Card Play at MP Part One

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!

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.

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.

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

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.

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

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 72 -- KT7 K7 K KT2 K2 T K72 T7 7 T72 T2 2

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 64 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 J654 32 P= 24.22% x (1/15) = 1.629 654 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.