python - Binomial Model Implementation Trouble - American and European options come out equal

I'm Trying to implement the binomial option price model in python and get reasonable performance by using memoization. I checked the output against a black and scholes model and for European options it seems to be working. However, when try to price an American option, I get the same result as a European and I can't for the life of me figure out why. Can anyone help or point me in the right direction ? Thanks

import numpy as np
from functools import lru_cache
steps =40
riskFreeRate=0.215
stepSize = 1/36
@lru_cache(maxsize=1000000) # Memoize the result to reduce number of calls

def callOption(price,strike=100,sigma=0.1,american=False):
    u =np.exp(sigma*np.sqrt(stepSize)) #The factor by which price increases
    d =np.exp(-1*sigma*np.sqrt(stepSize)) # factor by which price descreases
    p =(np.exp(riskFreeRate*stepSize) -d) / (u-d) #Probability that price goes up
    @lru_cache(maxsize=steps**2)  # Per memoized callOption, memoize the value at a given step
    def atTime(step):
        exVal = np.max([price-strike,0]) # The excercise value at this time
        if step==steps:
            val =np.max([price-strike,0]) # if this is a terminal node 
        else:

            pd = np.round(price*d,3) # The new up price, 
            pu = np.round(price*u,3) # The new down price
            #Rounding the prices means we remeber fewer nodes with minimal affect on accuracy  

            down = callOption(price=pd,sigma=sigma,strike=strike,american=american)(step+1) # Get the value of the next node when price went down
            up = callOption(price=pu,sigma=sigma,strike=strike,american=american)(step+1) # Get the value of the next node when price went up
            discount = np.exp(-1*riskFreeRate*stepSize) # the discount rate
            val = (p*up+(1-p)*down)*discount # THis is the binomial value of the option at this node
            if american : 
                #If its an american option, the value is the greater of the binomial value or excercise value

                val = np.max([val,exVal]) 
        return val
    return atTime