[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums

Probability of hitting a checker from a long running start

Posted By: ah_clem
Date: Tuesday, 8 July 2025, at 1:35 p.m.

In Response To: Probability of hitting a checker from a long running start (rambiz)


Yes, thanks for the corrections. It now converges to .387755102040816238 in about 300 iterations which is the same value that Bob posted. Here's the output for the first 24 iterations: 

 

 

1 0.3055555555555556 

2 0.3333333333333333 

3 0.3888888888888889 

4 0.433641975308642 

5 0.46064814814814814 

6 0.5555555555555556 

7 0.2941529492455418 

8 0.3595679012345679 

9 0.39752657750342935 

10 0.3903987578113092 

11 0.39325417238225885 

12 0.4455006382411218 

13 0.3808167395933886 

14 0.37082682390895694 

15 0.39584246240410503 

16 0.39051131293266794 

17 0.37425113504779933 

18 0.39742751753016803 

19 0.3714784662583534 

20 0.40114428387815315 

21 0.38069741326472967 

22 0.3806539554810836 

23 0.3760543563411474 

24 0.404552291102044 

 

and the modified code: 

def prob(length): 

    hit = [0,11,12,14,15,15,17,6,6,5,3,2,3] #number of shots from n away 

    hit.extend([0,0,1,1,0,1,0,1,0,0,0,1]) 

    short = [0,0,0,2,3,4,4,6,5,4,2,2,1] #number of ways to roll exactly n 

    short.extend([0,0,0,1,0,0,0,1,0,0,0,1]) 

    p=[0] # p[n] is the probability of hitting from n pips away 

    for n in range(length +1): 

        if n == 0: 

            continue 

        if  n <= 24: #possibly a shot this roll 

            p.append(hit[n]/36) 

        else: 

            p.append(0) #no possibility of a shot this roll 

        for i in range(n):  

            #add the probabilities of all the rolls that are short of the blot 

            if i == 0: 

                continue 

            if n-i > 0 and n-i < len(short): 

                p[n] = p[n] + short[n-i]*p[i]/36 

    for n in range(length +1): 

      print(f'{n} {p[n]}') 

     

prob(350)

Messages In This Thread

 

Post Response
Your Name:
Your E-Mail Address:
Subject:
Message:

If necessary, enter your password below:

Password:
 

 

[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums is maintained by Stick with WebBBS 5.12.