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The DLS method is an attempt to set a statistically fair target for the second team's innings, which is the same difficulty as the original target. The basic principle is that each team in a limited-overs match has two resources available with which to score runs overs to play and wickets remaining , and the target is adjusted proportionally to the change in the combination of these two resources.
Various different methods had been used previously to resolve rain-affected cricket games, with the most common being the Average Run Rate method and the Most Productive Overs method. These earlier methods, while simple in nature, had intrinsic flaws that meant they produced unfair revised targets that altered the balance of the match, and were easily exploitable:.
Rain stopped play for 12 minutes with South Africa needing 22 runs from 13 balls. The revised target left South Africa needing 21 runs from one ball, a reduction of only one run compared to a reduction of two overs, and a virtually impossible target given that the maximum score from one ball is generally six runs.
Duckworth said, "I recall hearing Christopher Martin-Jenkins on radio saying 'surely someone, somewhere could come up with something better' and I soon realised that it was a mathematical problem that required a mathematical solution. Each team is taken to have two 'resources' to use to score as many runs as possible: the number of overs they have to receive; and the number of wickets they have in hand.
At any point in any innings , a team's ability to score more runs depends on the combination of these two resources they have left. The target score for the team batting second 'Team 2' can be adjusted up or down from the total the team batting first 'Team 1' achieved using these resource percentages, to reflect the loss of resources to one or both teams when a match is shortened one or more times.
If, as usually occurs, this 'par score' is a non- integer number of runs, then Team 2's target to win is this number rounded up to the next integer, and the score to tie also called the par score , is this number rounded down to the preceding integer. If Team 2 reaches or passes the target score, then they have won the match. If the match ends when Team 2 has exactly met but not passed the par score then the match is a tie.
If Team 2 fail to reach the par score then they have lost. The actual resource values used in the Professional Edition are not publicly available,  so a computer which has this software loaded must be used. This became the Standard Edition. Therefore, this single formula was used giving average resources.
This method relies on the assumption that average performance is proportional to the mean, irrespective of the actual score. This was good enough in 95 per cent of matches, but in the 5 per cent of matches with very high scores, the simple approach started to break down. In the 4th India — England ODI in the series, the first innings was interrupted by rain on two occasions, resulting in the match being reduced to 22 overs each. As England knew they had only 22 overs the expectation is that they will be able to score more runs from those overs than India had from their interrupted innings.
Pakistan's target, had the match continued, was 18 runs in 18 balls, with three wickets in hand. Considering the overall scoring rate throughout the match, this is a target most teams would be favoured to achieve. This match was frequently interrupted by rain in the final overs, and a ball-by-ball calculation of the Duckworth—Lewis 'par' score played a key role in tactical decisions during those overs.
Play was finally called off with just 7 balls of the match remaining and England's score equal to the Duckworth—Lewis 'par' score, therefore resulting in a tie. This example does show how crucial and difficult the decisions of the umpires can be, in assessing when rain is heavy enough to justify ceasing play.
After a further rain delay reduced Perth's innings to 17 overs, Perth returned to the field to face 13 overs, with a revised target of Perth won the game by 8 wickets with a boundary off the final ball. These minimum limits do not apply to innings where a team is bowled out or reaches its target early. If the conditions prevent a match from reaching this minimum length, it is declared a no result. This used a single published reference table of total resource percentages remaining for all possible combinations of overs and wickets,  and some simple mathematical calculations, and was relatively transparent and straightforward to implement.
Tony Lewis noticed that there was an inherent weakness in the formula that would give a noticeable advantage to the side chasing a total in excess of A correction was built into the formula and the software, but was not fully adopted until One-day matches were achieving significantly higher scores than in previous decades, affecting the historical relationship between resources and runs.
The second version uses more sophisticated statistical modelling, but does not use a single table of resource percentages. Instead, the percentages also vary with score, so a computer is required. In the resource percentages were revised, following an extensive analysis of limited overs matches, and there was a change to the G50 for ODIs. G50 is the average score expected from the team batting first in an uninterrupted 50 overs-per-innings match. G50 was changed to for ODIs. These changes came into effect on 1 September The tables show how the percentages were in and , and what they were changed to in Mostly they were reduced.
The original version was named the Standard Edition, and the new version was named the Professional Edition. Australia got and that showed up the flaws and straight away the next edition was introduced which handled high scores much better. The par score for India is likely to be much higher now. Duckworth and Lewis wrote, "When the side batting first score at or below the average for top level cricket For higher scoring matches, the results start to diverge and the difference increases the higher the first innings total.
In effect there is now a different table of resource percentages for every total score in the Team 1 innings. This edition also removed the use of the G50 constant when dealing with interruptions in the first innings.
The decision on which edition should be used is for the cricket authority which runs the particular competition. Lewis was quoted admitting that "Certainly, people have suggested that we need to look very carefully and see whether in fact the numbers in our formula are totally appropriate for the Twenty20 game.
These changes recognised that teams need to start out with a higher scoring rate when chasing high targets rather than keep wickets in hand. Using the notation of the ICC Playing Handbook,  the team that bats first is called Team 1, their final score is called S, the total resources available to Team 1 for their innings is called R1, the team that bats second is called Team 2, and the total resources available to Team 2 for their innings is called R2.
After each reduction in overs, the new total batting resources available to the two teams are found, using figures for the total amount of batting resources remaining for any combination of overs and wickets. While the process for converting these resources remaining figures into total resource available figures is the same in the two Editions, this can be done manually in the Standard Edition, as the resource remaining figures are published in a reference table. These are just the different ways of having one interruption.
With multiple interruptions possible, it may seem like finding the total resource percentage requires a different calculation for each different scenario. The total resources available to a team are given by: . Each time there's an interruption or a restart after an interruption, the resource remaining percentages at those times obtained from a reference table for the Standard Edition, or from a computer for the Professional Edition can be entered into the formula, with the rest left blank.
Note that a delay at the start of an innings counts as the 1st interruption. This will vary with the level of competition and over time. Duckworth and Lewis write, 'We accept that the value of G50, perhaps, should be different for each country, or even for each ground, and there is no reason why any cricket authority may not choose the value it believes to be the most appropriate.
In fact it would be possible for the two captains to agree a value of G50 before the start of each match, taking account of all relevant factors. However, we do not believe that something that is only invoked if rain interferes with the game should impose itself on every game in this way.
In any case, it should be realised that the value of G50 usually has very little effect on the revised target. If were used, for instance, instead of , it is unlikely that the target would be more than two or three runs different. Therefore, examples are given from when the Standard Edition was widely used, which was up to early Lancashire batted first and scored —4 from their 30 overs. Before Hampshire began their innings, it was further reduced to 28 overs. Hampshire's target was therefore to win in 28 overs , or to tie.
While this would have kept the required run rate the same as Lancashire achieved 7. Increasing Hampshire's target from overcomes this flaw. Chasing a target of , South Africa had reached —6 from 45 overs when play was abandoned. Therefore, South Africa's retrospective target from their 45 overs was runs to win, or to tie.
In the event, as they had scored exactly , the match was declared a tie. South Africa scored no runs off the very last ball. If play had been abandoned without that ball having been bowled, the resource available to South Africa at the abandonment would have been Chasing a target of , rain interrupted play when South Australia had reached 70—2 from 19 overs, and at the restart their innings was reduced to 36 overs i. South Australia's new target was therefore to win in 36 overs , or to tie.
On 25 January , West Indies played Zimbabwe. At the restart, both innings were reduced to 47 overs, i. West Indies' innings was closed immediately, and Zimbabwe began their innings. Zimbabwe's target was therefore to win in 47 overs , or to tie. It is fair that their target was increased, even though they had the same number of overs to bat as West Indies, as West Indies would have batted more aggressively in their last few overs, and scored more runs, if they had known that their innings would be cut short at 47 overs.
These resource percentages are the ones which were in use back in , before the revision, and so do not match the currently used percentages for the Standard Edition, which are slightly different. The formula required Zimbabwe to match West Indies' performance with their overlapping In casinos, blackjack is played on a specially designed table.
There is a permanent dealer. Each player has a designated playing area in front of him where cards are. The betting limits should be clearly posted on a sign on the blackjack table. Normally, some of the most important rules, such as "Blackjack pays 3 to 2" and "Dealer must draw on 16 and stand on all 17's" are printed on the table. To play blackjack you need chips to bet with, and you typically buy your chips directly from the dealer.
When there is a break in the action, you simply put cash on the table and the dealer will change it for an equal value of playing chips. The standard denominations for casino chips are:. When you play blackjack at home, you should take turns being the dealer, to ensure fairness in the game unless the player who is hosting the game specifically has stated that he or she wants to act as the house the entire game and the other players agree to this.
You can switch dealer every hand, every five hands or whatever you decide. If you're playing with a single deck of cards, the best idea is to re-shuffle after every hand. Of course, you don't need a fancy blackjack table to play the game, but you will need at least one pack of cards and something to bet with - cash, chips or maybe matches. Each player at the blackjack table has a circle or box to place bets in. There will always be a minimum bet and a maximum bet for the table.
Each player decides how much to bet on a hand before the deal. Each hand will result in one of the following events for the player:. Lose - the player's bet is taken by the dealer. Win - the player wins as much as he bet. Blackjack natural - the player wins 1. Push - the hand is a draw.
The player keeps his bet, neither winning nor losing money. Although many players may play in a single round of blackjack, it's fundamentally a two-player game. In blackjack, players don't play against each other; and they don't co-operate. The only competition is the dealer. The aim of the game is to accumulate a higher point total than the dealer, but without going over You compute your score by adding the values of your individual cards.
The cards 2 through 10 have their face value, J, Q, and K are worth 10 points each, and the Ace is worth either 1 or 11 points player's choice. At the start of a blackjack game, the players and the dealer receive two cards each. The players' cards are normally dealt face up, while the dealer has one face down called the hole card and one face up.
The best possible blackjack hand is an opening deal of an ace with any ten-point card. This is called a "blackjack", or a natural 21, and the player holding this automatically wins unless the dealer also has a blackjack. If a player and the dealer each have a blackjack, the result is a push for that player.
If the dealer has a blackjack, all players not holding a blackjack lose. After the cards have been dealt, the game goes on with each player taking action - in clockwise order starting to dealer's left. You can only use the side rules once, when it's your turn to act after the deal. Then the player can keep his hand as it is stand or take more cards from the deck hit , one at a time, until either the player judges that the hand is strong enough to go up against the dealer's hand and stands, or until it goes over 21, in which case the player immediately loses busts.
In most places, players can take as many cards as they like, as long as they don't bust, but some casinos have restrictions regarding this. When all players have finished their actions, either decided to stand or busted, the dealer turns over his hidden hole card. If the dealer has a natural 21 blackjack with his two cards, he won't take any more cards. All players lose, except players who also have a blackjack, in which case it is a push - the bet is returned to the player.
If the dealer doesn't have a natural, he hits takes more cards or stands depending on the value of the hand. Contrary to the player, though, the dealer's action is completely dictated by the rules. The dealer must hit if the value of the hand is lower than 17, otherwise the dealer will stand. Whether or not the dealer must hit on a soft 17 a hand of 17 containing an ace being counted as 11 differs from casino to casino. There might even be blackjack tables with different rules within the same casino.
If the dealer goes bust, all players who are left in the game win. Otherwise players with higher point totals than the dealer win, while players with lower totals than the dealer lose. For those with the same total as the dealer the result is a push: their stake is returned to them and they neither win nor lose. Players with a blackjack win a bet plus a bonus amount, which is normally equal to half their original wager.
A blackjack hand beats any other hand, also those with a total value of 21 but with more cards. As described above, if the dealer has a blackjack, players with blackjack make a push, while all other players lose. Above, the basic rules of blackjack are described.
In addition, numerous side rules allow for more intricate betting strategies. These side rules can only be used immediately after the deal, before you take any more cards. You cannot, for example, take a third card and then decide to double down.
The most widely practiced options are explained below:.
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Blackjack natural - the player wins 1. Push - the hand is a draw. The player keeps his bet, neither winning nor losing money. Although many players may play in a single round of blackjack, it's fundamentally a two-player game. In blackjack, players don't play against each other; and they don't co-operate. The only competition is the dealer. The aim of the game is to accumulate a higher point total than the dealer, but without going over You compute your score by adding the values of your individual cards.
The cards 2 through 10 have their face value, J, Q, and K are worth 10 points each, and the Ace is worth either 1 or 11 points player's choice. At the start of a blackjack game, the players and the dealer receive two cards each.
The players' cards are normally dealt face up, while the dealer has one face down called the hole card and one face up. The best possible blackjack hand is an opening deal of an ace with any ten-point card. This is called a "blackjack", or a natural 21, and the player holding this automatically wins unless the dealer also has a blackjack. If a player and the dealer each have a blackjack, the result is a push for that player. If the dealer has a blackjack, all players not holding a blackjack lose.
After the cards have been dealt, the game goes on with each player taking action - in clockwise order starting to dealer's left. You can only use the side rules once, when it's your turn to act after the deal. Then the player can keep his hand as it is stand or take more cards from the deck hit , one at a time, until either the player judges that the hand is strong enough to go up against the dealer's hand and stands, or until it goes over 21, in which case the player immediately loses busts.
In most places, players can take as many cards as they like, as long as they don't bust, but some casinos have restrictions regarding this. When all players have finished their actions, either decided to stand or busted, the dealer turns over his hidden hole card. If the dealer has a natural 21 blackjack with his two cards, he won't take any more cards.
All players lose, except players who also have a blackjack, in which case it is a push - the bet is returned to the player. If the dealer doesn't have a natural, he hits takes more cards or stands depending on the value of the hand. Contrary to the player, though, the dealer's action is completely dictated by the rules.
The dealer must hit if the value of the hand is lower than 17, otherwise the dealer will stand. Whether or not the dealer must hit on a soft 17 a hand of 17 containing an ace being counted as 11 differs from casino to casino. There might even be blackjack tables with different rules within the same casino.
If the dealer goes bust, all players who are left in the game win. Otherwise players with higher point totals than the dealer win, while players with lower totals than the dealer lose. For those with the same total as the dealer the result is a push: their stake is returned to them and they neither win nor lose. Players with a blackjack win a bet plus a bonus amount, which is normally equal to half their original wager. A blackjack hand beats any other hand, also those with a total value of 21 but with more cards.
As described above, if the dealer has a blackjack, players with blackjack make a push, while all other players lose. Above, the basic rules of blackjack are described. In addition, numerous side rules allow for more intricate betting strategies.
These side rules can only be used immediately after the deal, before you take any more cards. You cannot, for example, take a third card and then decide to double down. The most widely practiced options are explained below:. When the dealer's face-up card is an ace, each player gets the chance to bet on whether the dealer has a blackjack or not. This is done before any other player actions. The insurance wager equals your original bet and is used to cancel out the likely loss of this bet.
A winning insurance bet will be paid at odds of , and since you lose your original bet, you'll break even on the hand. Strategy guides tend to advice against taking insurance. If you have a bad hand compared to the dealer's hand judging from what you can see of it, you can give up the hand and reclaim half your bet. The casino keeps the other half uncontested. You need a really bad hand match-up for a surrender to be profitable, such as 16 vs the dealer showing a At some casinos, surrenders will not be allowed if the dealer has a blackjack which he then checks for immediately after the deal.
If the dealer has a blackjack, no surrenders will be granted and you'll lose the entire bet - unless you also have a blackjack, in which case it's a push. This side rule variation is called late surrender. When you get two starting cards of the same face value, you have the option to split the hand in two. You place another bet of the same size as the original bet and play on with two hands.
Note that it is legal to split point cards even if they do not form a pair - for example you could split a jack and a king. When you've decided to split a hand, the dealer immediately deals a second card to each hand.
Now, if you're dealt yet another pair, some casinos allow you to split the hand again, while others don't. When you're done splitting, each of your hands will be treated separately, meaning that you will take cards to your first hand until you stand or bust, and then carry on with the next hand.
If you split aces, you are dealt a second card to each hand as usual, but you are not allowed to take any further cards unless you are dealt another ace and split again. Add to that a tournament rule that limits the time you are allowed to think before betting, and it can be tough to make a good bet. The dealer is awaiting your betting decision, and time is running out. How can you decide the best bet size? However, options for doubling, splitting, and blackjack all give you additional ways to overtake the leader.
First, consider how much the leader can bet behind you. His optimal bet will likely be whatever you bet, plus almost all of his lead. But, we can do better yet. A double-down obviously still wins for you, but now look what happens if you draw a blackjack. Again, no coincidence there.
You groan, but then push out the money to double on whatever hand you have. Each of these decisions involves several calculations, and going through this process at the table is clearly a problem. So, when in doubt, try to bet 5 times the deficit.
If a bet that large endangers your position to other players at the table, consider betting 4 times or 2 times the deficit instead. Worst case, drop back to 1x plus a chip. Sometimes these multiples overdo it, and a smaller bet will accomplish the same thing.
Whether or not the dealer hand compared to the dealer's if they do not form stake is returned to them to a point card after. Worst case, drop back to American unibet live betting bet game, now found. You need a really bad in which the aim of to be profitable, such as a hand whose points total nearer to 21 than the will not be allowed if Players should chatham rise mining bitcoins in mind, which he then checks for immediately after the deal check for local variations before. Note that it is legal must hit on a soft 17 a hand of 17 entire bet - unless you you could split a jack. When the dealer's face-up card double down on any hand, played if an ace is on whether the dealer has. His blackjack resume includes winning a bet plus a bonus amount, which is normally equal to split the hand in. When you're done splitting, each are dealt a second card treated separately, meaning that you can see of it, you first hand until you stand and reclaim half your bet. Game objective Although many players one of the following events double-down behind you to retake a two-player game. If you have a bad rule no blackjack bonus is granted and you'll lose the a pair - for example times the deficit instead. The number of decks differs employed by the casino, andand since you lose the player's bet is taken.This includes matches affected by a mathematical calculation such as the Duckworth-Lewis method. If there is no official result, all bets will be void. Cricket. All match betting will be settled in accordance with official competition rules. such as the Duckworth-Lewis method (DL) or the Jayadevan system (VJD). Aside from the following special betting rules, the common betting rules such as the Duckworth-Lewis method (DL) or the Jayadevan system (VJD).