I read and re-read the solutions here on the 'short spin', and knowing the positions of numbers on the wheel, but it wasn't working for me. I find a simple do or die strategy is most effective. Just keep spinning regardless of what you've got left on the board. As an example, I hit the most common numbers first off yet still ended up clearing the wheel by hitting just one of two open spots against eighteen skulls.
Should you hit a skull, use your Xbox controller's guide button to pause the game and then choose 'Start Over'. Of course, you won't turn a profit in tickets this way, but you increase your chances of clearing out the wheel in a shorter time. It is, after all, just a game of chance. Sooner or later your luck will prevail.
However, if you're playing the cautious game and wish to bank some extra tickets for buying prizes at the same time, you need to play the odds more selectively.
For this scenario add up the number of skulls you have on the board, remembering to add one more to the total (as the wheel starts with one skull already in place). You can then weigh up whether to spin again, or cut and run.
A good rule of thumb is to spin again for any odds that are 50/50, or even 60/40 in the Barkers favour. As with the 'do or die' strategy, remember to use the guide button on your controller to quickly restart after any loss to maximise your gains.
Good luck! (You'll need it!)