The auction is a competition - you and your partner with your suit and
the opponents with theirs. When there is an imbalance in the strangth
between the two sides there is a clear winner, the other have to
concede. But who will be victorious when strength is fairly equal?
Fortunately there is a concept that comes to your aid. Jules Verne came
up with his, well let's call it a law, that states that when the
resources are fairly equal the total number of tricks that CAN be
made (whatever they are) by both sides added together will be
equal to the sum of the trumps held by each side. Its called the Law of
Total Tricks. Loi des levees totale.
The application of ths law depends on the suits involved, the
vulnerability & the scoring at part scores. By the time the auction
has reached the critical point a good knowledge of the trumps in each
party will be common knowledge.
Suits matter significantly as for example a battle between Spades and
Hearts favour Spades as Hearts would need to go 1 bidding level higher
and highr means more risk.
Vulnerability matters, the risk of pushing it vulnerable is to attract
a serious penalty if doubled - the dreaded: -200. Bridge scoring will
tell you that's more than any part score makes and therefore your one
step further is costly.However if non-vulnerable pushing one too far,
even if doubled, costs: -100 and that loss is less than the what the
opponents would have made if left in their last bid - and that's a
possible win of 1 or 2 IMPs.
So the law can help you: Suppose you think each side has 9 trumps thenm the total numbr of tricks each side can make
add up to 9+9 or 18. Suppose you are bidding in Hearts and the
opponents in Spades and your bid of 3H has been topped by the opponents
with a bid of 3S - you have reached the critical decision point. If you
PASS the opponents will probably score 14 0 or possibly 170 or be
defeated by 1 trick. Your other choice is to compete - bidding 4H and
expecting to be defeated by 1 trick. So if non-vul it will cost you -50
or -100 if doubled and if vulnerable -100 or -200. If your luck is in
you just might make it scoring 420 or 620 depending on your
vulnerability. If your luck is right out you may be defeated by 2
tricks losing if doubled -300 or -500!
So theres the choice: The risks and the gains.
If the total of trumps is 17 (8+9) or 16 (8+8) very similar arguments follow.