The following is a quote from Littlewood's A Mathematician's Miscellany:
(3) The following will probably not stand up to close analysis, but given a little goodwill is entertaining.
There is an indefinite supply of cards marked 1 and 2 on opposite sides, and of cards marked 2 and 3, 3 and 4, and so on. A card is drawn at random by a referee and held between the players A, B so that each sees one side only. Either player may veto the round, but if it is played the player seeing the higher number wins. The point now is that every round is vetoed.
If $A$ sees a 1 the other side is 2 and he must veto. If he sees a 2 the other side is 1 or 3 ; if 1 then B must veto ; if he does not then A must. And so on by induction.
(4) An analogous example (Schrodinger) is as follows.
We have cards similar to those in (3), but this time there are $10^n$ of the ones of type $(n, n+1)$, and the player seeing the lower number wins. A and B may now bet each with a bookie (or for that matter with each other), backing themselves at evens. The position now is that whatever A sees he 'should' bet, and the same is true of $B$, the odds in favour being 9 to 1. Once the monstrous hypothesis has been got across (as it generally has), then, whatever number $n$ $A$ sees, it is 10 times more probable that the other side is $n + 1$ than that it is $n - 1$. (Incidentally, whatever number $N$ is assigned before a card is drawn, it is infinitely probable that the numbers on the card will be greater than $N$.)
While I was able to follow (3), I don't understand (4). Why is it that
whatever number $n$ $A$ sees, it is 10 times more probable that the other side is $n+1$ than that it is $n−1$
The last statement makes no sense to me either. And why is this example analogous to (3)? I would be very grateful for an explicit explanation spelling out what the author means.