# How to bet on a tossup

October 18, 1959

The origin of certain popular terminology is often cloaked in mystery, but there can be little doubt of why an even chance is often referred to as a tossup. As to whether a toss of a coin is ever a strictly even chance—that, my friends, is an entirely different problem.

Consider, for example, the case of the penny that has come up heads on 12 consecutive tosses. How would you bet on the 13th toss? If you are a mathematician, you might bet either way, knowing that previous events have no effect on the present odds. If you are with the majority, you might bet on tails, figuring that it was about time for the tide to turn. But if you are a realist you will bet on heads again, figuring—until convinced otherwise—that there just might happen to be a bit more weight on one side of the penny.

The expert's edge at the bridge table does not need to be much more than the ability to sense which side of the tossup happens to be carrying that little bit of extra weight. For example:

Both sides vulnerable South dealer

NORTH

[King of Hearts]
[5 of Hearts]
[King of Clubs]
[Queen of Clubs]
[Jack of Clubs]
[9 of Clubs]
[4 of Clubs]
[Jack of Diamonds]
[10 of Diamonds]
[3 of Diamonds]

WEST

[Queen of Hearts]
[8 of Hearts]
[6 of Hearts]
[2 of Hearts]
[Ace of Clubs]
[8 of Clubs]
[6 of Clubs]
[King of Diamonds]
[7 of Diamonds]
[5 of Diamonds]

SOUTH

[Ace of Hearts]
[Jack of Hearts]
[4 of Hearts]
[7 of Clubs]
[3 of Clubs]
[Ace of Diamonds]
[2 of Diamonds]

EAST

[10 of Hearts]
[9 of Hearts]
[7 of Hearts]
[3 of Hearts]
[10 of Clubs]
[5 of Clubs]
[2 of Clubs]
[Queen of Diamonds]
[9 of Diamonds]
[8 of Diamonds]
[6 of Diamonds]
[4 of Diamonds]

SOUTH

WEST

PASS
PASS
PASS

NORTH

2 [Club]
PASS

EAST

PASS
PASS
PASS

If there were flaws in the bidding, it would have required the perfect opening lead—a diamond—to point them out. Assured of a 10-point minimum in North's hand by the response of two clubs, South was amply justified in his strongly urging jump rebid in spades. North, on his part, had too much over that minimum to bid merely four spades. And South, with three aces, had the control cards North's bid seemed to be inquiring about.

West briefly toyed with the thought of opening a trump, but discarded that idea for an excellent reason. The bidding warned that North's club suit would furnish a flock of discards once the ace had been knocked out, so it was necessary to find the setting trick in a hurry.

But hearts wasn't the place to find it. South won the first trick with his jack, drew trumps, knocked out the ace of clubs and got rid of his diamond loser on dummy's jack of clubs to bring home his slam.

"I guessed wrong," apologized West. "It seemed a tossup whether you had the king of hearts or the queen of diamonds, and there was a slight advantage in the heart lead because it would not throw away a trick if you had the jack of hearts instead of the king."

West's reasoning was true as far as it went. But, like the bettor's feeling that it was about time for a tail to turn up, it did not apply to this particular toss of the coin. It would do no good merely to save a trick; South, you'll observe, could have made his contract even if he did not hold the jack of hearts. West needed to find a defensive trick in a hurry.

Therefore, the only cards that mattered, assuming that the opponents held three aces, were the king of hearts and the queen of diamonds. From a strictly mathematical view, there was as good a chance that East had been dealt one of these cards as the other. But, looking at his own hand, West should see considerably more likelihood his partner would hold a queen rather than a king.

Why? Because the opponents had reached a slam lacking the 9 high-card points West could see in his own hand and—if that slam could be defeated—another king or queen which East must hold. To put it simply, there was more chance partner held a queen than a king.

Against loose bidders, we'll grant that this may be a slim advantage. But how much extra weight do you need to decide which way you'll bet on a tossup?

EXTRA TRICK
To decide which of two cards your partner is more likely to hold, visualize the strength of declarer's hand lacking one card or the other. The holding that best fits his bidding should give you your answer.

PHOTO

HOLE YARDS PAR R1 R2 R3 R4
OUT
HOLE YARDS PAR R1 R2 R3 R4
IN
Eagle (-2)
Birdie (-1)
Bogey (+1)
Double Bogey (+2)