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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.

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  • $\begingroup$ The best strategy is already described in the link you posted $\endgroup$ – Repmat Sep 15 '17 at 17:40
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    $\begingroup$ Yeah, I didn't realize that placing the x's in a vertical column was not allowed. Too bad, though. Makes the game strategy pretty trivial! $\endgroup$ – AS3Noob Sep 15 '17 at 17:44
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In your link explaining the rules of the game it says:

To win a prize, the contestant must get three Xs in a row horizontally or diagonally.

So completing a column would not guarantee a win. In fact it would guarantee not winning.

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  • $\begingroup$ In particular, "contestants are not allowed to place all three of their Xs on the same side of the board to create a vertical row (although this is no longer explicitly stated)". $\endgroup$ – Kodiologist Sep 15 '17 at 16:44
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Ok, I did some more thinking and I think both strategies if possible to be enacted would result in the same overall odds!

Strategy 1: go for 3 corners

25% that 2 bonus x's are secured: 2/3 chance to win 50% that 1 bonus x is secured: 1/3 chance to win 25% that no bonus x is secured: 0 chance to win

Overall game chance to win using this strategy is 1/3

Strategy 2: go for vertical column

25% that 2 bonus x's are secured: 3/3 chance to win 25% that 1st bonus x is secured and placed in same column as original x, but 2nd bonus x is missed: 0 chance to win 25% that 1st bonus x is missed, but 2nd x is secured and placed in opposite column corner from original x: 1/3 chance to win 25% that no bonus x is secured: 0 chance to win

Overall game chance to win using this strategy is 1/3

I guess the original strategy makes for better tv :-)

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