Blackjack betting strategy wikipedia
The first scientific and mathematically sound attempts to devise a basic strategy were published by Roger Baldwin, et al in In , Edward Thorp published his findings of an optimal blackjack strategy using a high-speed digital computer. Julian Braun continued this work and published what most players know today as the correct basic strategy of the game. Foundational blackjack strategy is all about knowing what move gives you the best chance of winning based on the cards you and the dealer are currently showing. They’re basically a “cheat sheet” you can keep on hand to tell you what the best move is in any MATMM.MEg: wikipedia.
Martingale (betting system)
From Wikipedia, the free encyclopedia. Theorem 1: If a gambler risks a finite capital over many plays in a game with constant single-trial probability of winning, losing, and tying, then any and all betting systems lead ultimately to the same value of mathematical expectation of gain per unit amount wagered. Namespaces Article Talk. Casino game Game of chance Game of skill List of bets Problem gambling. See: Gambling games. The probability that the gambler will lose all n bets is q n. February
A betting strategy also known as betting system is a structured approach to gambling , in the attempt to produce a profit. To be successful, the system must change the house edge into a player advantage — which is impossible for pure games of probability with fixed odds, akin to a perpetual motion machine. Mathematically, no betting system can alter long-term expected results in a game with random, independent trials , although they can make for higher odds of short-term winning at the cost of increased risk, and are an enjoyable gambling experience for some people.
Strategies which take into account the changing odds that exist in some games e. Theorem 1: If a gambler risks a finite capital over many plays in a game with constant single-trial probability of winning, losing, and tying, then any and all betting systems lead ultimately to the same value of mathematical expectation of gain per unit amount wagered.
Some Horse racing betting systems can be based on pure statistical analysis of the odds, while others also analysis of physical factors e. Common forms of betting systems for horse racing are:. From Wikipedia, the free encyclopedia. Strategy for wagering. Gulf Professional Publishing. Retrieved See: Gambling games. Gambling mathematics Mathematics of bookmaking Poker probability. See: Gambling terminology. Casino game Game of chance Game of skill List of bets Problem gambling.
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.
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.
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.
Blackjack is the American version of a popular global banking game known as Twenty-One , whose relatives include Pontoon and Vingt-et-Un. Players do not compete against each other. It is played with one or more decks of 52 cards, and is the most widely played casino banking game in the world.
Players are each dealt two cards, face up or down depending on the casino and the table. In the U. In most other countries, the dealer only receives one card face up. The value of cards two through ten is their pip value 2 through Face cards Jack, Queen, and King are all worth ten. Aces can be worth one or eleven. A hand's value is the sum of the card values. Players are allowed to draw additional cards to improve their hands. A hand with an ace valued as 11 is called "soft", meaning that the hand will not bust by taking an additional card.
The value of the ace will become one to prevent the hand from exceeding Otherwise, the hand is called "hard". Once all the players have completed their hands, it is the dealer's turn. The dealer hand will not be completed if all players have either busted or received blackjacks. The dealer then reveals the hidden card and must hit until the cards total up to 17 points.
At 17 points or higher the dealer must stay. At most tables the dealer also hits on a "soft" 17, i. You are betting that you have a better hand than the dealer. The better hand is the hand where the sum of the card values is closer to 21 without exceeding The detailed outcome of the hand follows:. Blackjack has over rule variations.
Since the s, blackjack has been a high-profile target of advantage players , particularly card counters , who track the profile of cards that have been dealt and adapt their wagers and playing strategies accordingly.