Artificial Intelligence & Probability

The concept that machines can be creative is a strange one. In the 19th century, the scientific community lost faith in humans’ ability to be objective. New scientific methods were invented in order to circumvent our reliance on human expertise, including the replacement of humans with mechanical machinery.
A new logic arose that described publicly observable information and was not dependent upon human understanding. This new logic was supposed to replace human inference with strict, publicly observed mechanical rules.
The hypothetical Turing machine, thought of by Alan Turing in 1936 can, despite its simplicity, simulate any computer algorithm no matter how complicated and is the basis of modern computing.
How does this relate to bridge?
We appreciate a creative bridge player for finding new ideas in bidding, play and defence not previously thought of. In contrast, machines in general, and bridge engines in particular, cannot be creative: Machines represent our modern paragon of objectivity, as they cannot deviate from their pre-assigned rules or actions. Therein lies the soul of the scientific revolution of the 19th century.
Bridge engines calculate following restricted rules, finding plays that from a human perspective are sometimes very creative. This is not because the machines are creative in themselves: We cannot calculate like a machine, and rely heavily on our prior knowledge, trying to apply it to situations that we tackle at the bridge table.
Our ability to find new ways of implementing this knowledge or adapting ourselves to situations to which previously known rules do not apply, is the reason we ascribe creativeness to the seemingly creative machine plays. None of this is relevant to the description of machines’ work, as they simply obey rules without deviation. We became so fascinated with machines’ abilities to calculate that we began believing that we humans are ourselves a kind of machine. This is a historic irony, as computers were invented in order to remedy the human flaw of being creative.
Computers are machines and they do not think, rather, they calculate as per pre-assigned rules. Artificial intelligence is thus not real; rather, we find sophisticated ways to use calculators for intelligent tasks. Yet these programs do not imitate the creative way humans tackle these problems.
The programming of a bridge computer will of necessity include a significant amount of probability theory. For example, the computer will be ‘taught’ the principle of restricted choice.
If we consider these two card combinations:

yeh1

In the first example the play for the maximum number of tricks is to finesse the jack and then finesse the ten.

In the second example you finesse the queen and then play the ace.

Yves CostelEach holding has the same number of cards, yet with Example 1 you should finesse twice, and with Example 2 you should finesse only once.

The reason is that in the first example you are missing equal cards (PiccheKQ). If East held PiccheKQ doubleton, he had a choice of plays – he could win with either the king or the queen. In the second example, if East held PiccheKJ doubleton there is no choice – he would always win with the king.

One of the perplexing areas in bridge theory is how the probability percentages of various suit divisions and honour locations change as the play progresses. Percentages calculated at the start of a deal – a priori percentages – are not set in stone. As you gain information from trick to trick, percentages change – sometimes drastically. Exactly how much they change is often difficult to determine, not only because of subjective factors but because of misconceptions in probability theory.

For example, suppose you have a finesse for a king. Before any cards are played, this is clearly a 50-percent chance; but as play continues it may become greater or smaller depending on what you discover about the distribution of the opponent’s cards. If you learn that East has four cards in the suit and West has only one, the finesse then becomes an  80% chance (4-1 odds in your favour).

The best computer engines can apply these principles to the play of a bridge hand and the recent World Computer Championships in Wroclaw witnessed one of the best-played deals in the history of the event:

yeh2

yeh3

West led the queen of clubs. As the cards lie, there is only one sequence of plays to make 6Quadri and the bidding suggests the successful line. Diamonds can be 2-2 or 3-1, and you must decide which, as you will need two entries to hand – one to take a heart finesse and one to run the diamonds. Given West’s length in hearts and spades, Wbridge5 determined that West holding a singleton diamond honour (jack or 10) was more likely that a 2-2 break.

The play proceeded: FioriA, QuadriQ overtaken with the ace, heart finesse, diamond finesse and run diamonds. This was the five-card end position:

When South played the Quadri2, West had no good discard. At the table, West discarded the queen of spades, declarer dummy’s four of hearts. Declarer led a spade to West’s ace and the heart return was won by dummy’s queen, leaving dummy to score the ace of hearts and declarer the king of spades.

Despite this display of brilliance, I am confident that all the teams competing in the Yeh Online Bridge World Cup would be able to defeat the World Computer Champion!

Mark Horton