💰 Blackjack Odds - Probability, Return to Player and House Edge Explained

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Blackjack is a solvable game and I 've solved it! No system of betting can rescue a losing game. Hot Network Questions. Sign up or log in Sign up using Google. If anyone out there knows how to mathematically model this, I would be happy to test out the mathematical theory and compare against the program. We're switching to CommonMark. Ross Millikan Ross Millikan k 24 24 gold badges silver badges bronze badges. The betting strategy doubles your base wager each loss, and returns it to the base wager after each win. But I'm not quite sure how to calculate the math behind this and how to calculate the probability for winning a single blackjack hand. With the Martingale betting system , I figured that I am more likely to gain a profit than to lose credits. Instead of trying to figure out the math behind it, I wrote a simple computer program that runs trials at each permutation of start balance, base wager, and target. Sign up using Email and Password. Home Questions Tags Users Unanswered. The total expectation is I am now working on a Monte Carlo simulation to see the convergence between the theoretical and simulated expectation. Featured on Meta. Am I favored to gain profit in this specific type of blackjack? Ask Question. Take a look at the results here , Using Mathematica. I have 10, credits to work with. This allows me to lose up to 12 hands before I am bankrupt. It is still too complicated to compute by hand, so people resort to computer modeling. What is the probability of winning a blackjack hand? What posts should be escalated to staff using [status-review], and how do I…. I am looking forward to meeting others with the same calcs to exchange views and opinions. Sign up to join this community. You can't calculate the chance of winning a hand until you specify the strategy you will follow. It's somewhat obvious, but you maximize your gain by using the lowest base wager as percentage of start balance. So far I'm attributing the variance in results to statistical error. You use a random number generator to deal a lot of hands and count how many you win. Mathematics Stack Exchange works best with JavaScript enabled.{/INSERTKEYS}{/PARAGRAPH} Viewed 18k times. Active Oldest Votes. I found an online blackjack that has no minimum or maximum bet limit. Active 1 year, 7 months ago. Post as a guest Name. You are correct that with Martingale you are more likely to win than lose a given series, but if the basic bet is losing the losses will be large and probable enough to give a negative expectation. There is no insurance policy and 21 on both sides are always a tie. Linked 1. Related 6. Sign up using Facebook. It only takes a minute to sign up. {PARAGRAPH}{INSERTKEYS}Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. The maximum avg run length was 15 trials, so I'd say this is definitely a feasible betting strategy. I 've done the calculation in mathematica as well as excel to double check. How can I calculate the probability for this? Question feed. Email Required, but never shown. On the other hand, if I win any of these 12 hands, I gain profit and just reset my bet to 1 again. The best answers are voted up and rise to the top. I figured with 10, credits, I can start my bet at 1, then go to 2, then 4, etc doubling my bet everytime I lose. The dealer stands on soft Also, in the event that both dealer and player gets blackjack, it is a push. To start, I tested identical proportions of parameters to compare results. Whether the game is in your favor is independent of the betting system. Asked 6 years, 8 months ago. Jonathan Jonathan 2 2 bronze badges. Under the rules infinite deck, dealer stands on soft 17, double down rights on any hand and no splitting yet! I was recently curious about this betting strategy as well.