Strange Coincidence
Lottery Winner
What would TV viewers think if the lottery lady announced that the numbers drawn from a bucket with 49 balls were 1, 2, 3, 4, 5, and 6? Since the probability of getting all six numbers right is about 1:14 million and there are 44 combinations of consecutive lottery number combinations (1, 2, 3, 4, 5, 6 through 44, 45, 46, 47, 48, 49), the chance of a straight in the lottery is about 1:318,000 – this means that the incredible event would occur relatively quickly with a fast draw generator.
Listing 4 shows an automatic drawing machine in the lotto_draw()
function. From 49 numbered balls in the numbers
list, it draws six random numbers and then removes them to prevent double draws. Since it takes a significant amount of compute time to remove an element from a Python list and move up the remaining elements to close the gap, the function swaps the value of the selected element with the last element in the list and reduces the list length size by one – much faster!
Listing 4
lotto
01 #!/usr/bin/env python3 02 import random 03 04 def lotto_draw(): 05 total = 49 06 draws = 6 07 numbers = list(range(1,total+1)) 08 size = total 09 result = [] 10 11 for _ in range(draws): 12 idx = random.randrange(size) 13 result.append(numbers[idx]) 14 numbers[idx] = numbers[size-1] 15 size -= 1 16 17 return sorted(result) 18 19 def is_consecutive(draw): 20 prev = "" 21 for number in draw: 22 if prev < 0: 23 prev=number 24 elif prev + 1 == number: 25 prev = number 26 else: 27 return False 28 return True 29 30 count = 0 31 while True: 32 count += 1 33 draw=lotto_draw() 34 if is_consecutive(draw): 35 print("%d: %s" % (count, str(draw))) 36 break
Following this algorithm, lotto_draw()
returns a sorted list of six randomly selected balls. The main program starting in line 30 uses is_consecutive()
to check whether the drawn numbers each differ only by one from their predecessor. If this is the case, line 35 prints the number of draws in count
and the lucky numbers that led to the termination. Figure 3 shows that this sometimes occurs after 30,000 passes; sometimes, however, it takes more than 800,000 – purely random, but within the calculated probability.
Python Tricks [3] by Dan Bader is recommended for implementing this and other cool Python tricks. It shows a multitude of everyday programming tasks with elegant Python solutions. It is perfectly suited for users of other programming languages (like Perl!) who are mainly interested in converting typical idioms into clean Python and don't want to start with Adam and Eve and "Hello World."
Infos
- Malkiel, Burton G. A Random Walk down Wall Street. Norton & Company, 2016: https://www.amazon.com/Random-Walk-Down-Wall-Street-ebook/dp/B00QH9NTSI
- Listings for this article: ftp://ftp.linux-magazine.com/pub/listings/linux-magazine.com/212/
- Bader, Dan. Python Tricks. Dan Bader, 2017: https://dbader.org/products/python-tricks-book/
« Previous 1 2 3
Buy this article as PDF
(incl. VAT)
Buy Linux Magazine
Subscribe to our Linux Newsletters
Find Linux and Open Source Jobs
Subscribe to our ADMIN Newsletters
Support Our Work
Linux Magazine content is made possible with support from readers like you. Please consider contributing when you’ve found an article to be beneficial.
News
-
Canonical Releases Ubuntu 24.04
After a brief pause because of the XZ vulnerability, Ubuntu 24.04 is now available for install.
-
Linux Servers Targeted by Akira Ransomware
A group of bad actors who have already extorted $42 million have their sights set on the Linux platform.
-
TUXEDO Computers Unveils Linux Laptop Featuring AMD Ryzen CPU
This latest release is the first laptop to include the new CPU from Ryzen and Linux preinstalled.
-
XZ Gets the All-Clear
The back door xz vulnerability has been officially reverted for Fedora 40 and versions 38 and 39 were never affected.
-
Canonical Collaborates with Qualcomm on New Venture
This new joint effort is geared toward bringing Ubuntu and Ubuntu Core to Qualcomm-powered devices.
-
Kodi 21.0 Open-Source Entertainment Hub Released
After a year of development, the award-winning Kodi cross-platform, media center software is now available with many new additions and improvements.
-
Linux Usage Increases in Two Key Areas
If market share is your thing, you'll be happy to know that Linux is on the rise in two areas that, if they keep climbing, could have serious meaning for Linux's future.
-
Vulnerability Discovered in xz Libraries
An urgent alert for Fedora 40 has been posted and users should pay attention.
-
Canonical Bumps LTS Support to 12 years
If you're worried that your Ubuntu LTS release won't be supported long enough to last, Canonical has a surprise for you in the form of 12 years of security coverage.
-
Fedora 40 Beta Released Soon
With the official release of Fedora 40 coming in April, it's almost time to download the beta and see what's new.