Blackjack is a card game, which has a combination of relatively simple rules, more or less predicted mathematical expectation of winning and mathematical correlation of probability of winning with the cards, which already have been in the use in the deck. Due to its simplicity, it is popular all over the world. Due to a lot of math involved in counting cards and expecting a certain outcome, it is also popular in professional gamblers and mathematicians.
Let’s skip the part with a description of rules (as you can become acquainted with them on your own on the Internet, as well as with the issue of what are Blackjack cards) and jump straight to existing tips and strategies of winning in blackjack.
Strategies of winning blackjack
- Know which cards to split in Blackjack. When a player has two cards of the same value, he may be offered by a dealer to split. But not all cards are equally useful when been split. Thus, why shouldn’t you split 10s in Blackjack, as well as any other two cards with pictures (J, Q, K) or pictures with ten is because this guarantees you to have 20 points – only one point from blackjack. The probability of victory holding these cards is huge. The same is true for a pair of 9s. On another hand, there are 8s, splitting which is almost always recommended because they give you 16, which is a no-way certain way to win from a math probability point of view. By splitting eights, you gain bigger chances of winning in each particular hand, not gaining too many points.
- Don’t make any additional bets (in addition to bet on splitting) because they all lead you to the loss in the long run. No matter what Blackjack insurance you do, the mathematical expectation of losing it is more than 2/3. Why? According to what we know about all possible probabilities in this game, the chances that a dealer will have a blackjack when he’s having ten-point card or ace is 4/13, which is 30.8% – it is lesser than 1/3. If you make a bet for insurance, when a dealer does have blackjack, you lose your basic bet and win the insurance bet in the proportion of 2:1, only eliminating any possible losses. If a dealer does not have blackjack, you lose your insurance, staying with your main bet. Losing insurances in the long run makes you lose money step by step.
- Counting cards. In the deck(s) used to play blackjack, every played card is assigned with a +1, 0 or -1 number, which makes it possible to swiftly calculate the probability of your winning depending on how many cards are left there. The lesser is the number, the lesser math expectation of winning you have, and vice versa. So, the bigger the current count is, the earlier you have to stop picking more cards or do the split.
Existing mathematical method
Aside from the mentioned methods of the game and the ability of players to do anything in the game, there is a purely investment-based method, which was elaborated by mathematician, scientist, and financial advisor John L. Kelly in 1956. It is called the Kelly criterion. The criterion is applicable only to all events that are subject to Bernoulli distribution (having a predictable result of two possible outcomes of the same event under given prerequisites). When applied to any other distribution probability, it does not work (for instance, you can’t apply it to roulette, for instance).
The essence of the method is to use the formula of the optimal bet , where K is the known bookmaker coefficient, V is the estimation of the probability by the player, and C is the coefficient of the size of the next bet depending on how much money you have in the bankroll.
Let’s say, your bankroll is 100 dollars, with K equal to 3, your V is equal to 0.4, and thus, C is equal to 0.1. 0.1*100 = $10 (you have to bet 10 dollars).
The obvious advantage of this approach is that it gives you the possibility to increase your bankroll in the long run when you have the correct estimations of K and V, which is actually the optimal and balanced investment strategy. The con of this criterion is that you don’t always know K and V correctly, which leads to either losses or too small wins. Also, you nearly can’t effectively make the calculations during the real play.