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July 27, 2010 // Posted in Uncategorized  |  No Comments

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More on Backgammon Part 2

February 7, 2010 // Posted in Uncategorized, backgammon, gambling, multiple hands (Tags: ) |  2 Comments

Betting and the Doubling Cube

The item not so far mentioned, and the one which has elevated (or reduced) backgammon into a gambling game for high stakes, is the doubling cube. The doubling cube is a die, usually larger than the others used in the game. on which appear the numbers 2, 4. 8, 16, 32 and 64. At the beginning of the game, the agreed stake for which the players are playing is one unit (it might be that each player stakes £1 or $1, or £5 or $10 or whatever).

The doubling cube is placed to one side of the board showing 64 uppermost (since there is no 1 on the cube). At any stage of the game a player who thinks he has the upper hand may offer his opponent a double before he takes his turn. The opponent either declines, in which case he loses the game and pays one unit, or accepts, in which case the cube is turned to 2 and the game continues with two units as the stake.

When a player accepts a double, the cube is placed on his side of the table, and only he is allowed to make the next double. Therefore, in a game of much doubling, each player will double alternately. The player declining a double pays the amount shown on the cube at the time.

There are three classes of win. A straight win is when the loser has begun bearing off, in which case he pays the stake shown on the doubling cube. The second class of win is known as a gammon. If a player loses before he has begun to bear off his men he is said to be gammoned, and pays twice the stake on the doubling cube. If a player loses while he still has a man in his opponent’s home board, or on the bar, he is backgammoned, and pays triple the stake on the doubling cube.

The maximum loss therefore is 192 units. Backgammons are rare, and it is usual in Britain not to play them. Players should agree beforehand whether or not to recognise backgammons. Chouette This is a means of enabling three or more players to share a game. One player (called the man in the box) plays against the others, only one of whom actually plays the moves.

He is called the captain. If the man in the box wins, he remains in the box, and the next player in line becomes the captain, the losing captain going to the back of the line. If the captain wins, he becomes the man in the box for the next game, the next in line becoming captainand the losing man in the box going to the back of the line. Other players may advise the captain, but he makes all decisions on the play and doubling.

All players pay or are paid by the man in the box, who if he is playing against two players is in effect 178 for double stakes. Any player may accept or decline any double made by either the man in the box or the captain, but he cannot double unilaterally. If he declines he pays the man in the box the stake shown on the cube. Should the captain decline a double, he pays up and moves to the back of the line, and the remainder of the game is played by the player first in precedence to accept the double.

More on Backgammon part 1

February 3, 2010 // Posted in Uncategorized, backgammon, gambling, multiple hands (Tags: , ) |  7 Comments

There is reason to believe that the first games played in which men were moved around a board used the principle of throwing dice to determine the movements of the men.

Games of this sort have been played for 5000 years, and backgammon and pachisi (an early form of ludo) are probably the oldest of these games still played in something like their original form. The name backgammon first appeared in the seventeenth century, although the French name for the game, tric-trac, is older.

The conception of doubling is about fifty years old, and has contributed to the present popularity of backgammon, on which a great deal of gambling now takes place. Backgammon is played on a board by two players, each of whom has fifteen men (also called stones or pieces). It is a race game, each player trying to move his men round and off the board before the other.

The starting position is shown in Figure 6:5. The triangular spaces on the board are known as points. The points are numbered in the illustration to enable the moves to be described, and the raised ledge which divides the board into two halves is labelled ‘bar’, although on the actual board there is no annotation. Each player has a home board and an outer board.

In the illustration the home boards are shown on the right, although the board could be reversed from left to right, with the home boards on the left. Traditionally, the home board is on the side of the window, or source of light. The men move in opposite directions towards their home board: in the set-up illustrated, black men move clockwise and white anti-clockwise.

The first object of each player is to move all his men j into his home board (i.e. on to his pointsnumbered 1 to 6) whence he can begin to bear] them off. Each player has two dice. For the first roll only each player throws one die. The playerj who rolls the higher number has the first mo and takes the numbers shown on the two dice as his first roll. Throughout the game, if a die is cocked, i.e. resting on a man or against the bar or the side of the board, both dice must be re-thrown.

On his turn, a player must move his men. according to the totals shown on his dice, | each total being independent. If he throws 1 and 4, he cannot move one man five spaces. He can move one man one space and another i four, or he can move the same man one space and four, or four and one. Except when bearing off, a man can only be moved the exact! number shown on the die. for instance if a is thrown none of the men on the home H point can be moved, as a move of 6 would carry it off the board.

Another restriction is that no man can be moved onto a point already occupied by two ormoreoftheopposing men. A player with two or more of his men on a point is said to have made the point. No point can be occupied by men of different colours. If a player has one man only on a point, that man is known as a blot. An opposing man can now occupy the point, when it is said that the blot is hit.

A man hit is removed to the bar, and the player with a man on the bar must re-enter him if possible on his next turn. He is not allowed to move another man until he has re-entered the man on the bar. A man must re-enter on his opponent’s home board. If the throw is 6-3, and the opponent has made both these points (he starts the game with his 6-point made) then the man on the bar cannot be re-entered and the turn is forfeited. If a player throws a double, he must move the number thrown four times. Again, the four moves are independent.

Sometimes a player cannot move men in accordance with the two numbers thrown (or four if a double is thrown) in which case he makes the move or moves he can and forfeits the other or others. It sometimes happens that he can move in accordance with either of the numbers thrown but not both, in which case he must move according to the higher number and forfeit the lower. When it comes to bearing off, i.e. moving men from the home board off the board, special rules apply.

A player must move his men according to the rules already given, with the option, where applicable, of bearing off a man or of moving a more backward man forward. For example, if he has men on his 6-point and on his 2-point, and one of his dice indicates 2, he may bear off a man from the 2- point or move a man from the 6-point to the 4-point. Sometimes, however, he will not be able to move a man according to these rules. For example, he might throw 5-4, and have four remaining men on the 1, 2, 3 and 4- points.

In this case he may bear off the man on the 4-point, corresponding to his throw of 4. For this throw of 5, he must bear off the man on the highest point remaining, in this case the man on the 3-point. Now, with men on the 1 and 2-points, he must win on his next throw (as double-1 will entitle him to Four moves of 1) unless his opponent bears all his men off next turn, or unless his opponent has a man on the bar, which he can re-enter with a throw of 1 or 2 and hit the blot.

The Game of Red Dog

January 11, 2010 // Posted in gambling, poker (Tags: , , ) |  2 Comments

Also known as high-card pool, red dog is a game for up to ten players.Each player in turn deals. Before the deal each player contributes an agreed number of units to a pool. The dealer gives each player five cards, one by one, face down, and places the stock face down in front of him.

With nine or ten players, each player has four cards each. The player on dealer’s left examines his hand and bets a stake ranging from one unit to the entire pool that he has a card of the same suit and higher than the top card of the stock.

Dealer turns over the top card, and if the player can show a higher card in the suit, he is paid by the dealer from the pool the amount of his bet. If he loses, he adds his bet to the pool after showing his cards to the other players. Ace counts high. When the first player has won or lost, his cards and the top card are placed face down in a discard pile and the player on his left is the next to play.

When the whole pool is won, or if at the beginning of a fresh deal it has fallen below an agreed minimum, all players replenish it equally. Shoot, or slippery sam, is a similar game to red dog, but is a banking game. Each player in turn, when dealer, puts a sum in the centre as the pool. The amount of the pool can be agreed beforehand; otherwise a minimum should be agreed.

Shoot is possibly unique among banking games in that the advantage is with the players. The dealer deals each player three facedown cards, one by one, and each player at his turn, after examining his cards, bets any amount from an agreed minimum to the amount in the pool that he can beat the top card in its suit. A player betting the whole pool ’shoots the pool’ by announcing ’shoot”.

As in red dog, the dealer exposes the top card. and the player takes from or adds to the pool the amount of his bet. When the pool is taken, the player on the dealer’s left puts up a pool and becomes dealer. Each player when dealer deals three rounds, when he may withdraw the pool and pass the bank to the next player. He has an option of a fourth and final deal if he wishes.

Strategy in red dog and shoot comes from remembering the cards already exposed in the deal and calculating how many cards remain to beat your hand and how many remain that you beat. A player holding +A-J-JV10 in shoot knows that he can beat any diamond, nine of twelve clubs and eight of twelve hearts. Any spade beats him. If he were first to play he would have 29 chances to win, 20 to lose.

If four cards have been exposed, he might have 27 chances to 18 to win, or odds of 3-2 on. He should bet heavily. The best staking plan is to shoot every time the odds favour you, and to bet the minimum when they do not, but a player using this strategy will not be popular with his fellow players.

The Game of Napoleon – A Poker Relative

January 11, 2010 // Posted in Uncategorized, gambling, multiple hands, napoeleon, poker (Tags: , , ) |  1 Comment

The game of Napoleon, or nap, is played with a standard pack of 52 cards, ace counting high. The first dealer is decided by any agreed method, and subsequently the deal passes to each player clockwise. All players, including dealer, are dealt five cards, face down, one at a time.

There is then °ne round of bidding, each player in turn from the dealer’s left being given the opportunity to contract to make a stated number of tricks, with trumps the suit of his choice. After the first bid, subsequent bids must be in lending order. The bids are Two. Three. Four or Nap (all five tricks). The player who contracts to make the most tricks (the declarer), then leads to the first trick. The first card led indicates trumps. Tricks are won in the normal manner of trickmaking games, the winner of each trick leading to the next. The declarer receives or pays to all other players depending upon whether or not he makes his contract.

Payment is at the following rate: Contract Two Three Four Nap Declarer wins 2 units 3 units 4 units 10 units Declarer pays 1 units 3 units 4 units 5 units Overtricks and undertricks do not carry bonuses or penalties, and settlement is made immediately. In order to give the game more variety, some players allow further bids. Misery, a contract to lose all tricks, there being no trumps, ranks between the bids of Three and Four, and pays or loses 3 units to each player.

Wellington is a bid which can be made only above nap, and is a contract to win all five tricks at double stakes (i.e. it wins 20 and loses 10). Blucher is a bid which can be made only over Wellington, and pays triple stakes for a contract of five (30 and 15).

Peep nap allows the player who has bid nap to exchange a card for the top card of the pack if he wishes. Purchase nap allows each player, if he wishes, to look at the top card of the pack before bidding, by contributing one unit to a pool. The player who becomes declarer, if he has paid to look at the top card, is allowed to take it into his hand in exchange for another card before leading.

Strategy

The best play comes from estimating the likelihood of missing cards being in the pack or in another player’s hand. With four or five hands dealt, it is more likely than not that a missing card is sleeping, i.e. in the pack. A player holding three of a suit, which he might make trumps, should know that it is about 16^ 1 against any specific other player holding three or more trumps.

Should there be six players, it is about 4-1 against any other player holding three or more trumps. Therefore a player with AKx in the trump suit and an outside ace can expect to make four tricks about four times in five.

A player holding AK only in the trump suit against five other players has a 6-4 on chance of clearing trumps, and with an outside ace should make three. A player with four small trumps, on the other hand, in a game of five players, will find it is 2-1 on another player holding two trumps, and even with an outside ace cannot expect to make more than three.

The Game of Gin rummy – a Poker Relative

November 23, 2009 // Posted in Uncategorized, gambling, gin rummy, multiple hands, poker (Tags: , , , , ) |  No Comments

A game of recent invention, gin rummy was developed from the parent game of rummy, or rum, in the early days of the present century, and popularised in the 1940s when it became a craze in Hollywood among the film stars. tandard pack of 52 cards, ace counting low.

Each player draws a card to decide dealer, the higher deals. Thereafter the winner of each hand deals the next. Dealer deals ten cards to each player, beginning with non-dealer, the remaining cards being placed face down between the players to form the stock, the top card being turned over to become the up-card, and to begin a discard pile. Non-dealer may take the up-card into his hand, replacing it with a discard from his hand. If he refuses the up-card, dealer may take it.

If he declines it, non-dealer takes the top card from the stock into his hand, and discards a card, which might be the same card. Thereafter each player in turn draws from the stock or the discard pile, and discards.

The object of the game is to form sets, either with three or four cards of the same rank, or three or more cards of the same suit in sequence. After drawing, a player may knock, i.e. he lays down his hand in sets and makes his discard.

He is allowed to lay down unmatched cards if they total 10 or less. Each unmatched card has its pip value, aces counting as one and court cards as ten. No player may draw a card when the stock is down to two cards; if the player who takes the fiftieth card does not knock the hand is abandoned. If the knocker lays down all his cards with none unmatched he is said to go gin.

When a player knocks, unless he has gone gin, the other player shows his sets, and is allowed to lay off any unmatched cards on the sets of the knocker. For example, if the knocker has a set of three kings, his opponent might lay off the fourth king if he holds it. If the knocker has a sequence of 4-5-6 of hearts, his opponent might lay off 7-8 of hearts. After laying off, if the knocker has the lower count in unmatched cards, he scores the difference of the counts.

If he has declared gin, he also scores a bonus of 25. If the opponent has an equal or lesser count, he is said to undercut the knocker, and scores the difference, if any, plus a bonus of 20. A knocker going gin cannot be undercut: if his opponent discovers he also has gin, there is no difference in the counts, but knocker scores the bonus of 25. The Hollywood scoring is complicated, and is recorded on a card like that in Figure 6:4. The first time that a player scores he enters his score in the first of the three columns against box 1.

The second time he enters his score in the second column against box 1 and also adds the points to his score in the first column, writing the total opposite box 2. The third time he scores he enters the score in the third column, and adds the points to those already scored in the first two columns. Thereafter, each score is added on to all three of the columns.

When a player’s score reaches 100 in a column, he wins the column and scores 100 points for winning it plus 20 points for each box he has won more than his opponent. If the opponent has scored more boxes, 20 points are deducted for each extra box.

If a player fails to score in a column, he is said to be blitzed, and the score of the winner of the column is doubled. Once a column is won, no more scores are added to it. A player blitzed in the first column must enter his first score in the second column.

If a player wins all three columns, his final score is the sum of the three totals. If both players win a column, the player with the higher score wins by the differena- in the two scores. Settlement is at a rate per point, or ten points, to be agreed beforehand.

Strategy

The best play lies in remembering the discards, so that no attempt is made to form a set 168 that is impossible or difficult to make because all or some of the required cards are buried in the discard pile. It should be appreciated that a combination of *6 +6 +5 affords four chances of a set with^6-J-6 +4 and +7 whereas ^A+A+2 affords only three. A holding like +8 +7-J-10 .J.8-J-7 affords six chances of a set, including one of four cards, and whichever set is formed, two matching cards can still be kept. A sequence is more valuable than a set of three of a kind, as more cards can be added to it, two immediately at each end of a sequence, one only on a threesome.

The cards the opponent takes from the discard pile, and the cards he discards, should be noted to form a picture of his hand. Cards which might help him should be kept both to block him and to afford laying off opportunities should he knock. Other things being equal it is better to hold low cards than high cards, so that any adverse score is kept down and also because they afford opportunities to knock.

Most gin hands are won on two sets and three or four unmatched cards. The early discards tend to be high cards, and it is often worth holding potential highcard sets early in the game. If such sets are not formed after four or five discards, however. they might be expensive to hold.

The longer the game continues, the more wary a player must be of knocking with a high total of unmatched cards, as it is likely that his opponent might undercut him. It is not usually good policy, when it is possible to knock, to hold on hoping for gin.

The Game of Brag – Poker’s Ancestor

September 15, 2009 // Posted in Brag, gambling, poker (Tags: , , , ) |  2 Comments

An ancestor of poker, brag was the most popular card game of England in the sixteenth century, and is still very popular today. It is very similar to poker, played with a normal pack. The deal passes in rotation, each player including the dealer receiving three cards face down.

The dealer places a stake up to an agreed limit in the pot, and the player on his left has the first option of throwing in, calling (i.e. equalling the dealers stake) or raising. When the stake is raised. each player in turn must raise his stake to the new level to stay in, as in poker. When all bets are equal, there is showdown. There ’s 166 no draw for fresh cards. The classes of hands are shown in Figure 6:3. In brag, a run, or straight, ranks higher than a flush. The probability of obtaining a flush with three cards is greater than that of obtaining a run, although with five cards, as in poker, the straight is more likely.

A prial in brag ranks higher than a running flush, although its probability is slightly higher. When two hands are equal, the winning hand is determined on the same principle as in poker. There are two exceptions. The highest hand is a prial of 3s, ranking above aces, and the highest run is A-2-3, ranking above A-K-Q. These rules must be understood and agreed by all players before play begins.

Strictly, runs and flushes are not recognised in brag, the classes of hand traditionally being Prial (or pair-royal), pair, or no-pair (highest card wins). More action is generated by three cards, known as braggers, being wild, the ace and 9 of diamonds and jack of clubs. A natural hand ranks higher than a hand of the same class with a bragger. Modern players Prefer to play the game as described above, although some impatient players like to speed 11 up further with the use of black 2s as wild.

A popular version of brag is seven-card brag, which can be played by up to seven players. Each player is dealt seven cards, discards one, and makes the two best brag hands he can with the remaining six. Each player puts an agreed stake into the pot before each deal. There is no betting, and a player must win both hands before he takes the pot. If the pot is not won, it remains for the next deal, when it is added to. Each successive deal in which the pot is not won makes the pot more worth winning. little strategy can be practised-in brag, as there is no draw and no indication of the opposing strength.

Players must know the probabilities in Figure 6:3 and the betting habits of their opponents. It is worth noting that with four players, a hand of ace high will be enough to win about half the deals, and a pair of aces over two-thirds of them.

Other Card Games

July 23, 2009 // Posted in gambling, multiple hands, poker (Tags: , , ) |  9 Comments

The former British Prime Minister, Harold Macmillan, enjoyed a variation of red dog and shoot called farmer’s joy, in which all players, including the dealer, put an ante into a pool, and the dealer then turns up the cards until a 7 or lower appears. He then deals three face-down cards to the players, who without looking at them bet in turn that they can beat the up card in its suit.

Ace counts high. The bet must be between one unit and the total units in the pool. The dealer deals one round before passing the cards to the next player. A player’s chances depend upon the number and suits of the cards turned up by the dealer before the final up card. If the first card turned is a 7, the player’s chance of beating it is about 7-4 against. If it is a 2, his chances are slightly better than 5-4 on winning. If the fourth card turned up is a 2, and it is the first of its suit, the player’s chance of winning becomes 17-12 on.

In the majority of deals. therefore, the player’s chance will be between 6-4 on and 6-4 against, and experience wi” soon teach a player to estimate it fairly accurately without doing the sums. There are, of course, several other card Black’s outer board 12 11 10 Black’s home board 6 5 4 3 2 1 12 11 10 9 White’s outer board 3 2 1 White’s home board Figure 6:5, the layout at the start of a game of backgammon. Traditionally, the home board is nearest the window or other source of light.

The actual board is not marked with any annotation, which is included to facilitate the explanation of the game. I 72 games designed specifically for gambling, many of them excellent games. Ecarte is a game for two players which Nico Zographos was fond of playing for small stakes before he took on the heavy punters at the Deauville and Monte Carlo baccarat tables.

It is a game with endless scope for studying probabilities. Pope Joan is a very old gambling game originally Played on an attractive decorated circular wooden table with compartments, some of which are found today in museums and ar>tique shops.

It is a pleasant game played °n one of these tables. A modern simpler Variation is the game known variously as newmarket, boodle and stops in Britain, and ?”chigan, Saratoga and Chicago in America, ‘hese games and others could well be disc. Ussed in this book, did space allow. Descrip- ‘ons of them can be found in authoritative °°ks on card games (see bibliography), and the reader can have the pleasure of working out the probabilities and optimum strategies for himself.