After spending a lot of time with the accelerometer sample code in Arduino and mapping my movements to a CSV, I wrote some code to handle the RPS when the arm is moved in the normal "throwing chops" motion.

#include <Wire.h>
#include <Adafruit_MMA8451.h>
#include <Adafruit_Sensor.h>

#define TIMEUPDOWN  150
#define TIMEBETWEEN 800
#define THRESHDOWN  -8000
#define THRESHUP    8000

Adafruit_MMA8451 mma = Adafruit_MMA8451();
int fistPumpCount = 0;
int lastUp = 0;
int lastDown = 0;

void setup(void) {
  Serial.begin(9600);
  
  Serial.println("Let's throw chops!");
  
  if (! mma.begin()) {
    //Serial.println("Couldnt start");
    while (1);
  }
  //Serial.println("MMA8451 found!");
  
  mma.setRange(MMA8451_RANGE_2_G);
  
}

void loop() {
  unsigned long timeStamp = millis();  

  mma.read();
  int fistPump = mma.y;

  if(fistPump > THRESHUP) {
    
    int timeDiff = timeStamp - lastUp;
    if( timeDiff > TIMEUPDOWN ) {
      lastUp = timeStamp;
      if( timeDiff < TIMEBETWEEN ) {
        fistPumpCount++;
      } else {
        fistPumpCount = 1;
      }
      Serial.print("Pump Up: ");
      Serial.print(fistPumpCount);
      Serial.println();
    }
  }

  if(fistPumpCount == 3) {
    randomSeed(timeStamp);
    int roshambo = random(1,4); // Stupid exclusive bit
    switch(roshambo) {
      case 1:
        Serial.println("Rock");
        break;
      case 2:
        Serial.println("Paper");
        break;
      case 3:
        Serial.println("Scissors");
        break;
    }
    fistPumpCount = 0;
  }
}