1. Card Play at MP
Part One

2. The Normal Contract
Make reasonable plays that risk the contract to gain overtricks
A finesse that results in an overtrick or -1
A “percentage” endplay
50+% risks that either provide an overtrick or risk the contract should be taken in MP. However, remember to find a better line of play if it is possible!

3. The Abnormally Good Contract
Make the Hand
Use Safety Plays to Ensure a Good Score
It becomes necessary to play safe in a good contract because it isn’t a good bet to turn a 75% board into a 90% board when it risks losing the board entirely. The key to winning MPs is to keep every board at or above average.

4. The Abnormally Bad Contract
Consider alternative contracts
Assume the cards lie unfavorably
It’s necessary to assume the cards lie unfavorably in a situation like so: You are declaring 3D when the rest of the field is in 3N, which is likely to make. You need to assume an abnormal lie of the cards so that 3N fails, as otherwise you will lose the board no matter how you do in 3D.

5. Don’t Overcomplicate it
Maximize Overtricks in Normal Contracts
Play Safely in Abnormal Contracts
Defend Based on Percentages
Always Consider Other Possible Results

7. Restricted Choice – The Monty Hall Dilemma
With two equivalent honor cards outstanding, if one drops, it is better to finesse the other. The queen and jack are equivalent cards Think of them as “goats” xx GG One Case Gxx G Two Cases
Pavlicek’s explanation
AKxxx T987
AK9x Qxx
Remember that the missing honors must be equivalent. The holding AQTx xxx is NOT a restricted choice situation. If the math confuses you, the first link explains the issue well by looking not only at the contestant’s problem, but Monty’s problem. Essentially, the moral is that new information affects the odds.

8. Vacant Places Count the cards known to be held by the opponents
The “spaces” available for cards in question help suggest probability that a card is in a specific hand
E.g. When an opponent opens a 3- level preempt, they have 6 vacant spaces for cards in the non- preempt suit

9. Determining the Card Combinations Possible
Number of possible combinations = 2N, where N = # of outstanding cards
E.g. If there are four cards outstanding, there are 16 total combinations
KT72 KT
KT K7 K
KT K2 T
K T
T T

10. Calculating the % Success of a Line of Play
Compare relevant distributions to total possible distributions
AKTx Qxx
The best play (in a vacuum) for four tricks is drop the J total combinations x 2 (6-0) Irrelevant – Know to finesse or offside x12 (5-1) Irrelevant – Know to finesse x30 (4-2) Jxxx xx exists 10 times -> x20 (3-3) xxx Jxx exists 10 times -> When the suit is played up to the finesse/drop decision, the holdings left are J P= 24.22% x (1/15) = J32 P= 35.53% x (1/20) = 1.775
“When the defenders hold only insignificant cards, their following in a suit acts to eliminate the extreme splits while the relative probabilities of the remaining splits are unchanged from their original values. When the defenders hold significant cards in a suit, their following w/ insignificant cards increases the chance of an even split in the suit. With one honor missing, if the numbers of plausible plays reach equality for the remaining combinations, the relative probabilities are the same as would be calculated from the current vacant places” - MacKinnon
This process is hardly necessary at the table, but it is illustrated for completeness. A typical bridge player only needs to understand how suits break most of the time. Usually, logical deduction will leave statistics in the dust.