This question is in regards to the Secret X game on Price is Right. It's basically tic-tac-toe, but without the O's. Please see the link below for more details on how the game is played.

<http://priceisright.wikia.com/wiki/Secret_%27X%27>

In all the times I've watched contestants play the Secret X game on the Price is Right game show, I've seen contestants attempt to place the original X plus the 2 bonus X's in 3 out of the 4 corners of the tic-tac-toe board in order to give themselves a 2/3 chance of winning the prize.

I am wondering why the contestants wouldn't just try to place the original plus the bonus X's through a whole column and guarantee themselves the prize assuming they win both of the bonus X's.

I can see that the strategy would get more complex if the contestant fails to secure the first bonus X, but does secure the 2nd bonus X. In that case, they could switch to the usual strategy and have 1/3 chance to win the prize.

I can also see that if they win the first bonus X and place it in the same column as the original X, they will lose the game if they don't win the 2nd bonus X as well since in that case there is no way to form a tic-tac-toe.

Could someone help me understand what would be the optimal game play strategy based on what the math says? Thanks! 

Edit: let's also assume 50% chance to secure each bonus X.