Work the Shell - Coping with Aces

Somehow, writing this Blackjack game is starting to feel like the programmatic equivalent of that Three Stooges skit where “slowly he turned, step by step...”, but we're still going to have to work on the core logic of the game before we're ready to write the fun interface elements.

This month, in fact, we might well find that we have to tear some of the earlier script apart and rebuild it to compensate for a troubling aspect of the game of Blackjack: an Ace can be either high or low, which is to say that it can be worth one or 11 points. Dealt two aces, you then have a number of different possible values, and that's a problem.

It turns out that there's a sneaky way you can solve this problem simply by maximizing the value of the first Ace encountered, as long as the overall value of the hand doesn't exceed our cap of 21 points. So, two Aces would be worth 11 + 1 automatically (the first is maximized, but the second is not because it would push us over 21 points).

The portion of the code that must be rewritten to compensate for this Ace valuation strategy is the handValue function:

function handValue
{
   # feed this as many cards as are in the hand
   handvalue=0  # initialize
   for cardvalue
   do
     rankvalue=$(( $cardvalue % 13 ))
     case $rankvalue in
       0|11|12 ) rankvalue=10   ;;
       1       ) rankvalue=11   ;;
     esac

     handvalue=$(( $handvalue + $rankvalue ))
    done
}

This is the “before” picture from last month. Notice that the second line in the case statement currently assigns a rank value of 11 to every Ace encountered. Clearly that's a bug!

To change it, however, I need to add a new variable that keeps track of whether I've already seen a previous Ace in the hand. I ingeniously call that seenAce:

function handValue
{
   # feed this as many cards as are in the hand
   handvalue=0  # initialize
   seenAce=0
   for cardvalue
   do
     rankvalue=$(( $cardvalue % 13 ))
     case $rankvalue in
       0|11|12 ) rankvalue=10   ;;
       1       ) if [ $seenAce -eq 1 ] ; then
           rankvalue=1
         else
            rankvalue=11 ; seenAce=1
         fi ;;
     esac

     handvalue=$(( $handvalue + $rankvalue ))
    done
}

Looks like it'll do the job—or will it?

The problem here is best illustrated with a hand like 9 + 10 + A. That's a valid Blackjack hand and should be worth 20 points. But handValue will score it as 30 points, and the program will incorrectly classify that hand as a bust.

Solving this isn't too hard once the problem is recognized, but that's the great challenge of writing any code, isn't it? To anticipate and characterize bugs and glitches properly. The solution is often quite simple, but knowing there's a bug in the first place, ah, that's where the great programmers find their calling!

The solution in this situation is that we need to deduct ten points from the hand score if it's more than 21 points and there's an Ace—a condition that turns out to be added easily to the tail end of the function:

     handvalue=$(( $handvalue + $rankvalue ))
    done

    if [ $handvalue -gt 21 -a $seenAce -eq 1 ] ; then
        handvalue=$(( $handvalue - 10 ))
    fi
}

This is the first time I've used a complex conditional statement in our script, but you're already familiar with this type of multi-expression conditional. If we were using a C-like language, the conditional might look like:

if ( ( handvalue > 21 ) && (seenAce == 1))

The snippet in the shell script shown above is the equivalent conditional, with the -a serving as the logical AND statement. It wouldn't work in this context, but -o is the logical OR statement in a shell test conditional too, and if you need to, you can use parentheses for grouping.

To test our new code, I'm going to replace the main body of the program temporarily with a few preloaded test hands and see what kind of hand values are returned:

echo "Starting out with two aces..."
handValue 1 14
echo "handvalue = $handvalue"

echo "now testing 9 + 10 + A"
handValue 9 10 1
echo "handvalue = $handvalue"

echo "and, for good luck, testing K + A"
handValue 12 1
echo "handvalue = $handvalue"

First, I'll run this with the original handValue function, anticipating mistakes:

Starting out with two aces...
handvalue = 22
now testing 9 + 10 + A
handvalue = 30
and, for good luck, testing K + A
handvalue = 21

Yup. That's not good. We'd be quickly run out of Vegas for that sort of counting.

Now, I'll slip in the new seenAce code segments explained earlier and try this same set of test hands:

Starting out with two aces...
handvalue = 12
now testing 9 + 10 + A
handvalue = 20
and, for good luck, testing K + A
handvalue = 21

What do you know, it looks like we've come up with a savvy way to allow the Ace to have two possible values without a major rewrite of the code.