| Hand of the Month
Last month's column featured a most unusual hand: the up card was the Jack of Hearts, and South (the dealer), held this collection:
 A
 K Q
 A
 A
South declared "loner," and grumbled about having to discard an Ace (Spades), as he added the Right to his hand. Although, the Loner was not a sure thing, it was still a possibility. Surely, the hand would score at least one point!
Five minutes later, this hand was up in smoke! The West player nailed it with an incredible holding, and defense. Can you conjecture as to what West held, and the line of play, resulting in the defeat? Here is a contrived West hand, specifically constructed to beat South (see analysis below):
 K
 A 10 9
 J
 None
There is a lot more here than meets the eye. Firstly, West has a four trump. Why did he not order to South? Passing made no sense here. Secondly, South now has a choice of discarding an Ace (after he takes the Right into his hand). This is a most critical decision. If South could see West's hand, he would keep the Ace of spades, and unload one of the minor suit Aces. Obviously, he does not know this, and thus is forced to guess. If South does keep the spade Ace, he will survive West's 4-trump onslaught.
Let's examine the play: West leads his spade King. South takes the Ace, and plays whatever other Ace he kept. West trumps with the nine, and leads his Left. South lets go of the Queen, and wins the last two tricks with the Right-King. (West is end played). If West initially leads the Left or his Ace, South will win the Right, cash the Ace of Spades, and get off lead with the Ace of diamonds. Then he waits to win his third trick.
What happens if South guesses wrong and lets go of the spade Ace? West still leads his King of spades, and South must trump with the King or Queen. However, this fatally weakens his hand. The only hope is the lead of one his minor suit Aces. West trumps in with the nine, and plays either the Left or the Ace. South takes the Right, and must choose which way to concede the last two tricks to West.
In summary, if you know which Ace South is going to discard, then you can construct the West hand to defeat South. However, this is not realistic and true to the game. Thus, South will win this hand in most cases, unless he makes a bad guess, AND West happens to have the KING of the suit which South voids. Whew!
Euchre odds & probabilities: part I
This is the first of two installments. Euchre is a game that is based on a combination of three factors -- the luck of the deal, the strength of the partnership, and the application of psychology/intuition. To begin with, there are three cards hidden in the "kitty" (after the up card is revealed.) Thus, 12.5% of the deck is unknown.
The great Cribbage pioneer, Joseph Wergin was also an accomplished Euchre player and expert. He published an interesting listing of probabilities. Here are a few: · The probability of being dealt Right, Left, Ace-King Queen (any suit) and having the upturned card matching this suit is 1 in 100,947 · The number of possible 5 card hands when using a 24-card Euchre deck is 42,504 (see Quiz question below) · The odds of receiving one Jack (any color) in a 5-card hand is 5 out of 24. · The odds of being dealt the Right and Left in any suit is 5 out of 5,313 Robert W. of Indianapolis, IN forwarded this rather intriguing information (below) to me. Bob is a very accomplished live player, with several wins to his credit. Interestingly enough, he prefers the individual's Round Robin (different partners after every eight hands). He also enjoys "Reverse" Euchre in which the object of the game is to lose as many points as possible!
Did you wonder what the probability of certain scenarios are in the game of Euchre? Euchre is a trump game played with 24 cards (9 through Ace.) Five cards are dealt to each player leaving a kitty of 4 cards. The top card is flipped over and is called the up card. The up card is important because everyone must reject the up card as the trump suit before bidding on an alternate trump suit.
What is the probability of being dealt a specific number of cards in the same suit as the up card?
Please bear in mind that there are four players. So the expected number of occurrences per hand is 4 times this value. What this means is that if there is a 30.312% probability that you will get 2 cards suited to the up card. Then an average hand will see 1.21 players have exactly 2 cards suited to the up card. The following averages would be expected per hand (also assuming 12 hands per game): · 1.69 players will have 1 card suited to the up card (every 0.59 hands or 20 times per game) · 1.21 players will have 2 cards suited to the up card (every 0.83 hands or 14 times per game) · 0.32 players will have 3 cards suited to the up card (every 3.10 hands or 3.88 times per game) · 0.03 players will have 4 cards suited to the up card (every 33 hands or every 2.75 games) · 0.0007 players will have 5 cards suited to the up card (every 14285 hands or every 1200 games) Question of the month· How many different (5 card hands) can be dealt with a standard 24-card deck? · If you agree with 42,504, please verify this number, as being accurate. · If you do NOT agree with 42,504, then re-calculate and present a different number | |
