DtD Die Probabilifier | Python Fiddle

from bisect import bisect_left

def rl(array): return range(len(array))
def fastIndex(a, x):
    i = bisect_left(a, x)
    return i

class DtDTabulator():
    
    def __init__(this, x, y, explosion=10, reroll=0):
        this.x = int(x)
        this.y = int(y)
        this.kaboom = int(explosion)
        this.reroll = int(reroll)
        this.paths = 10-this.reroll
        this.activeRolls = [([(0, True)]*this.x,1.0)]
        this.probabilities = [0]*1000
        this.done = 0 #the largest value whose probability is finished being calculated
        
    def sumRoll(this, roll): return sum([die[0] for die in roll[-this.x:]])
        
        
    def iterate(this, log = False):
        
        '''roll all die that need to be rolled, splitting them off into all possibilities'''
        newRolls = []
        for roll in this.activeRolls:
            branchedRolls0 = [roll]
            for i in range(this.x):
              if roll[0][i][1]:
                branchedRolls1=[]
                for broll in branchedRolls0:
                  for d10 in range(this.reroll+1, 11):
                    branchedRolls1.append((broll[0][:], broll[1]/this.paths))
                    branchedRolls1[-1][0][i] = (broll[0][i][0]+d10, d10 >= this.kaboom)
                branchedRolls0 = branchedRolls1
            newRolls.extend(branchedRolls0)
        print 'Rolled %i rolls, resulting in %i new rolls.'%(len(this.activeRolls), (len(newRolls)))
        
        '''move all rolls that still need to be rolled into active rolls, and tabulate those that have stopped exploding'''
        this.activeRolls = []
        for roll in newRolls:
            roll[0].sort(key=lambda die: die[0])
            isActive = False
            for die in roll[0]: isActive = isActive or die[1]
            if isActive: this.activeRolls.append(roll)
            else:
                this.probabilities[this.sumRoll(roll[0])] += roll[1]
        print 'Determined that %i of those rolls are still exploding.'%len(this.activeRolls)
                
        '''consolidate identical rolls and calculate the new this.done'''
        rollRef = []
        probRef = []
        for roll in this.activeRolls:
            i = fastIndex(rollRef, roll[0])
            if i<len(rollRef) and rollRef[i] == roll[0]:
                probRef[i] += roll[1]
            else:
                rollRef.insert(i, roll[0])
                probRef.insert(i, roll[1])
        this.activeRolls = [(rollRef[i], probRef[i]) for i in rl(rollRef)]
        this.done = min([this.sumRoll(roll) for roll in rollRef])
        print 'Consolidated that number into %i unique rolls, with probabilities now calculated up to %i.'%(len(this.activeRolls), this.done)

x = DtDTabulator(5,4)
x.iterate(log=True)
x.iterate(log=True)

Python Fiddle

Python Cloud IDE