TLDR: If you're using Sucker Punch in a 1v1 last mon scenario, your best strategy is to calculate 1/(1+Sucker PP), generate a random number from 0 to 1, and use your non-sucker attack if the number is lower. For example, you should use your non-sucker attack 1/9 of the time if you have 8 Sucker Punch PP on that turn.
If you're playing against Sucker Punch in this scenario, nothing you do matters, so the best strategy to increase your odds is to get your opponent to waste as many Sucker Punches as possible before it comes to that point.
Note: Everything here assumes that the non-sucker punch player does not have moves like Encore, Disable, or Substitute, which significantly increase the odds of them winning.
Why there is no way to outplay Sucker Punch
By bbg
burninator0 and I started arguing on Showdown this morning about the probability of winning a last-mon Sucker Punch mindgame and we ended up finding some very surprising results. Most notably, there is nothing the player facing Sucker Punch can do to have better odds of winning a Sucker Punch mindgame in a 1v1 scenario.
This is not just true statistically but also in practice. The only thing that affects the probability of either player winning is the strategy being used by the Sucker Punch player, and we've found the optimal strategy as well. It turns out that, if the Sucker Punch player is following the optimal strategy and has all 8 PP remaining, the probability of winning is 8/9 for the Sucker Punch player. There is nothing the non-Sucker Punch player can do to affect these odds.
We started off by thinking about the probabilities in the case where both players choose their moves randomly. There is a 50% chance that
uses Sucker Punch or Kowtow Cleave and a 50% chance that 
uses Calm Mind or Aura Sphere. There are 4 possibilities:
- 25% of the time, suckers and uses Aura Sphere, so wins.
- 25% of the time, uses Kowtow Cleave and uses CM, so wins.
- 25% of the time, uses Kowtow Cleave and uses Aura Sphere, so wins.
- 25% of the time, suckers and uses CM, so the mindgame continues and loses 1 pp.
Every turn, there is a 50% chance that wins and a 25% chance that wins. There is also a 25% chance that the mindgame continues. So, before anything happens, 's chance of winning on turn T of the 1v1 situation is (.25)^T. Adding up these values from T=1 to 8 shows that 's chance of winning approaches 1/3. Another way to think about this is that, on every turn that the game ends, Latios will win 1/3 of the time, and the only other scenario brings up that same scenario again, except for the small chance that Kingambit uses all 8 of its pp and Latios is guaranteed the win.
burninator then theorized that both players' optimal strategy is to attack (not sucker) 1/(1+remaining pp) of the time. Their intuition turned out to be almost exactly right. Burninator proved this calculating out the probability of winning each turn with this strategy and considering the situation to be in a Nash Equilibrium, which is a concept I don't completely understand. All they had to do then was show that the next-closest strategies resulted in worse odds for the player, which they did by instead having use Sucker Punch 1/pp and 1/(2+remaining pp) of the time.
At the same time, I was coding a tiny simulation for this situation which allowed me to adjust the number of remaining PP and the likelihood of each player attacking on a given turn. I ran 100 million trials for a bunch of different likelihoods using this function:
I confirmed the same thing that burninator had observed--Kingambit should calculate 1/(1+remaining pp) every turn and choose to attack with something other than Sucker Punch that much of the time. For example, if I have 6 Sucker Punch PP left, I should use Kowtow Cleave 1/7 of the time.
The most interesting part of this is that I widely varied the likelihood that the non-sucker punch player attacks with a move that OHKOes Kingambit (i.e. uses Aura Sphere). wins just as often if it always attacks turn 1, if it does not attack until has used up all of its Sucker Punch PP, if it attacks 50% of the time every turn, if it uses the same strategy as based on the opponent's Sucker Punch PP, or if it uses the slight variants of that strategy that we showed to be worse for the user. No matter what, Latios wins only 1/9 of the time.
Kingambit's optimal strategy does not change no matter how much PP it has. However, its winrate does decrease according to the number of PP it starts with. If Kingambit has only 3 Sucker Punch PP, it will win 3/4 of the time from the beginning of the scenario. More generally, Kingambit wins PP/(1+PP) of the time, and Latios wins 1/(1+PP) of the time.
burninator and I also ran this scenario in a 1v1 Custom Game 31 times before we got bored, with them using this strategy on and me choosing between my two options according to "intuition." They won 27/31 games. I'm personally more convinced by the numbers from the 100 million trials.
Thanks for reading and thanks again to burninator0.
If you're playing against Sucker Punch in this scenario, nothing you do matters, so the best strategy to increase your odds is to get your opponent to waste as many Sucker Punches as possible before it comes to that point.
Note: Everything here assumes that the non-sucker punch player does not have moves like Encore, Disable, or Substitute, which significantly increase the odds of them winning.
Why there is no way to outplay Sucker Punch
By bbg
burninator0 and I started arguing on Showdown this morning about the probability of winning a last-mon Sucker Punch mindgame and we ended up finding some very surprising results. Most notably, there is nothing the player facing Sucker Punch can do to have better odds of winning a Sucker Punch mindgame in a 1v1 scenario.
This is not just true statistically but also in practice. The only thing that affects the probability of either player winning is the strategy being used by the Sucker Punch player, and we've found the optimal strategy as well. It turns out that, if the Sucker Punch player is following the optimal strategy and has all 8 PP remaining, the probability of winning is 8/9 for the Sucker Punch player. There is nothing the non-Sucker Punch player can do to affect these odds.
We started off by thinking about the probabilities in the case where both players choose their moves randomly. There is a 50% chance that
uses Sucker Punch or Kowtow Cleave and a 50% chance that uses Calm Mind or Aura Sphere. There are 4 possibilities:- 25% of the time,
suckers and uses Aura Sphere, so wins.- 25% of the time,
uses Kowtow Cleave and uses CM, so wins.- 25% of the time,
uses Kowtow Cleave and uses Aura Sphere, so wins.- 25% of the time,
suckers and uses CM, so the mindgame continues and loses 1 pp.Every turn, there is a 50% chance that
wins and a 25% chance that wins. There is also a 25% chance that the mindgame continues. So, before anything happens, 's chance of winning on turn T of the 1v1 situation is (.25)^T. Adding up these values from T=1 to 8 shows that 's chance of winning approaches 1/3. Another way to think about this is that, on every turn that the game ends, Latios will win 1/3 of the time, and the only other scenario brings up that same scenario again, except for the small chance that Kingambit uses all 8 of its pp and Latios is guaranteed the win.burninator then theorized that both players' optimal strategy is to attack (not sucker) 1/(1+remaining pp) of the time. Their intuition turned out to be almost exactly right. Burninator proved this calculating out the probability of
winning each turn with this strategy and considering the situation to be in a Nash Equilibrium, which is a concept I don't completely understand. All they had to do then was show that the next-closest strategies resulted in worse odds for the player, which they did by instead having use Sucker Punch 1/pp and 1/(2+remaining pp) of the time.At the same time, I was coding a tiny simulation for this situation which allowed me to adjust the number of remaining PP and the likelihood of each player attacking on a given turn. I ran 100 million trials for a bunch of different likelihoods using this function:
Java:
public static boolean sucker(int pp) {
// returns true if I win as the non-Sucker Punch player
boolean they_suckered = false;
boolean i_attacked = false;
double opp_threshold = .5;
double my_threshold = .5;
while (pp > 0) {
// how often the opponent attacks (does not sucker)
opp_threshold = (double)1/(1+pp);
// how often i attack
// this doesn't seem to matter
my_threshold = (double)1/(1+pp);
double opp_choice = Math.random();
double my_choice = Math.random();
they_suckered = (opp_choice > opp_threshold);
i_attacked = (my_choice < my_threshold);
// i win if i attacked and they didn't sucker
if (i_attacked && !they_suckered) return true;
// mindgame keeps going if they suckered and i didn't attack, and they lose 1 pp
pp--;
if (!i_attacked && they_suckered) continue;
// i lose in the two other scenarios
return false;
}
// they're out of sucker pp so i win
return true;
}I confirmed the same thing that burninator had observed--Kingambit should calculate 1/(1+remaining pp) every turn and choose to attack with something other than Sucker Punch that much of the time. For example, if I have 6 Sucker Punch PP left, I should use Kowtow Cleave 1/7 of the time.
The most interesting part of this is that I widely varied the likelihood that the non-sucker punch player attacks with a move that OHKOes Kingambit (i.e.
uses Aura Sphere). wins just as often if it always attacks turn 1, if it does not attack until has used up all of its Sucker Punch PP, if it attacks 50% of the time every turn, if it uses the same strategy as based on the opponent's Sucker Punch PP, or if it uses the slight variants of that strategy that we showed to be worse for the user. No matter what, Latios wins only 1/9 of the time.Kingambit's optimal strategy does not change no matter how much PP it has. However, its winrate does decrease according to the number of PP it starts with. If Kingambit has only 3 Sucker Punch PP, it will win 3/4 of the time from the beginning of the scenario. More generally, Kingambit wins PP/(1+PP) of the time, and Latios wins 1/(1+PP) of the time.
burninator and I also ran this scenario in a 1v1 Custom Game 31 times before we got bored, with them using this strategy on
and me choosing between my two options according to "intuition." They won 27/31 games. I'm personally more convinced by the numbers from the 100 million trials.Thanks for reading and thanks again to burninator0.
