September 03, 2007 Archives

Mon Sep 3 09:18:29 CDT 2007

Blackjack - nesman64

I have a small interest in blackjack and the statistics involved with it. I worked in a casino long enough that I know better than to try and beat the house. On the other hand, if the dealer has to play to 17, you can win about 1/3 of your hands without drawing a card.

I know that it's been done before, and probably at length, but I want to investigate different strategies for blackjack. I'm working on the early stages of a blackjack program. It's still in pseudocode, but it's starting to look a lot more like a blackjack program and less like a Rube Goldberg blackjack machine.

A 2 3 4 5 6 7 8 9 T J Q K
When I started with it November 11, 2005, I had plans of making a 2 dimensional array [4x13] and randomly choosing from it for each draw. After a card was chosen, it's value in the array would change to tell the program not to choose it again. This created two problems.
  1. Broken odds
  2. Inefficient card selection

Broken odds
The first problem with this method is that the only draw with correct odds would be the first with 1/52. Using the array method, lets pretend we're choosing suit then rank. Each draw, you get a 25% chance of getting a heart. Still pretending, lets say you get 7 hearts out of the first 12 cards. Your odds of getting a heart in the next draw should be 6/40 (15%), but using the array method, you'll always get a chance at a heart 1/4 of the time. This happens on a smaller scale when you draw rank first. With my plans of running this hundreds of times to check the odds on different strategies, even a small variance will kill it.

Inefficient card selection
Also related to my wish to run this at length unattended, I needed to clean up the card selection. Your first card is always valid, but each card(x)after that, has an x/52 chance of being invalid. Invalid cards must be redrawn. Simply choosing the next higher card doesn't seem like a problem at first, but it greatly adds to the problem with skewed odds. When you're halfway through the deck, you average 2 cards per 3 draws. When you're down to the last few cards, you could easily draw 20 invalid cards before getting one you can count. I don't know how many attempted draws it would average to get through a deck, but it would easily be 500, I think.

As of November 20 or so, I "shuffle" the deck with a kind of random bubble sort. I made a system that uses a natural model to shuffle. I start with a single dimension array 52 elements long (I might skip this step in the future) and filter the values into 2 smaller arrays. Then, (and I'm still working on cleaning up the end of this) I sort the 2 smaller arrays back into the longer one, starting at the top and randomly deciding which of the smaller arrays contribute a card to the large one. I've heard that with a real deck, after the seventh shuffle the cards achieve optimal randomness. Any shuffling after the seventh is unneeded. I may adjust this after I get a working model coded and can see where the cards end up.

This next part isn't pretty, but it's my current note file. Reading it now, I don't understand what I meant by some of it.

arr deck(1-52)  0-51 really (don't forget to adjust card,suit
card = deck[x] %13 1=A, 11=J, 12=Q, 13=K
suit = deck[x] %4 1=C, 2=D, 3=H, 4=S
shuffle deck: rnd_bubbly_sort(deck[])*a bunch of times;
draw = read deck[x]; x++ draw from the top of the deck

How many decks?
Starting bet? (0 -> How many hands?)
Increase ?X

if bet
	(record ending cash / number of turns)
	(number of wins / number of turns)

Store card names seperate from values? so J=Q=K=10
Maybe figure card for display then mangle value for score

Updates on Blackjack (page 2). Turns out that the finished product will have almost nothing from the first version :)

Posted by Nesman | Permanent Link | Categories: blackjack, linux