Continuing from the previous post

We established that there are 5 guaranteed turnovers and we could, if we wanted to, obtain the following position if we ignored the identity of the newly-turned cards.

Obviously in practice we would never ignore the new turnovers, but this shows a “worst-case scenario” and is a useful benchmark to keep in mind (on second thoughts if every face-down card is a politician then perhaps we should be aiming for the fewest guaranteed turnovers).

Bad jokes aside, we can immediately tell that if any of the new cards is an ace we get an extra turnover. Similarly, a 3, 5 or Q is a good card. Further thought shows that 7 is good. Are there any other good cards?

Suppose we go back to the start position. Recall there were three Sixes but only two Sevens, so we could choose only two out of the three columns containing Sixes. One of the columns involves exposing a Queen and moving it onto a King. Aha! That means a Jack is also a good card.

I believe there are no other good cards (check this!) In summary: going back to the start position

• if we turn any one of A,3,5,7,J,Q then we are guaranteed more than 5 turnovers.
• If we turn any one of 2,4,6,8,9,0,K then we only have exactly 5 turnovers

Well done if you came to the same conclusion. Even better if you found an error in my analysis 😊

Recall that we had to choose a move before looking at the next card. The most obvious option seems to be column 7 which builds two suited connectors (5/6 in diamonds and 6/7 in clubs), and this does not cost any outs, assuming I haven’t missed anything.

Okay, I agree this analysis was probably a bit over the top for experienced players, but I think it’s useful for a newbie to get used to this kind of thinking. Of course there is more to Spider than counting guaranteed turnovers (especially when you are not close to being forced to deal another 10 cards). In some cases it is wise to “sacrifice” turnovers if we can gain some other advantage, such as getting an empty column or completing a suit. But that lesson comes later😊

Note that Cy the Cynic or Unlucky Louie (borrowing characters from Frank Stewart’s excellent Bridge website) would probably choose to turnover column 7 without doing any calculation – two easy suited connectors and a turnover can hardly be a serious error at this early stage. But I think the calculation exercise is useful because

• we have some idea of whether the game is going well or badly.
• You never know if some trick play can be used to gain an edge over the obvious play.

Here is a possible outcome after replacing politicians with actual cards. One can readily compute we get 2 more turnovers on top of our guaranteed 5.

EXERCISE: Start a new game by dealing 10 extra cards from the stock. Calculate the guaranteed turnovers and the probability that the first newly turned card will yield at least one extra turnover. To keep things simple, (i) assume you get to look at the new card before making your first move, (ii) any rank occurs with probably 1/13 (iii) when you see the new card you are allowed to call the suit (but not the rank).

That’s it for now. Next lesson: Empty columns (aka holes)