Probabilities of Hax

[peregrine monkey]

Before you read any further, these are NOT my calculations. I got them from Smogon.

Anyone who's played been on Shoddy, or even played competitive Pokemon knows that people hate hax. It can be incredibly frustrating when you're about to win a match and the opponent's Scizor gets a Bullet Punch crit and sweeps the rest of your team. But I came across some intriguing calculations on the Smogon forums.

Chance of a critical hit occurring with N attacks
1 attack(s)............0.0625
2 attack(s)............0.12109375
3 attack(s)............0.176025390625
4 attack(s)............0.2275238037109375
5 attack(s)............0.2758035659790039
6 attack(s)............0.32106584310531616
7 attack(s)............0.3634992279112339
8 attack(s)............0.4032805261667818
9 attack(s)............0.4405754932813579
10 attack(s)...........0.47553952495127305
11 attack(s)...........0.5083183046418185
12 attack(s)...........0.5390484106017048
13 attack(s)...........0.5678578849390983
14 attack(s)...........0.5948667671304047
15 attack(s)...........0.6201875941847543
16 attack(s)...........0.6439258695482072

This by itself is not that remarkable. It basically means that it is fairly likely to get a crit after 12 or so attacks. But if you look at these:

Chance of a critical hit OR a 10% effect occurring with N attacks
1 attack(s)............0.15625
2 attack(s)............0.2880859375
3 attack(s)............0.399322509765625
4 attack(s)............0.4931783676147461
5 attack(s)............0.572369247674942
6 attack(s)............0.6391865527257323
7 attack(s)............0.6955636538623367
8 attack(s)............0.7431318329463465
9 attack(s)............0.7832674840484799
10 attack(s)...........0.8171319396659049
11 attack(s)...........0.8457050740931072
12 attack(s)...........0.8698136562660592
13 attack(s)...........0.8901552724744874
14 attack(s)...........0.9073185111503488
15 attack(s)...........0.9217999937831068
16 attack(s)...........0.9340187447544964

It shows that after five attacks, it is likely for a 10% secondary effect attack to crit OR trigger its secondary effect. And that's only a 10%.

Chance of a critical hit OR a 20% effect with N attacks
1 attack(s)............0.25
2 attack(s)............0.4375
3 attack(s)............0.578125
4 attack(s)............0.68359375
5 attack(s)............0.7626953125
6 attack(s)............0.822021484375
7 attack(s)............0.86651611328125
8 attack(s)............0.8998870849609375
9 attack(s)............0.9249153137207031
10 attack(s)...........0.9436864852905273
11 attack(s)...........0.9577648639678955
12 attack(s)...........0.9683236479759216

and

Chance of a critical hit OR a 30% effect with N attacks
1 attack(s)............0.34375
2 attack(s)............0.5693359375
3 attack(s)............0.717376708984375
4 attack(s)............0.8145284652709961
5 attack(s)............0.8782843053340912
6 attack(s)............0.9201240753754973
7 attack(s)............0.9475814244651701
8 attack(s)............0.9656003098052679
9 attack(s)............0.9774252033097071


This shows that a crit or secondary effect with a 20% or 30% chance to occur will be almost certain to occur after seven and five attacks respectively. This means that Gyarados' Waterfall has a 68% chance of critting or flinching after four turns. That's more than hypnosis' accuracy. Even more startling, Zapdos' Discharge has a 71% chance of critting or paralyzing after only three turns. As Zapdos is meant to be a tank in most cases, this is not very much time at all.

But wait! There's more:

Chance of a 70% accuracy attack hitting N times consecutively.
1 attack(s)............0.7
2 attack(s)............0.49
3 attack(s)............0.343
4 attack(s)............0.2401
5 attack(s)............0.16807
6 attack(s)............0.117649
7 attack(s)............0.0823543
8 attack(s)............0.05764801

So "miss hax" with a move like focus blast is not really hax at all. After three attacks, your chance of hitting is very low.

So next time someone curses at you for paralyzing their Pokemon with Discharge, alert them to this information. They probably won't listen, being the lowlifes that they are, but you'll feel all warm and fuzzy inside for doing a good deed.

 

[Greenstreet]

Even more startling, Zapdos' Discharge has a 71% chance of critting or paralyzing after only three turns. As Zapdos is meant to be a tank in most cases, this is not very much time at all.

I love statistics.

 

[Pink Reaper]

This shows that a crit or secondary effect with a 20% or 30% chance to occur will be almost certain to occur after seven and five attacks respectively. This means that Gyarados' Waterfall has a 68% chance of critting or flinching after four turns. That's more than hypnosis' accuracy. Even more startling, Zapdos' Discharge has a 71% chance of critting or paralyzing after only three turns. As Zapdos is meant to be a tank in most cases, this is not very much time at all.

This needs to be clarified, there's technically only a 68% probability that Waterfall would crit/flinch on the fourth move. Assuming static chance there's only a 20% chance of an actual flinch and a 6.25% chance of crit on the fourth move, because pokemon doesn't(Or rather shouldn't) have variable returns. Probability Vs. Chance basically equates to what is expected to happen vs what will happen. After 3 attacks with no flinch/crit you would EXPECT one from the fourth or fifth move but without variable returns there's still only a 20% chance per move.

So what im basically saying is, haxkiss is gay.

 

[Da-D-Mon-109]

:flame:
So, it might be more effective in battle to go with moves with chances off effect and extra attributes than to just use pure power, right?
:flame:

 

[ss118]

pretty much. That's why spamming CB Waterfalls with Gyarados works sometimes.

 

[0RLY]

This needs to be clarified, there's technically only a 68% probability that Waterfall would crit/flinch on the fourth move. Assuming static chance there's only a 20% chance of an actual flinch and a 6.25% chance of crit on the fourth move, because pokemon doesn't(Or rather shouldn't) have variable returns. Probability Vs. Chance basically equates to what is expected to happen vs what will happen. After 3 attacks with no flinch/crit you would EXPECT one from the fourth or fifth move but without variable returns there's still only a 20% chance per move.

So what im basically saying is, haxkiss is gay.

I concur.

So... uh, I'm gonna pretend to not be smart for a second and ask: how did we get 68% from all those absurdly long decimals? Besides, I don't think any of this will really come into place because really, when is Gyarados really going to use Waterfall 4x in a row unless it's a 1v1 against Hippowdon or something. Also, Aqua Tail is the shizzle.

 

[peregrine monkey]

I concur.

So... uh, I'm gonna pretend to not be smart for a second and ask: how did we get 68% from all those absurdly long decimals? Besides, I don't think any of this will really come into place because really, when is Gyarados really going to use Waterfall 4x in a row unless it's a 1v1 against Hippowdon or something. Also, Aqua Tail is the shizzle.

Chance of a critical hit OR a 20% effect with N attacks
4 attack(s)............0.68359375

Rounded is 68%.

Also, Gyarados might use Waterfall 4 times in a row if it's sweeping a team. The flinch or crit might kill something sent out to revenge you.

Edit: Aqua Tail is not the shizzle, sir, it sacrifices accuracy and a secondary effect for power.
Doubledit: Ignore the above statement, it merely proves I know nothing about slang.

 

[WouW]

Edit: Aqua Tail is not the shizzle, sir, it sacrifices accuracy and a secondary effect for power.

Lol self-contradiction.

waterfall is for *****es. like kingdra.

you wouldn't want to be a ***** would you?

More accurate statements ftw

 

[ungulateman]

Would you like to have a DD Gyarados sweep ended because Aqua Tail missed?

Would you like to flinch your opponent's counter for Gyarados and successfully sweep because of Waterfall?

 

[WouW]

Would you like to have a DD Gyarados sweep ended because Aqua Tail missed?

Would you like to flinch your opponent's counter for Gyarados and successfully sweep because of Waterfall?

Would you like to miss an OHKO because Waterfall didn't cut it?

Would you like to rely on hax to work instead of fail?

Also, I don't see how these calcs were made anyway. First there is 0.625 chance to crit, but with a 10% effect it changed to 0.5625. And to 0.5 with 20% moves.
Plus, I second what Reaper said - there's a 50% probability to crit with your 11th attack, but there's still only a 6,25% chance - plus, 50% is still far from guaranteed.

 

[DonkeyKongUh]

The calculations are saying that after these amount of turns it shows the odds of getting a crit or secondary effect ONCE in those amount of turns. So if you look at the gyarados waterfall, if you do it 4 times there's a 68% chance 1 of those waterfalls was a crit or flinch. The actually probably of the attack criting of flinching each time remains the same.

 

[WouW]

The calculations are saying that after these amount of turns it shows the odds of getting a crit or secondary effect ONCE in those amount of turns. So if you look at the gyarados waterfall, if you do it 4 times there's a 68% chance 1 of those waterfalls was a crit or flinch. The actually probably of the attack criting of flinching each time remains the same.

 

[peregrine monkey]

It's love how everyone's just reiterating what Reaper said.

Also, thanks Reaper for clarifying that point on probability.