Counting cards during play
Learning to count the cards is vital for effective play to make your contract as declarer, and also to defend effectively.
Beginning players try to keep track of 13 cards in each of 4 suits. This is difficult for 1 suit and nearly impossible for 4 suits (most players only have 10 fingers - don't laugh it is poor etiquette).
Every player can see dummy. A common method is to count the cards you have in each suit, add the number in dummy, and subtract that number from 13. Now you only count the cards you CANNOT see in each suit, these are in the two concealed hands.
This is a good situation for declarer, if she has a 5-3 fit in the 2 hands in trumps, she knows that the defenders have 5 trumps between them. The question now is the distribution, i.e. one of 5-0, 4-1, 3-2.
As declarer you should start counting in the trump suit and then apply the same principle to the other suits according to their importance in the contract.
It is a little trickier for the defenders because one of the hands with missing cards is friendly, the other is the enemy. You use the same strategy to count cards in your partner's hand and declarer's hand.
As players advance in skill they learn to signal through the cards they play to communicate the length and strength of their suits to their partner.
Unassuming Cue Raise
One of the most powerful bids that one can add to the bidding armoury is the Unassuming Cue Raise.
It is used by Responder at their first response to partner's opening bid after an intervening overcall. It is also used by an Advancer over any call by the Responder.
In both instances it tells your partner that you have 10+ total points and a fit (3+ cards) in their suit.
The Responder makes the call by bidding the Overcaller's suit at the next lowest level.
The Advancer makes the call by bidding the Opener's first bid suit at the next lowest level.
Responder's options when the intervening Defender makes a Takeout Double of the opening bid
With 10+ pts Redouble. It does not show support of the opening bid, so Opener should pass when it is their turn to bid and wait for Responder's second bid. It does show overwhelming strength opposite an opening hand, and this tells the Opener that any subsequent double by Responder of a bid by the Advancer or Overcaller is for penalties.
With 6-9 pts bid as though the double was not made.
With a very weak hand and a long suit consider a preemptive bid or weak raise of partner's suit, otherwise pass.
How should I compete over a preemptive opening by the opponents?
A simple strategy is to bid your own suit (5+) with an opening hand, or double for takeout with 16+HCP.
Your hand needs to be slightly stronger to double a 3 level preempt than a 2 level preempt because you may be forcing your partner to bid at the 4 level.
Over 4H/S 4NT asks partner to choose game in a minor.
Always be prepared for your partner to convert your takeout double into a penalty double.