Yet, if you have 16 points, the strategy indicates you should surrender if the dealer is showing 10 or more points. The only times that bet amounts influence expected return are during tournaments and when a rebate percentage is involved, as discussed in the answers above. Some casinos allow an early surrender, which you do before the dealer checks to see if they have a blackjack. 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. This would make the formula look like this:. How many hands should I expect to play till I lost 8 hands which is my stopping point? After I posted it, I received a message from a blackjack genius, who goes by the handle "Cacarulo.
Betting Strategies and the Kelly Criterion
However progressive systems will turn a choppy neutral session into a bad one. Consider what would happen if you alternated between a win and a loss the entire session. I play the negative system in black jack meaning I double every time I lose until I Win. I wanted to what the odds are of losing 4,5,6,7,8,9 hands in a row? How many hands should I expect to play till I lost 8 hands which is my stopping point? The name for this system is the Martingale.
Ignoring ties the probability of a new loss for a hand of blackjack is So the probability of losing 8 in a row is. This just goes to show that you should always have double or split money available if you need it. 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. I was reading through some of your past Ask the Wizard columns and saw your calculation of the probability of a string of losses in the August 4, Column.
My question though is what does that really mean? Is it that when I sit down at the table, 1 out of my next playing sessions I can expect to have an 8 hand losing streak? Or does it mean that on any given loss it is a 1 in chance that it was the first of 8 losses coming my way?
I know, I know, its some sort of divine intervention betting system I am talking about and no betting system affects the house edge. Besides every once in awhile throwing down a bigger bet just adds to the excitement and for some reason it seems logical that if you have lost a string of hands you are "due" for a win.
I have no problem with increasing your bet when you get a lucky feeling. What is important is that you play your cards right. Unless you are counting cards you have the free will to bet as much as you want. As I always say all betting systems are equally worthless so flying by the seat of your pants is just as good as flat betting over the long term.
When I said the probability of losing 8 hands in a row is 1 in I meant that starting with the next hand the probability of losing 8 in a row is 1 in The chances of 8 losses in a row over a session are greater the longer the session.
I hope this answers your question. First let me say I love your site and will be visiting each of the advertisers to help support it. I hope you are doing very well financially as you are undoubtedly saving a lot of people a lot of money.
My question is do you have any advice for Blackjack players participating in Blackjack tournaments? I have participated in a few and have came very close to advancing to the "money" round with no real strategy other than stay close to the leaders on the table and bet it all on the last hand. Any advice would be greatly appreciated! Thanks for the kind words. I appreciate the thought of visiting the advertisers. So unless you might actually play there is no pressure any longer to click through the banners.
Blackjack tournaments are not my strong subject. Wong says that if you are behind to bet opposite of the leader, small when he bets big, and big when he bets small.
If you are in the lead then you should bet with the second highest player. The book gets into much more detail. Speaking of supporting my site, it helps to click through my Amazon links when buying books there. How do you calculate the expected return for a blackjack game with a. Does it matter if you flat bet assuming that the bets are relatively small compared to the BR or bet based on the Kelly criterion, or does the Kelly criterion just affect the risk of ruin?
Your expected loss of this play is 0. The betting system will not affect the expected loss, but will affect the volatility. Does losing a hand at blackjack increase the probability that the composition of the deck is in your favor? More specifically, is your expected return on one hand ever positive after a given net loss since the last shuffle? The answer is emphatically yes! In fact, betting strategy is critical for anyone who wants to be a profitable blackjack player.
But betting strategy can be much more complex than that. Figuring that out requires the player to take into account the size of their bankroll, as well as the size of their edge over the house. One method of figuring out the optimal bet size is to use the Kelly Criterion. The Kelly Criterion is an attempt to maximize the rate at which a player can make money when they have an edge without having a significant risk of ruin.
The formula is basically as follows:. This would make the formula look like this:. In this case, the Kelly Criterion suggests betting. Of course, players rarely have such a huge edge, and blackjack is a bit more complex since the player sometimes wins differing amounts, and sometimes is forced to wager additional money on a hand.
Play Now Read Review. Highly rated blackjack casino Vegas style blackjack Welcomes American players. Betting Systems Over the years, many people have tried to come up with betting systems that could beat various casino games. If you have 15 points or 17 and the dealer is showing a hard 17 or more, the strategy says to surrender. You would not surrender, however, if the dealer shows a soft 17 or lower hand. Yet, if you have 16 points, the strategy indicates you should surrender if the dealer is showing 10 or more points.
Like all blackjack strategies, this also adjusts for the number of decks in use. Another advanced play that can affect blackjack strategy is buying of insurance to protect yourself against the dealer hitting When the dealer is showing an Ace as the up card, you can lay up to half your original wager on whether or not the dealer has a point card in the hole. If the dealer does have blackjack, then you get paid 2 to 1 on your insurance wager.
A lot of players of 21 will choose to buy insurance if they get a hand worth 19 or 20 points off the deal, but the dealer is showing an ace. They view buying insurance as a way to protect a strong hand, but you still could lose both wagers, or wind up with a push and a loss. If your hand is worth 19 points, and the dealer has a 9 in the hole, you would lose your bet, as well as the insurance. The only time it is useful is to card counters who are deep into counting off multiple decks, a situation that is not accounted for by strategy cards.
Card-counting is a strategy that makes it possible to beat certain blackjack games if the conditions are right. Movies often inaccurately portray this as memorizing every card that has already come out of the deck. There are actually a number of different count techniques, but the gist of all of them is to keep a count of how many high-value, middle-value and low-value cards have already come out. When lots of high-value cards are still in the deck, the player has a statistical advantage over the dealer, since their probability of hitting a natural blackjack is increased which pays out more than a standard winning hand.
They are also mathematically more likely to be successful when doubling down, and the dealer is more likely to bust when being forced to hit on a 12 or higher. The most basic counting technique has players add one unit to the count for when a low card comes out, and subtract one unit when a high card 10 and face cards comes out.
The 7 to 9 cards are considered neutral value and not tracked. As the count value gets higher, the player has more of an advantage and bets higher. There are more complicated counting techniques that are considered more accurate and profitable, but there is an increasing trade-off between tracking the count and continuing to play with the perfect strategy needed to make the system work.
Even with perfect play, it takes a large bankroll and sometimes many hours of play to see a significant profit from card counting. Unfortunately, card counting is completely useless at video blackjack games such as the ones seen on Game King machines , as well as the similar online counterparts. Live video streaming blackjack creates an interesting possibility for card counting. Players can use strategy cards without detection to take some of the mental workload off, focusing solely on their count.
They may also be able to use apps and software that aid in counting, though apps that interact directly with the casino software may be detected and get the player kicked out.
The absolute biggest player-unfriendly rule is when the house has the dealer win any sort of push. This can swing the house edge from 3. Short pays increase the house advantage by anywhere from 0.
Individually these rules each give the dealer about a fifth of a percent of an advantage, and all three together give the dealer about a full half of a percent. Certain other rules have a negative impact, like not allowing the player to split beyond three hands, but they generally have a trivial impact on the house advantage in isolation.
There are no government or state laws prohibiting card counting, including at online games. Some regions actually have laws preventing casinos from barring card counters, like Atlantic City and Mississippi. However, outside of these odd exceptions, casinos are largely free to set the terms of their games and rules about player conduct. This means they are allowed to bar players they suspect of card counting.
One might get in trouble for suspected card counting at a live video streaming blackjack game, however. Casinos usually track card counters by their changes in bet size, especially as the shoe runs out. This means they need to monitor an extended period of play to determine if someone is actually counting cards. Once a card counter is identified and asked to leave a casino, however, they can expect that information to be shared with some amount of other casinos and to find themselves unwelcome at their blackjack games even if they have never played there before.
You need to keep an eye on the chip piles of other players relative to your own, and also be mindful of how far along you are in the tournament to determine the best bet amount for any given hand. Some general tips are to match the biggest bettor when you are leading in chips, bet opposite of the leader when you are trailing in the chip count, and hold back one chip when everyone else goes all-in on the final hand.
This technique involves observing a table and keeping count without actually playing, then jumping in only when conditions are favorable. Some tables forbid new players from joining in the middle of a shoe specifically because of this technique. This practice is more common at smaller casinos that consistently have more demand for blackjack action than they do available table space.
Online casinos rarely bother with this as a theoretically infinite amount of players can be accommodated at any time.