On the Hollywood Squares, I wondered again yesterday what is actually the better strategy since you can lose a game on a wrong answer.

1) Trying to block and risk giving your opponent a win, or

2) Or try a square that if you get it right sets you up for a win when the opponent picks the square and gets it wrong.

This was something I was thinking of while watching the show as well. And, based on my rudimentary thoughts and computations, it seems better to try and block. Here's a scenario to illustrate:

Number the boxes on the board from 1 through 9, with 1 being the top left and 9 being the bottom right. Assume, by way of argument, that X controls boxes 4 and 5, and O controls box 1. Further, we assume that, for each question, the player has a 50% of getting it right, and each correct answer is independent of all others.

O really has two logical moves here: (1) go for box 6 and the block, or (2) go for box 3 to try and set up for a win.

Notice that, in either case, X has a 50% chance of the win with box 6, either on his own, or with a miss from O. So, let's see what happens to O in each case:

(1) O has a 50% chance of a successful block, forcing X to go elsewhere to try and establish a new winning path (likely box 7).

(2) O has a 50% chance of getting box 3, but then also needs X to miss box 6. If this happens, then O has two paths to victory, but, by our assumptions, this is only a 25% chance. Should O go for 3 and miss, then, even if X misses 6, box 7 can now give X the win.

The way I see it, O is counting on two questions in a row going his/her way in (2) for it to be a favorable outcome, but only needs one question going his/her way in (1), and the onus is now back on X to start over again. Plus, regardless of what happens to X in box 7, O goes for box 3 and, if successful, now has two paths to victory anyway. Thus, in (1), the ball is fully in O's court, and it's his/her game to lose at that point. Otherwise, in (2), O is counting on an X miss.

So, in this scenario, it is definitely better for O to just go for the block, even with the risk of a miss and giving X the game. Too many things need to go right for O to try any other strategy and have the outcome be better.

I tried designing other scenarios and pretty much came up with the same idea; namely, I don't see any competitive advantage (assuming the questions are 50-50 toss-ups) to not trying for the block.

That's my quickie argument for trying for the block, but, as HS is not a mathematical game, obviously, YMMV.

/yes, I analyzed a game show that's been off the air for 36 years...

//wouldn't be the first time!

Anthony