static NSDictionary* const letterValues = @{ ..... } in a method does not compile

You can only set a static variable during initialization with a constant. @{} creates an object, thus not a constant.

Do this instead:

- (void)awakeFromNib
{
    [super awakeFromNib];

    static NSDictionary* letterValues = nil;

    static dispatch_once_t onceToken;
    dispatch_once(&onceToken, ^{
        letterValues = @{
          @"A": @1,
          @"B": @4,
          @"C": @4,
          // ...
          @"X": @8,
          @"Y": @3,
          @"Z": @10,
          };
    });


    ...
}

Some other answers here suggest a check for nil instead of dispatch once, but that can cause issues when creating multiple tiles at the same time (via threads). dispatch_once implements the required locking.

You can use static, but the assignment can't be made on the same line. Try this:

- (void)awakeFromNib {
    [super awakeFromNib];

    static NSDictionary* letterValues = nil;
    if (!letterValues) {
        letterValues = @{@"A": @1,
                         @"B": @4,
                         @"C": @4,
                         // ...
                         @"X": @8,
                         @"Y": @3,
                         @"Z": @10};
    }
    ...
}

The reason is that the @{<key> : <value>} syntax is translated by the compiler into an Objective-C method ([[NSPlaceholderDictionary alloc] initWithObjects:forKeys:count:]), which cannot be resolved at compile-time.

NSDictionary objects can't be created at compile time. However, if you need a static object, you can create one. You can, for example, use the initialize method, like this:

static NSDictionary* letterValues;

+ (void)initialize
{
    if (self == [MyClass class]) {
        letterValues = @{
                         @"A": @1,
                         @"B": @4,
                         @"C": @4,
                         @"X": @8,
                         @"Y": @3,
                         @"Z": @10,
                         };
    }
}

The if statement is there to prevent multiple calls of your code in MyClass subclasses.