As an example of the value of a thorough knowledge of these odds to a careful player, suppose he had to win two rounds of a plain suit, of which he held six cards; or to lead the ♡7, having three higher. The suit would be the better play, because it takes in only one heart, while the lead of the heart might take in four.
The following table shows the exact number of times in 1,000 deals that a heart would probably be discarded on a plain suit led, according to the number of cards in the suit held by the leader, and the number of times the suit was led:
| Cards held by the leader. | 1, 2, 3, 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|
| Times hearts will be discarded:— | |||||
| On first round | 44 | 63 | 122 | 200 | 315 |
| On second round | 358 | 430 | 659 | 857 | 1000 |
| On third round | 842 | 1000 | 1000 | 1000 | 1000 |
This shows that 158 times in 1,000, when the leader has 1, 2, 3, or 4 cards of the suit, it will go round three times, because 158 is the balance necessary to bring our last figure, 842, up to 1,000. Reducing this to a small fraction, the odds are about 5⅛ to 1 that a suit will not go round three times without affording to some player the chance of discarding hearts on it. This calculation shows the hopeless nature of all hands that contain at least three cards of each suit, unless the smallest card in every suit is below a 6; for if any one of the suits is led three times, it is even betting that you will have to win the third round, and 5⅛ to 1 that you get a heart on it if you do.
PLAIN-SUIT LEADS. The favourite lead with most heart players is a singleton; or, failing that, a two-card suit. This is a mistake, unless the singleton is a high card; for if the adversaries are sharp players they will at once suspect the nature of the lead, and carefully avoid the suit. But if you wait until some other player opens the suit, it will very probably be led twice in succession. The best original plain-suit lead is one in which you are moderately long, but have small cards enough to be safe, and from which you can lead intermediate cards which probably will not win the first trick.
A very little experience at Hearts will convince any one that it is best, in plain suits, to play out the high cards first. This agrees with the theory of probabilities; for while the odds are 22 to 1 against your getting a heart on the first round of a plain suit of which you have 4 cards, the odds are only 2 to 1 against it on the second round, and on the third they are 5⅛ to 1 in favour of it. Accordingly, on the first round most players put up their highest card of the suit led, no matter what their position with regard to the leader; but in so doing, they often run needless risks. The object in Sweepstake Hearts is to take none, and the most successful players will be found to be those who play consistently with the greatest odds in their favour for taking none.
Suppose that you hold such a suit as A 10 9 7 4 2. This is a safe suit; because it is very improbable that you can be compelled to take a trick in it. The best lead from such a suit is the 10 or 9. If the suit is led by any other player, the same card should be played, unless you are fourth hand, and have no objection to the lead. This avoids the risk, however slight, of getting a heart on the first round, which would be entailed by playing the ace. In Sweepstake Hearts it is a great mistake to play the high cards of a suit in which you are safe; for no matter how small the risk, it is an unnecessary one. In the case we are considering, when you have six cards of the suit, the odds are 7 to 1 against your getting a heart if you play the ace first round. That is to say, you will probably lose one pool out of every eight if you play it. Take the greatest odds in your favour, when you have only four cards of a suit; they are 22 to 1 against your getting a heart the first round, so that you would lose by it only once in 23 times. But this is a heavy percentage against you if you are playing with those who do not run such risks, for you give up every chance you might otherwise have in 5 pools out of every 110.
When you have a dangerous hand in hearts, but one absolutely safe long suit, it is often good play to begin with your safe suit, retaining any high cards you may have in other suits in order to get the lead as often as possible for the purpose of continuing your safe suit, which will usually result in one or more of the other players getting loaded.
When you have at least three of each plain suit it is obvious that you cannot hope for any discards, and that you must take into account the probability of having to win the third round of one or more suits, with the accompanying possibility of getting hearts at the same time. If you have the lead, this probability must be taken into account before any of the other players show their hands, and as it may be set down as about 5⅛ to 1 that you will get a heart, any better chance that the hand affords should be taken advantage of.