Double Down Strategy for Blackjack Another advanced blackjack strategy is the double down, which gives you a chance to double your wager and potential winnings after the initial deal. The idea is for you to lay an additional wager, but you can only get one more dealt card.
- In the double down strategy, the player is given a chance to double the bet in exchange for a stand after getting one more card. The extra bet is placed in the box next to the original bet. When playing in brick and mortar casinos, you may need to put the extra chips beside the original bet just outside the betting box, and pointing to it with one finger.
- I’ve been playing blackjack for quite awhile using basic strategy, mostly betting an even unit each hand. Occasionally I will increase the bet because I 'feel' like I am going to win the next one. I would think that just about all recreational players bet on feel once in a while at least.
A martingale is any of a class of betting strategies that originated from and were popular in 18th century France. The simplest of these strategies was designed for a game in which the gambler wins the stake if a coin comes up heads and loses it if the coin comes up tails. The strategy had the gambler double the bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake. The martingale strategy has been applied to roulette as well, as the probability of hitting either red or black is close to 50%.
Since a gambler with infinite wealth will, almost surely, eventually flip heads, the martingale betting strategy was seen as a sure thing by those who advocated it. None of the gamblers possessed infinite wealth, and the exponential growth of the bets would eventually bankrupt 'unlucky' gamblers who chose to use the martingale. The gambler usually wins a small net reward, thus appearing to have a sound strategy. However, the gambler's expected value does indeed remain zero (or less than zero) because the small probability that the gambler will suffer a catastrophic loss exactly balances with the expected gain. (In a casino, the expected value is negative, due to the house's edge.) The likelihood of catastrophic loss may not even be very small. The bet size rises exponentially. This, combined with the fact that strings of consecutive losses actually occur more often than common intuition suggests, can bankrupt a gambler quickly.
Intuitive analysis[edit]
The fundamental reason why all martingale-type betting systems fail is that no amount of information about the results of past bets can be used to predict the results of a future bet with accuracy better than chance. In mathematical terminology, this corresponds to the assumption that the win-loss outcomes of each bet are independent and identically distributed random variables, an assumption which is valid in many realistic situations. It follows from this assumption that the expected value of a series of bets is equal to the sum, over all bets that could potentially occur in the series, of the expected value of a potential bet times the probability that the player will make that bet. In most casino games, the expected value of any individual bet is negative, so the sum of lots of negative numbers is also always going to be negative.
The martingale strategy fails even with unbounded stopping time, as long as there is a limit on earnings or on the bets (which is also true in practice).[1] It is only with unbounded wealth, bets and time that it could be argued that the martingale becomes a winning strategy.
Mathematical analysis[edit]
The impossibility of winning over the long run, given a limit of the size of bets or a limit in the size of one's bankroll or line of credit, is proven by the optional stopping theorem.[1]
Mathematical analysis of a single round[edit]
Let one round be defined as a sequence of consecutive losses followed by either a win, or bankruptcy of the gambler. After a win, the gambler 'resets' and is considered to have started a new round. A continuous sequence of martingale bets can thus be partitioned into a sequence of independent rounds. Following is an analysis of the expected value of one round.
Let q be the probability of losing (e.g. for American double-zero roulette, it is 20/38 for a bet on black or red). Let B be the amount of the initial bet. Let n be the finite number of bets the gambler can afford to lose.
The probability that the gambler will lose all n bets is qn. When all bets lose, the total loss is
The probability the gambler does not lose all n bets is 1 − qn. In all other cases, the gambler wins the initial bet (B.) Thus, the expected profit per round is
Whenever q > 1/2, the expression 1 − (2q)n < 0 for all n > 0. Thus, for all games where a gambler is more likely to lose than to win any given bet, that gambler is expected to lose money, on average, each round. Increasing the size of wager for each round per the martingale system only serves to increase the average loss.
Suppose a gambler has a 63 unit gambling bankroll. The gambler might bet 1 unit on the first spin. On each loss, the bet is doubled. Thus, taking k as the number of preceding consecutive losses, the player will always bet 2k units.
With a win on any given spin, the gambler will net 1 unit over the total amount wagered to that point. Once this win is achieved, the gambler restarts the system with a 1 unit bet.
With losses on all of the first six spins, the gambler loses a total of 63 units. This exhausts the bankroll and the martingale cannot be continued.
In this example, the probability of losing the entire bankroll and being unable to continue the martingale is equal to the probability of 6 consecutive losses: (10/19)6 = 2.1256%. The probability of winning is equal to 1 minus the probability of losing 6 times: 1 − (10/19)6 = 97.8744%.
Blackjack Bet Spread
The expected amount won is (1 × 0.978744) = 0.978744.
The expected amount lost is (63 × 0.021256)= 1.339118.
Thus, the total expected value for each application of the betting system is (0.978744 − 1.339118) = −0.360374 .
In a unique circumstance, this strategy can make sense. Suppose the gambler possesses exactly 63 units but desperately needs a total of 64. Assuming q > 1/2 (it is a real casino) and he may only place bets at even odds, his best strategy is bold play: at each spin, he should bet the smallest amount such that if he wins he reaches his target immediately, and if he doesn't have enough for this, he should simply bet everything. Eventually he either goes bust or reaches his target. This strategy gives him a probability of 97.8744% of achieving the goal of winning one unit vs. a 2.1256% chance of losing all 63 units, and that is the best probability possible in this circumstance.[2] However, bold play is not always the optimal strategy for having the biggest possible chance to increase an initial capital to some desired higher amount. If the gambler can bet arbitrarily small amounts at arbitrarily long odds (but still with the same expected loss of 1/19 of the stake at each bet), and can only place one bet at each spin, then there are strategies with above 98% chance of attaining his goal, and these use very timid play unless the gambler is close to losing all his capital, in which case he does switch to extremely bold play.[3]
Alternative mathematical analysis[edit]
The previous analysis calculates expected value, but we can ask another question: what is the chance that one can play a casino game using the martingale strategy, and avoid the losing streak long enough to double one's bankroll.
As before, this depends on the likelihood of losing 6 roulette spins in a row assuming we are betting red/black or even/odd. Many gamblers believe that the chances of losing 6 in a row are remote, and that with a patient adherence to the strategy they will slowly increase their bankroll.
In reality, the odds of a streak of 6 losses in a row are much higher than many people intuitively believe. Psychological studies have shown that since people know that the odds of losing 6 times in a row out of 6 plays are low, they incorrectly assume that in a longer string of plays the odds are also very low. When people are asked to invent data representing 200 coin tosses, they often do not add streaks of more than 5 because they believe that these streaks are very unlikely.[4] This intuitive belief is sometimes referred to as the representativeness heuristic.
Anti-martingale[edit]
This is also known as the reverse martingale. In a classic martingale betting style, gamblers increase bets after each loss in hopes that an eventual win will recover all previous losses. The anti-martingale approach instead increases bets after wins, while reducing them after a loss. The perception is that the gambler will benefit from a winning streak or a 'hot hand', while reducing losses while 'cold' or otherwise having a losing streak. As the single bets are independent from each other (and from the gambler's expectations), the concept of winning 'streaks' is merely an example of gambler's fallacy, and the anti-martingale strategy fails to make any money. If on the other hand, real-life stock returns are serially correlated (for instance due to economic cycles and delayed reaction to news of larger market participants), 'streaks' of wins or losses do happen more often and are longer than those under a purely random process, the anti-martingale strategy could theoretically apply and can be used in trading systems (as trend-following or 'doubling up'). (But see also dollar cost averaging.)
See also[edit]
References[edit]
- ^ abMichael Mitzenmacher; Eli Upfal (2005), Probability and computing: randomized algorithms and probabilistic analysis, Cambridge University Press, p. 298, ISBN978-0-521-83540-4, archived from the original on October 13, 2015
- ^Lester E. Dubins; Leonard J. Savage (1965), How to gamble if you must: inequalities for stochastic processes, McGraw Hill
- ^Larry Shepp (2006), Bold play and the optimal policy for Vardi's casino, pp 150–156 in: Random Walk, Sequential Analysis and Related Topics, World Scientific
- ^Martin, Frank A. (February 2009). 'What were the Odds of Having Such a Terrible Streak at the Casino?'(PDF). WizardOfOdds.com. Retrieved 31 March 2012.
Playing with a strategy is the surest way to make money when playing Blackjack. Keep in mind when playing that the dealer must draw while he has 16 and must stand on 17, and that you don’t have to reach 21 to win, but only rank higher than the dealer. So don’t be tempted to hit in cases where the dealer is likely to bust.
When playing blackjack, it is important to be aware of the rules of the casino as this may impact on the strategy that you are looking to play. The above blackjack strategy chart is based on the following casino rules:
- The dealer will stand on a soft 17
- There are 4 to 8 decks
- Double after split
If the casino tells the dealer to hit when they have a soft 17, the following changes should be taken on board:
- When the dealer has an Ace, you should double hard 11
- When the dealer has a 2, you should double Ace-7
- When the dealer has a 6, you should double Ace-8
- When the dealer has an Ace, you should surrender at 15, 17 and at 8-8.
There are three separate categories of hands and each hand will have a chart.
Once you receive your two cards, you should look at the chart to find the corresponding cards on the chart’s left hand side. Next, you should observe the up-card of the dealer and then look for the value which corresponds to this at the top of the blackjack strategy chart.
The table to the right breaks down the moves of this blackjack strategy, where the left columns shows the player’s starting hand, and the right columns show what to do according to the dealer’s open card. The action you should take will be found in the box where the row and column intersect.
Hard Hands
In blackjack, the majority of hands are defined as hard hands. The basic definition of a hard hand is one that does not hold an Ace or a pair. Examples of hard hands will be K-5, 4-7 or 7-10.
Soft Hands
Any hand where there is an Ace present will be defined as a soft hand. This means that examples of a soft hand would be A-3, A-5 or A-Q.
Pairs
As you would expect, a pair occurs when your hand has two cards of the exact same value. Examples of pairs would be 4-4, 8-8 or Q-J. An A-A would also be referred to as a pair.
Blackjack Keep Doubling Bet
Knowing this information makes it easier to plan ahead and make the best decisions for whatever hand you have been dealt with. If you have been dealt an A-6 and the dealer has a 7 for an up-card, you should first of all start with the soft section of the chart. When you find A-6 and then compare it to the value under 7 for the dealer, you will see that the recommended advice is H, which means that you should hit.
When To Double Down
One of the more attractive options for blackjack players in a game comes when they have the chance to double down. This is only possible when a hand has two cards. This allows a player to double their bet and to take one (and one only) additional card to add to the hand. An example of this would when you hold an 11 from your initial two cards (a 7-4) and the dealer has a 5 for their up-card. This position would represent a strong opportunity to win from taking one more card so having the chance to increase the size of bet from this position would be sensible.
Players have the opportunity to double down up to the size of the original bet but there is no need to double down exactly. This means you “double down” for a smaller rate. It is important to bear in mind that by doing this you give up the rights to be able to receive another card but if the strategy indicates it, you should look to double down wherever possible.
When To Split Aces
Giving that splitting Aces can give players a great chance of winning well, many casinos will limit players to only being able to draw an additional card for each of the aces. It should also be remembered that if you split Aces and then draw a 10 or a card with a value of 10, most casinos will not consider this to be a blackjack and the 3:2 odds will not be applicable. These limitations may cause some players to question whether it is wise to split aces but yes, if the opportunity arises, you should always look to split Aces. This is because it increases the opportunity to hit 21 and as this is the main of blackjack, it is something that players should be looking out for.
The great thing about a blackjack strategy card is that it will provide you with advice for every single possible blackjack hand. It is also possible to use the advice in the charts for multiple totals. An example would be when you start with a 3-4 and then take the hit and you receive another 4, which will take you up to 11. You should then look at the hard section of the chart for 11, look along to find whatever the upcard dealer figure is and then make your decision based upon the advice provided. You will see from the hard section that if the dealer has an Ace for an upcard, you shout hit and if the dealer has any other card as an upcard, you should double hit, if you are allowed to.
It is important to remember that while a blackjack strategy will help you to play the advised moves and in the long run should help you to win more often, there is no such thing as a perfect strategy. A good blackjack strategy will help to lower the benefit of the house advantage for the casino but it will not be enough to totally negate it or overturn it. A good blackjack strategy can help players to perform better but losses can still can occur so make sure to only gamble with what you are comfortable losing.
How To Deal Blackjack
Blackjack Double Bet Strategy
All players are dealt two cards, that should be facing upwards while the dealer should give themselves two cards. One should be facing up and the other should be facing down.
The dealer should always look to see if their card is either a face card, a 10 or an Ace. If this has occurred, the dealer should say “Insurance”, which enables players to place an additional bet, to a value of equal to or less than their original bet. This insurance bet pays out at 2 to 1 if the dealer obtains blackjack.
Blackjack Strategy Sheet
The dealer should then look at their hole card and if they have blackjack, it should be stated right away. If this occurs, the house is the winner unless a player has also obtained blackjack. In this outcome, the hand will be determined as a push.
The dealer should then take it in turns to finish the request of every player, beginning with the player that is to the left of the dealer. If the player requests a hit, the dealer should provide them with a card. This process should continue until a player states that they are happy to stop or until they go bust, which is to go over 21.
Any player that requests a split, which can only occur if they hold a pair, should be given two cards, with one card going to each hand. There will be a need for the player to place an additional wager which is the same as their initial wager.
How To Bet Blackjack Chart
If a player wishes to double down, they should be provided with an additional card. The double down process sees a player placing an additional bet and they are only allowed to receive one additional card after doubling down.
What Is Free Bet Blackjack
The rest of the dealers hand should be played out once all of the players have completed their own hand. One the dealer reaches a value of at least 17, they should stop dealing themselves cards. At this point, the dealer should check to see if any card beats their hand, which is to check and see if any player has a hand that is closer to 21 than the dealers. Any player that has won should receive a payout of one to one.