare

Chance of 80% accuracy move with 30% secondary effect activating:
- one hit: 24%
- two hits: 42.2%
- three hits: 56.1%
List of moves: Gunk Shot

Chance of 75% accuracy move with 20% secondary effect activating:
- one hit: 15%
- two hits: 27.8%
- three hits: 38.6%
List of moves: Dragon Rush

Chance of 75% accuracy move with 30% secondary effect activating:
- one hit: 22.5%
- two hits: 39.9%
- three hits: 53.5%
List of moves: Iron Tail

Chance of 70% accuracy move with 10% secondary effect activating:
- one hit: 7%
- two hits: 13.5%
- three hits: 19.6%
List of moves: Blizzard, Focus Blast

Chance of 70% accuracy move with 30% secondary effect activating:
- one hit: 21%
- two hits: 37.6%
- three hits: 50.7%
List of moves: Hurricane, Thunder
 
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Knuckstrike

Hi I'm FIREEEE
#2
A lot of this is worded either weirdly or wrongly. I get what is written, but if you're explaining probability misconceptions you should be accurate.

Chance of 95% moves missing twice in a row, then thrice in a row: 0.25%, 0.125%

Should be 0.0125%

Chance of (10%/20%/..) secondary effects activating after two hits

Should be chance of 10%/20%/.. secondary effects activating after at most two hits. Activating after two hits is the same as activating after 1 hit.

Assuming you were not paralyzed on turn one, on turn two your chance is 56.25% to avoid full paralysis

Assuming you were not paralyzed on turn one, on turn two your chance is 75% to avoid full paralysis. This is literally the gambler's fallacy you were talking about lol.
Only if you do not assume you were not paralyzed on turn 1 and see the two turns as a single event can you say it's 56%

Many a time you say "on turn 2, the chance of gaining 2 turns is ..." while the turns are obviously separate.

Overall it's pretty poorly written, sorry. I think this should be rewritten before it's used as a guide to hax.
 

Kink

Same great taste with zero calories
is a Forum Moderatoris a Community Contributoris a Contributor to Smogonis a Tutor Alumnusis a Tiering Contributor Alumnus
Moderator
#3
A lot of this is worded either weirdly or wrongly. I get what is written, but if you're explaining probability misconceptions you should be accurate.

Chance of 95% moves missing twice in a row, then thrice in a row: 0.25%, 0.125%

Should be 0.0125%

Chance of (10%/20%/..) secondary effects activating after two hits

Should be chance of 10%/20%/.. secondary effects activating after at most two hits. Activating after two hits is the same as activating after 1 hit.

Assuming you were not paralyzed on turn one, on turn two your chance is 56.25% to avoid full paralysis

Assuming you were not paralyzed on turn one, on turn two your chance is 75% to avoid full paralysis. This is literally the gambler's fallacy you were talking about lol.
Only if you do not assume you were not paralyzed on turn 1 and see the two turns as a single event can you say it's 56%

Many a time you say "on turn 2, the chance of gaining 2 turns is ..." while the turns are obviously separate.

Overall it's pretty poorly written, sorry. I think this should be rewritten before it's used as a guide to hax.
Hey, thanks a lot for taking the time to correct some of the work and sharing some valuable information about stats and wording. We'll adjust the wording as soon as we can and hopefully it'll be a more accurate reflection of what the guide is supposed to be. Hopefully you will still find some use for it in the meantime, as there is other information that is correct.

edit: this is what happens when liberal arts majors try to get cute and do stats
 
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#4
A lot of this is worded either weirdly or wrongly. I get what is written, but if you're explaining probability misconceptions you should be accurate.

Chance of 95% moves missing twice in a row, then thrice in a row: 0.25%, 0.125%

Should be 0.0125%


Chance of (10%/20%/..) secondary effects activating after two hits

Should be chance of 10%/20%/.. secondary effects activating after at most two hits. Activating after two hits is the same as activating after 1 hit.

Assuming you were not paralyzed on turn one, on turn two your chance is 56.25% to avoid full paralysis

Assuming you were not paralyzed on turn one, on turn two your chance is 75% to avoid full paralysis. This is literally the gambler's fallacy you were talking about lol.
Only if you do not assume you were not paralyzed on turn 1 and see the two turns as a single event can you say it's 56%

Many a time you say "on turn 2, the chance of gaining 2 turns is ..." while the turns are obviously separate.

Overall it's pretty poorly written, sorry. I think this should be rewritten before it's used as a guide to hax.

Chance of 95% moves missing twice in a row, then thrice in a row: chance of missing- 5% - the first and second time which is .05 * .05 which is 0.0025 which is .25%, 3 is .05^3 is 0.000125 which is 0.0125%

Assuming you were not paralyzed on turn one, on turn two your chance is 56.25% to avoid full paralysis : he is referring to bayes theorem iirc, which is basically saying what are your chances given this previous outcome and he is correct. If you want I can do the full ass math problem for you but here you go https://en.wikipedia.org/wiki/Bayes%27_theorem

You're wrong phew lol calm down it aint that serious
 
#5
Chance of (10%/20%/..) secondary effects activating after two hits

Should be chance of 10%/20%/.. secondary effects activating after at most two hits. Activating after two hits is the same as activating after 1 hit.
It should read something like "Chance of n% secondary effects activating at least once in two hits, at least once in three hits", since the probabilities listed include the secondary activating on both hits of two and two or three hits of three.

Assuming you were not paralyzed on turn one, on turn two your chance is 56.25% to avoid full paralysis : he is referring to bayes theorem iirc, which is basically saying what are your chances given this previous outcome and he is correct. If you want I can do the full ass math problem for you but here you go https://en.wikipedia.org/wiki/Bayes%27_theorem
Since the probability of full paralysis activating is, as far as I can tell (correct me if I'm wrong), independent of whether full paralysis activated on the prior turn or not, Bayes' Theorem isn't the best tool. It gives correct answers, but it just degenerates into simple probability:
Code:
Bayes' Theorem
P(A|B) = P(B|A)*P(A)/P(B)
where
P(A)   = probability of A occurring (marginal probability)
P(B)   = probability of B occurring (marginal probability)
P(A|B) = probability of A occurring if B occurs (conditional probability)
P(B|A) = probability of B occurring if A occurs (conditional probability)

Let
P(A) = probability of full paralysis occurring on turn 1
P(B) = probability of full paralysis occurring on turn 2

Since P(A) and P(B) are fully independent, P(B|A) = P(B) (conditional probability = marginal probability)

therefore P(A|B) = P(B)*P(A)/P(B) = P(A)
Given this, Knuckstrike is correct in that the original post is not worded very well. It should say something like:
If you are Paralyzed, your chance to avoid full paralysis each turn is 75%. Over two turns, your chance to avoid full paralysis on both turns is 56.25%, your chance of being fully paralyzed on only one turn is 37.5%, and your chance of being fully paralyzed on both turns is 6.25%. Over three turns, your chance of avoiding full paralysis on all three turns is 42.19%, your chance of being fully paralyzed on only one turn is 42.19%, your chance of being fully paralyzed on two turns is 14.06%, and your chance of being fully paralyzed on all three turns is 1.56%.
 

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