In a game of 4 players, what are the odds that one player will wind up with all the spades?
One in every 635,013,559,600 hands (or, with a frequency of around 0.00000000000157).
635,013,559,600 is “52 choose 13” = “the number of ways to pick 13 items from a set of 52”, and only one of those ways is the one you want. The value is 13! * (52-13)! / 52!. See this page for background.
thank you!
This likelihood, BTW, is the same for bridge (spades’ smarter brother), not to mention whist (bridge’s no-nonsense grandfather).
One has to multiply this by four because there are four players. The OP’s question was that any player would end up with all the spades.
Ah, but it’s not that simple. The events aren’t independent, so a straight *4 doesn’t quite cut it here.
First time I played the game, that’s exactly what I got on the 1st deal*. Even so, I can’t stand the game. Bridge is a much better choice, IMHO.
*Personally, I don’t think it had all that much to do with chance, the dealer couldn’t shuffle to save his life.
What exactly is the difference between bridge and spades? I’ve always thought of spades as inside out hearts, and I’ve always wanted to learn to play bridge, but never met anyone who could teach me.
Nope, it’s a straight 4x.
So, indeed, if the OP is actually interested in any player (not one specific player) getting all the spades, then the chances are 1 in 158,753,389,900.
The mechanics of bridge is (relatively) straightforward. If you know how to play spades, you know how to play bridge, more or less. It’s the bidding in bridge that has a lot of the calculation. There are a whole bunch of conventions that communicate to your partner (and opponents) the distribution of cards in your hand. By carefully paying attention to your partner’s bids, as well as your opponents’ bids, you get an idea of what everyone’s hand is like. Bridge also differs from spades in that, if you win the contract, you play alone. After you lead, and your opponent plays, your partner hand is laid out for all to see, and you play from your partner’s hand.
Also, in spades, spades is always trump. In bridge, the bidding determines the trump suit, or it can end up with no trump suit at all.
Yes. Card games like whist and, moreso, bid whist, are most closely related to bridge.
But, like chess, the rules are easy, but mastering it is a bit more complicated…
Also, a warning, once you learn bridge, it breaks your brain for spades – you’ll never be able to play spades or even look at your spades hand again without wishing you were playing bridge.
Minor nitpick: in bridge, the contract winner (declarer) does not lead. The person to the left of declarer leads, then partner of declarer lays down his hand and becomes dummy.
Near the end of the last century, the local paper was reprinting various front pages of important events (e.g. attack on Pearl Harbor, Kennedy’s assassination, etc.) On the one for the sinking of the Titanic, there was an article at the bottom of the page about a bridge player who’d been dealt all 13 diamonds. The player opened 1 Diamond, his opponents both bid (partner passed, I think) and then he jumped to 7 Diamonds. Unfortunately for him, the opponents had decent hands and overbid him (7 Hearts, I think).
Now this player was foolish. There’s only two contracts that such a hand is good for: 7 D or the opponent to his right in a no trump contract. Seven diamonds is a lay down and the no trump is doomed to not win a trick. But since he can’t force his opponent to bid NT, he may as well bid the 7 D outright. After all his partner could pass with a poor hand and his opponents are given bidding space to find a suit (as actually happened) or they could also have passed, leaving the 1 D contract.
In duplicate, though, wouldn’t the LHO just bid 7NT as a sacrifice? In a rubber game, though, I could see 5 D as a better opening bid, perhaps to provoke a double.
It could have been a setup for the newbie. Or it was a new pack of cards, poorly shuffled as you say.
Not just a new pack of cards but poor shuffling during game play in general. There are a lot more perfect hands reported than should conceivably be possible given the odds. Some are attributed to being false reports, deck-stacking, cheating or pranks. Even ruling all that out, there are still too many verifiable perfect hands and the reason is imperfect shuffling. The cards have a tendency to group together during play. Someone leads with a spade, and 3 more spades pile on. Next trick they lead spades again and they now have 8 spades piled together. When the deck is imperfectly shuffled later that big group of spades gets broken into smaller groups of spades but still clustered in the same area of the deck. Over time they can wind up perfectly spaced 4 cards apart and give someone the perfect hand far more often than one in 160 billion times or whatever the exact odds are. That is why at casinos and in tournament play the dealers go to such extremes to shuffle fairly, including spreading the entire deck out on the table 1 card per spot and mixing them all up in a big jumble by hand. Just cutting the deck in two and fanning the stacks back together several times as is often the case during casual play doesn’t give a true shuffle. Expert players are said to exploit this by remembering what was played in earlier hands as they make decisions about the values of cards in their current hand, knowing that the imperfect shuffle will be creating non-random groupings of certain cards. There’s an interesting piece on this question in the Feb. 1935 issue of Science News.
:smack: Shows you how long it’s been since I’ve played bridge…
Not necessarily. Bidding 7 Diamonds outright indicates you have a hand like all 13 diamonds or perhaps 12 diamonds (including the ace) and another ace. If you have a hand like that it means there are lots of good cards for your opponents and they might have a good sacrifice in a suit, and that they don’t have to worry about your diamonds because either they or their partner will be void and can trump them.
Most bridge players now use an opening bid of 2 clubs to mean to partner: you may not pass (unless your right hand opponent bids so I’ll get another chance to bid) until we reach a “game contract”. (A slightly more old-fashioned player would bid 2 diamonds meaning the same thing but would also be indicating that his suit is diamonds as well).
In fact some partnerships use something called “two diamonds waiting”. That means that the partner of the two club opener automatically bids two diamonds to let his partner describe his hand. The bidding would then go something like this
2C[sup]1[/sup] P 2D[sup]2[/sup] P
3D[sup]3[/sup] P ??[sup]4[/sup] P
4N[sup]5[/sup] P ??[sup]6[/sup] P
7D[sup]7[/sup]
[sup]1[/sup] I have a strong hand
[sup]2[/sup] OK I’m listening
[sup]3[/sup] and Diamonds is my suit
[sup]4[/sup] some description of his hand as he can’t pass
[sup]5[/sup] Blackwood asking partner how many aces he has (though you don’t really care)
[sup]6[/sup] partner’s answer: 5C (I have none) 5D (I have 1) etc.
[sup]7[/sup] where I was going all along I was just trying to convince the opponents that I had lots of aces and kings and not some freaky hand like I actually do.
One interesting thing about this is that since partner first bid diamonds, he would be declarer (holding none of the trump suit) and possibly feeling nervous. Once your right-hand opponent leads his card, you get to put down dummy with all 13 diamonds and smile.
Interesting comments, OldGuy and guizot, but it should be noted that the hand was played in 1912. The current form of scoring wasn’t developed until 1925 and bidding conventions like the strong 2C are even more recent.