Rummikub - To Practice Set Theory, Groups, and Probability Part 2

Scoring Scoring in Sabra is exactly the same as in American. Each loser adds up the values of the tiles left on his rack, counting 30 points for a joker and face value for all other tiles, and scores this as a minus (negative) amount. The sum of all the losers’ scores is credited to the winner as a plus amount. At the end of the session, each player’s final score is totaled for the final results. The total of the plus scores should equal the total of the minus scores if all the arithmetic has been done correctly. In the rare case that all the tiles are used up before anyone goes Rummikub®, the player with the lowest count remaining on his rack is considered the winner. Each of the losers adds up his total remaining tile value, subtracts the winner’s total and scores the result as a minus amount, and the winner gets a plus score by totaling the losers’ scores. Strategy As you can see, the combinations and rearrangements in Sabra are endless, and as the game progresses the manipulating gets wilder. The beginning of a round may seem slow, especially if your initial meld is slow in coming in, but as the table fills up, the possibilities multiply and the opportunities to get rid of all those tiles that were piling up on your rack grow more and more varied. You have to think fast – and rethink as the plays you had in mind disappear before the turn comes around to you! In the early part of the game it is often good strategy to hold back and let the other players “open up the table” so that you can play off their tiles. When melding in the early part of the game, before the table is very full, it is wise to hold back the fourth tile of a Group or Run and meld only three, so that at your next turn you will have a meld to make and won’t have to draw a tile. Of course someone else might have the same tile, or manipulate the melds in a way which prevents you from using your tile. However, if you hold 7-7-7-7 in a Group and there is another 7 on the table, then you are pretty safe in holding back your 7 in the matching color. The fact that the tiles in any set containing a joker are frozen is also important strategically. For instance, let’s say that the table holds a yellow Run 8-9-10 and also a Group with yellow 11 – red 11 – joker. You hold the other yellow 11. You know that no one can manipulate the Group of 11’s, so you’re safe in holding out your yellow 11 until your next turn, when you can add it to the Run. INTERNATIONAL International is by far the most complicated and the most varied of the three versions of the game described in this book. Each player chooses from three different approaches to winning the game, and one of these approaches is further subdivided into forty different winning combinations. If that sounds intriguing, then you will enjoy playing the International way. Even the scoring of International is unusual. Not only are the final scores astronomical, but the method for computing them has been devised to add more spice to an already absorbing contest. As play proceeds the leading players receive minus scores for their efforts, but then at the end of the game session you perform some mathematical hanky-panky, and presto! When the final scores are calculated the winners are plus and the losers are minus, and you know exactly who owes what, and to whom. Set-up This game requires four or five players. When five people play the fifth player acts as dummy, sitting out the opening of the game and cutting in at regular intervals. To determine the dealer, the seating arrangement and, if necessary, the player who will be dummy, select four (or five) tiles in numerical sequence, place them face down on the table, shuffle and draw. High tile is the dealer, next highest sits to his right, and so on counter-clockwise around the table. The fifth player is dummy. He does not play until four rounds have been completed. He then replaces player #4 for four rounds, and after four more rounds player #4 comes back into the game, replacing player #3, and so on around the table. After the players have been seated according to the draw, place all the tiles face down on the table, shuffle them and then arrange all 106 tiles in stacks of seven. The odd tile, also face down, goes on top of the first stack, and the top tile of the last stack is turned face up to become the trump. The dealer deals out the stacks one at a time in two counter-clockwise rounds of the table, starting with player #2 on his right, who will have 15 tiles instead of 14. Players study their tiles and arrange them on their racks. Player #2 discards an unwanted tile, placing it face up on the table to his right, and the game begins. The object of the game is to be the first to get rid of all 14 tiles. This may be accomplished by putting together any of the 40 combinations to be described or by melding. Play is counter-clockwise and continues until one player declares himself the winner by calling “Rummikub®.” The Play of the Game A player at his turn may draw a tile from the pool or he may choose instead, whether or not he has already melded, to pick up the top discard tile of the player on his left. For his final draw he may take the trump tile to complete a Hand. Each player must pick up one tile and must discard one tile at each turn, so that the total remains 14. Discards are placed on the table to the player’s right, face up, and neatly stacked so that only the top tile is visible. You cannot win with 15 tiles. In order to declare yourself Rummikub® you must discard a tile, which you place upside down on your discard pile to indicate that the game is over. Then you display the tiles on your rack to the other players. The Meld Melding sets on to the table is relatively unimportant in international Rummikub®. It occurs only if a player decides to play the Open version, in which case the initial meld must total a whopping 50 points – a deterrent in itself. Tile 1 may be considered either high or low, but not both. That is, 1-2-3 is a valid run and so is 12-13-1, but not 13-1-2. As in American and Sabra, melding consists of laying sets on the table face up, or in adding tiles to a meld already on the table. Once a meld has been made it cannot be manipulated or taken back onto your rack. Jokers The joker may be substituted for any missing tile. Its value is the same as the missing tile. A player holding the missing tile may at his turn exchange it for a melded joker, but he must then use the joker immediately in another meld onto the table. He must then, of course, continue to play an Open game. If a player goes Rummikub® by discarding a joker, all scores for the round are doubled. The Winning Variations There are three ways to win in International Rummikub®. In order of their value they are Open, Foot, and Hand. There are 40 different Hand combinations as described on the following pages, but don’t let this discourage you. Each of these combinations is related in some way to the familiar idea of sets, and many are simple variations of point value or color. In any case, you are permitted to keep the list handy to consult as you play, along with the scoring table. In fact, it’s a good idea for each player to have his own. Open This is the only version of International which involves melding. The play is almost identical to the basic game of American with these two exceptions: 1. You need 50 points for your initial meld. 2. You may pick up your left-hand opponents top discard instead of drawing from the pool at your turn, whether you have melded or not. When you play an Open game and you have only three tiles remaining on your rack, you must announce it. When you are left with only one tile on your rack, you may only draw from the pool, not from the discard of your left-hand opponent. Playing an Open game, you may not draw the trump. Foot Foot is a closed game in which you do not meld at all, but accumulate tiles on your rack, even though you are in a position to make an initial meld. You may not meld individual tiles onto the melds of other players during the play of the round, but you may do so when you finally declare Rummikub® and expose all your tiles. To win a Foot you must be able to get rid of all of your tiles by organizing them into sets or adding them onto the melds of others. You must have at least one Run and the total of your 14 tiles must be at least 50. You may not pick up the trump tile as your final draw. It is not possible to win a Foot game unless someone is playing an Open game. If you can organize all of your tiles into sets without adding to an Open player’s melds, then you have a more valuable Hand combination. Hand All Hands are played closed. You do not meld at all, but expose your entire rack when you declare Rummikub®. These are the real “money” wins, ranging in value from 300 to 2600 points. There are 40 different winning configurations, each of which has three different point values. A Hand with no jokers scores highest, with one joker next, and two jokers least. For example, the basic Hand #1 scores 500 points with no jokers, 400 with one joker, and 300 with two jokers. The table below gives the scores for each Hand with and without jokers. This table should be available for any player to consult throughout the game. The Trump The trump tile plays an important role in the Hand game. Any player may draw the trump to finish out his Hand and win the game. Knowing that it is yours if you need it, you should consider it as one of your tiles throughout the round. If the trump is a joker it makes for a very exciting game indeed. It represents the winning tile to any player who is one tile away from winning – and that may mean “sudden death” for the other players. Winning Hand Game Arrangements In all of the Hands listed here which depend on the total number of points for the 14 tiles, the joker is counted the same as the tile it replaces, with one exception. For Piccolo 41 Odd, the joker is not counted in the total. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. Hand #1 – This is the basic winning pattern. All 14 tiles are in sets, including at least one Run. Hand Minor – Same as Hand #1 but including no tile higher than a 9. Tile 1 is low. Hand Minor 51 – Same as Hand Minor but the total value of all tiles adds up to 51 or less. Minor 51 Groups – Consists of Groups only with no tile higher than a 9 and the total of all 14 tiles adding up to no more than 51 points. Minor 51 Runs – Consists of Runs only with no tile higher than a 9 and the total of all 14 tiles adding up to no more than 51 points. Piccolo 41 Odd – Unmatched tiles, with or without sets, whose total is no more than 41 points. The joker is not counted in the total. Piccolo 41 Sets – Consists of sets only, either Groups or Runs, whose total is no more than 41 points. Piccolo 41 Runs – Consists of two, three, or four Runs with the tiles adding up to no more than 41 points. Piccolo 41 Groups – Four Groups, two of three tiles and two of four tiles, adding up to no more than 41 points. Grand Odd – Unmatched tiles, with or without sets, consisting entirely of tiles from 10 up, with the 1 tile considered high. The total value of the tiles does not matter. Grand Sets – Runs and Groups using only tiles from 10 up, with the 1 tile considered high. Grand Square – Contains eight tiles of the same numerical value; the other six tiles don’t matter. Four Colors – Four Runs of any value, each in a different color. Four Colors Minor – Same as Four Colors but including no tile higher than a 9. Four Colors Major – Same as Four Colors but including no tile higher than a 10. Three Colors – Consists of three Runs, each in a different color. Total tile value does not matter. Three Colors Minor – Same as Three Colors but including no tile higher than a 9. Three Colors Major – Same as Three Colors but including no tile higher than a 10. Two Colors – Either two, three, or four Runs, using tiles of only two colors. Two Colors Minor – Same as Two Colors but including no tile higher than a 9. Two Colors Major – Same as Two Colors but including no tile higher than a 10. Single Color Odd – The tiles are all in one color, but not in sets. Single Color Runs – Two, three, or four Runs, all of the same color. Royal – One single Run from low 1 to high 1. Sticks – Groups only, two of three tiles each and two of four tiles each. Sticks Minor – Same as Sticks but including no tile higher than a 9. Sticks Major – Same as Sticks but including no tile higher than a 10. Mosaic – One single Run from low 1 to high 1, with no two consecutive tiles of the same color. The two 1’s may be of the same color. Little Wave – Two separate Runs, from 1 to 7, with no two consecutive tiles of the same color. 30. Big Wave – Two separate Runs, from 8 to high 1, with no two consecutive tiles of the same color. 31. Little Wave Single Color – Two Runs from 1 to 7, both in the same color. 32. Big Wave Single Color – Two Runs from 8 to high 1, both in the same color. 33. Little Wave Two Colors – Two Runs from 1 to 7, each in a different color. 34. Big Wave Two Colors – Two Runs from 8 to high 1, each in a different color. 35. Seven Pairs – Seven pairs of identical tiles, regardless of color. 36. Seven Pairs Minor – Same as Seven Pairs but including no tile higher than a 9. 37. Seven Pairs Major – Same a Seven Pairs but including no tile higher than a 10. 38. Seven Pairs Single Color – Seven pairs of identical tiles, all in the same color. 39. Little Blitz – This occurs if you can declare yourself Rummikub® on your first turn after picking up your draw from one of the following: the pool, the discard of the player on your left, or the trump. 40. Grand Blitz – This occurs when your original 14 tiles form one of the Hands described above. You declare yourself Rummikub® at your turn without drawing at all. The player who is dealt 15 tiles originally can claim Little Blitz, but not Grand Blitz. Scoring Results for each game are computed by negative scoring. The winner of each round receives minus points. All the others – the losers – score plus points. As you will see, this is switched around in the final scoring so that the winners and losers for the day are clearly indicated. If the round is not finished by the time the entire pool is used up, scoring is as follows: Any player who has not melded receives 100 minus points. A player who has melded scores plus points for the sum of the tiles remaining on his rack. If a player wins by discarding a joker, all scores are doubled. If the winner’s score has been doubled because he discarded a joker as his final discard, then the losers’ scores are likewise doubled. The winner of an Open game scores minus 100 points. A Foot scores minus 200 points. If the winner of an Open game is the only player to have melded, he scores minus 200, as if he had won a Foot. The number of jokers, or the lack of them, does not matter in the scoring of Open or Foot. The scores of each winning Hand from #1 to #40, with no joker, one joker or two jokers, are listed in the following table. The winner scores the indicated amount as minus points. The losers all score plus points as follows: A player who has melded scores only the value of the tiles remaining on his rack, regardless of how much the winner has scored. The value of the tiles left in an Open player’s rack are face value for tiles 2 thru 10. Tiles 11 thru 1 are counted as 10 points each. To make the scoring easier many players adopt a table rule which states that, after adding the tiles left on a losing player’s rack, the total is rounded off to the next highest 10-point division. For example, 14 points are scored as 20, 51 points count as 60, and so on. A player who has not melded at all in a game which is won by an Open player or by a Foot scores plus 100 points. A player who has not melded at all in a game which is won with a Hand loses the exact amount that the winner has scored. That is, if one player goes Rummikub® with no jokers, Single Color Odd, he scores minus 1600 points, and any player who has not melded receives 1600 plus points for that round. A popular table rule which you might consider adopting involves the trump. According to this rule the player who has the tile which matches the trump, either in his original 14 tiles or later by drawing it, is entitled to an extra 50 minus points. This holds true for a joker as well as numerical tiles. If you decide to include this rule in your game, be sure that everyone agrees to it in advance, and remember to announce the matching tile and claim the 50 points during the course of the round. Strategy of the Open Game Winning an Open game pays the least amount of points – a mere 100, compared with anywhere from 300 to 2600 for winning with a closed Hand. However, playing Open does ensure that you will lose only a modest amount if an opponent should win. Once you have melded, all you will lose is the value of the tiles left on your rack. If an opponent goes out while your 14 tiles are still intact, you lose the exact amount that he wins, and that can be anywhere from 300 to 2600 points! At the same time, winning an Open game is usually easier than winning a Hand, and it may be your only way to end up with a winning score, no matter how small. Winning is always better than losing! Sometimes the discards of your opponents will tell you that you cannot possibly win a Hand. If you cannot reasonably switch to a different Hand, switch to an Open game. As the game progresses, if you feel that one of your opponents is about to go Rummikub®, that is certainly a good time to “chicken out” and cut your losses – provided, always, that you have 50 points to make the initial meld. Your tactics will also be influenced by the fact that one or more of your opponents has melded. Each time one of them switches to an Open game, it gives you more reason to hold out for a big Hand. That is, it decreases your chances of losing a large number of points since an Open player can only win 100 points, and that is all you will lose. Strategy of the Foot Game As soon as an opponent has melded, re-examine your tiles to see if you can convert a Hand which still lacks several tiles into a winning Foot game. Unless you are quite close to winning a large Hand, and think that your chances are good, it may be tactically wise to take a lesser win that is sure – the Foot game is worth 200 points – rather than gamble on the big win, with the accompanying big loss if you fail. Strategy of the Closed Game Remember that the more players who opt for the Open game, the less you have to lose and the more attractive it will be to hold out for a valuable win. If an Open player wins, you can lose only a modest amount, so the odds are on your side to hold out. Keep in mind a possible switch if the Hand you are aiming for fails to come in, or if the melds or discards of the other players inform you that it is impossible to make. For example, if you are playing for one of the Minor Hands, and hold only low-numbered tiles, you may be able to switch to Piccolo 41 Odd if necessary, or if you’re holding all high tiles, Grand Odd may be your way to win. Becoming familiar with the various patterns and learning to associate the related patterns makes you a flexible player – and a winning one. You should also realize that if you try for certain Hands it may be quite difficult to switch to an Open game on short notice. If you see a key tile in your planned Seven Pairs go into a discard pile across the table, it may be very hard to put together an initial meld which will let you switch to a safer Open game. Keep your eye on the trump tile at all times. Remember, it is yours if you need it to win. If an opponent picks up many tiles from the player on his left, this is a fair indication that he may be close to winning. Unless you happen to know that he frequently picks up tiles on speculation, considering melding to guard against a loss. Try not to “feed” the player on your right the tiles you think he may need. If he has picked up a high tile from your discard pile and then picks up a second seemingly unrelated high tile from you, by very, very cautious about feeding him a third! If at such a time you have the option of settling for a lesser win than the one you’ve set your heart on, in order not to give him a tile you think he needs to win, by all means do so. Try not to discard a tile which could be added to an existing meld. The player on your right may be one tile away from a Hand and decide to switch to a Foot for a quick win by drawing your discard and getting rid of his unwanted tile. By the same token, if there are melds on the table and you are one away from winning a Hand, consider drawing your left-hand opponent’s discard, or using a blind draw, to take a quick win with a Foot. Remember that after several turns around the table the chances that another player will win grow greater, and that means that your chances of losing increase accordingly. If all four players are closed, the gambling element is the greatest. Your own personality, as much as the tiles you hold, will dictate whether you go on with the gamble or “chicken out” and play it safe by melding. Calculating the Final Score Scores are entered after each round on a scorepad with a column for each player. To total each column at the end of the playing session, you add up a player’s minus scores and his plus scores separately. Subtract the smaller sum from the larger and give the result the same sign – plus or minus – as the larger figure. For example, a player’s wins total minus 3210 points and his losses total plus 1530. You write down the difference, 1680, as a minus at the bottom of the column. It is possible to keep a running score, adding and subtracting as you enter the score for each new round. If you prefer this method of scoring, add an extra column in which to enter the amount the winner receives for each round, in case it becomes necessary to check back on the accuracy of the scoring. Now comes the fun part! It sounds more complicated than it really is, and it adds a little International spice to the game. So sharpen your pencil and do a little simple arithmetic in order to figure out the end result of an exciting session of International Rummikub®. Sample Score for Four Players (a) Total Scores (b) Addition Factor (c) Primary Scores Player No. 1 -1200 +2320 +1120 (d) Sum of Primary Scores +29760 (e) Primary Scores x4 +4480 (f) Final Scores +25280 Player No. 2 +7800 +2320 +10120 Player No. 3 -2320 +2320 0 Player No. 4 +16200 +2320 +18520 +29760 +40480 -10720 +29760 0 +29760 +29760 +74080 -44320 The totals of each player’s column, line (a) in the example above, will now contain both plus and minus scores, but they do not tell you exactly how much each player has won or lost. As you can see, Players 1 and 3 were winners and Players 2 and 4 lost, but how much? Our first step is to convert all scores into plus amounts, and to do this we add the same number, an Addition Factor, to each column, line (b) above. This number can actually be any random number, since it will be used equally in each player’s column, but the easiest way to pick the Addition Factor is to change the sign of the largest minus to plus, as shown. In our example -2320 is the largest minus score, so we add 2320 to each player’s score at line (b). This gives us each player’s “primary score”, line (c). Next we add all of the primary scores together, and write in this sum below each primary score as line (d). Now, multiply the primary score of each player by 4 and write down the product in each column as line (e). We are almost at the end of our International machinations. We subtract line (e) from line (d) and we arrive at line (f), the final score for each player. As you can see, the winners, Players 1 and 3, now have plus scores. Player No. 1 has won 25280 points (dollars? drachma? rubles?) and Player No. 3 has won 29760 points. The losses of Players 2 and 4 are 10720 and 44320 points respectively. Their sum is equal to the sum of the winnings, which proves that our computations have been correct. If you would like to save a little time and don’t mind remembering a short formula you can avoid some of the math involved. When you have arrived at the total scores of each player, simply switch the plus or minus sign of your score, multiply by 3 and add the result to the scores of the other players. For instance, Player 1 had -1200 as a total score in our sample scoring. Using the shortcut formula we simply change the minus sign to a plus (1200), multiply by 3 (3600) and add the totals of the other three players (21680) to get the same final score, 25280. Sample Score for Five Players In computing the score for five players, you multiply the primary score of each player by five instead of four. (a) Total Scores (b) Addition Factor (c) Primary Scores Player No. 1 +3600 +1200 +4800 (d) Sum of Primary Scores +22030 (e) Primary Scores x4 +24000 (f) Final Scores -1970 Player No. 2 -1200 +1200 0 Player No. 3 +6060 +1200 +7260 Player No. 4 +3250 +1200 +4450 Player No. 5 +4320 +1200 +5520 +22030 0 +22030 +22030 +36300 -14270 +22030 +22250 -220 +22030 +27600 -5570 If you choose to use the shortcut method for figuring scores in an International session with five players, simply multiply your own score by 4 instead of 3 before adding the scores of your opponents. To take the first example shown in the sample scoring, Player 1 had 3600 as a total score. Using the shortcut formula we change the sign to minus (-3600), multiply by 4 (-14400) and add the totals of the other four players (12430) to get the final score, -1970.