Ok,

I understand the basic mathematical reasoning behind "blocking", but I was thinking about it before going to sleep last night and it seemed dubious to me.

Before anyone jumps and says I don't understand the concept, I do.

eg A

5

means opponent cannot have A

A

, A

A

, A

A

Therefore in theory, opponent is 50% less likely to have AA

But is this really true?

The way I see it there are 52 'slots' to be filled by the cards, any number of order of cards (52!) are possible.

Let's say you are SB and opponent is BB. You will get the 1st and 7th card of this string of 52 and your opponent will get the 2nd and 8th card in this order.

How is this combination

A

A

x x x x 5

A

x x x x x x x x x x .....

any less likely than

2

A

x x x x 7

A

x x x x x x x x.....

or even

A

A

x x x x A

A

x x x x x x x x......

Where the x is another random card.

In one case we get A5o and the other we get 72o. Any combination is not any more or less likely to happen than another. AA gets dealt at a specified frequency. So does A5. These frequencies are independent since every card is an independent unit in the deck and has just as much chance of being 1st in the deck as 28th. And sometimes they will overlap to give A5 vs AA.

Though us having the ace of diamonds makes three combinations of AA impossible, to me all this seems to prove is that we are not going to run our A

5

into A

A

, not that we are any less likely to be up against aces in any given hand just because we have been dealt A5.

I am sure there is a way to prove that blockers do actually make the difference but to me it seems rather suspect and I don't want to just accept things blindly. I imagine the proof is something like the Monty Hall Problem which doesn't seem like it should work but it does.