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The Maths Behind Blackjack

Thanks for everything so far. The questions I have are, what are these decisions based on. Feedback post: New moderator reinstatement and appeal process revisions. I assume this is the dealers hand. Thats a lot of calculations! Ok that does make a difference as you pointed out. But perhaps I am missing something. Question feed. How is it faster to simulate as opposed to just calculate? But I wanted to post one of a basic strategy table with the rules specified. But I still think it is doable for a given hand combination in less than possibly 2 or 3 seconds even on an 4 or 5 year old computer. Is there a specific formula that can be used so that I may program it and build my own tables. After the game is finished, all the cards are replaced in the deck and the deck is reshuffled to begin again this brings us back to point 1 to repeat the process for every game. Viewed 16k times. Active Oldest Votes. So you have seven ways to make 14 to play against in this case a 6 showing. Active 2 years, 4 months ago. This leaves only 3 cards whose value are known to us from which we make all our decisions 6. The reasons for questioning these tables are because almost every website or book quotes such tables without explaining the maths behind them. Basic strategy just gives the player almost an even chance. The best answers are voted up and rise to the top. Assume this for 2 reasons, first the count for card counters is irrelevant as there is not enough cards out to establish a pattern such patterns can affect the way you play using basic strategy and therefore the stats of the game. Featured on Meta. Home Questions Tags Users Unanswered. You have to take the prob of your hand busting, against the prob of the dealer busting. Sign up or log in Sign up using Google. Hot Network Questions. If I just had the steps to take for 1 example I would be very happy. One of the 4 cards above in point 3 are unknown because it is the dealers face down card 5. Sign up using Email and Password. You can calculate this either exactly or by simulation. Sign up to join this community.

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals math behind blackjack strategy related fields. The basic idea is to see if your math behind blackjack strategy of winning the hand is increased by drawing over standing.

The easier way is to simulate lots of hands. Again, you can calculate this either exactly or by simulation.

We always start with a full deck of cards. As the dealer total gets lower, the possibilities expand, as he can draw a small card and need to keep drawing.

However if your hand was an A3 soft 14you should double down. I would not say the basic strategy is useless, as playing that way reduces your losing percentage substantially from two alternatives: either never bust stop when you are at 12 or play like the dealer. Post as a guest Name.

Second it means we are always working from the same base numbers outlined below 2. But if you always start with a full math behind blackjack strategy the casino has the edge. Mathematics Stack Exchange works best with JavaScript enabled.

Here are the rules. The deck has 32 cards that are 6 or more, and 4 are accounted for. Finally if your hand was a 77, double 7 , you should split. It is not sufficient to get above even, but one part of a long term winning strategy will include losing as little as possible when you can't win. Francis Rodgers Francis Rodgers 1 1 gold badge 5 5 silver badges 12 12 bronze badges. Related 0. Is it possible to show how I can calculate them. Ed Thorp was the first to devise a system for beating casino blackjack, by simulating millions of deals on an IBM computer and turning the results into a card counting system. Taking your example: If the dealer up card is 6, and your two cards show a total of 14 perhaps 8 and 6, or 9 and 4, it does not matter the combination , you should stand take no more cards. Asked 8 years, 11 months ago. If you hit, you lose if you go over If you don't go over 21, you might get a higher total than the dealer. Thanks so far. I would appreicate it. With todays computers even a basic low spec laptop could calculate mathematically every probabbality for this given set of game rules and card combinations there is only 7 combos in a second or less. Meaning how exactly are the three examples above worked out. Sign up using Facebook. If the dealer up card is 6, and your two cards show a total of 14 perhaps 8 and 6, or 9 and 4, it does not matter the combination , you should stand take no more cards. I cannot include screenshots because I am new to this forum. Email Required, but never shown. The number of possibilities explodes. If so we dont know the down card is a Then calculate the rest as you did for every set of dealer hands before going on to the next player hand. Essentially what I am asking is how do you calculate your next move given a set of rules and a specific hand. I dont think there are may other combinations might be wrong. If you stand, you only win if the dealer busts. We have 1 full deck of 52 cards 3. Ross Millikan Ross Millikan k 25 25 gold badges silver badges bronze badges. Lets assume a very basic set of rules and table for them, these rules are unlikely to be seen in any casino and the reason is clear, there is only a 0. New post lock available on meta sites: Policy Lock. It only takes a minute to sign up.