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Conditional Expectation. Markov Chains. Game Theory. House Advantage. Betting Systems. Bold Play. Optimal Proportional Play. Card Theory. Slot Machines. House-Banked Poker. Video Poker. Trente et Quarante. Back Matter Pages About this book Introduction Three centuries ago Montmort and De Moivre published two of the first books on probability theory, then called the doctrine of chances, emphasizing its most important application at that time, games of chance.

The volume addresses researchers and graduate students in probability theory, stochastic processes, game theory, operations research, statistics but it is also accessible to undergraduate students, who have had a course in probability. But I'm not sure I understand your question exactly. Why do you think that one could win long term in a game where each play is and importantly, each play is independent?

I try this because everyone thinks it is impossible, but who knows. With negative progression systems you can make profit with more losses than wins which means that if for a large amount of bets you could make a profit IF you don't go on a big losing streak or have unlimited funds. My idea was that if you could somehow get a broke percentage of zero this could work!

Just always bet an amount equal to your total cumulative previous losses, and play until you win a bet. But, of course, it's quite silly to consider betting games with unlimited funds. Add a comment. Active Oldest Votes. GEdgar GEdgar Are there any processes that are not martingale? Of course. The easiest one is: bet only if you will win. There are also some interesting studies on "prophet" theorems, which compare your outcome this way, with your outcome if you do not know the future.

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And the end goal is to finish out your string of numbers and hit the desired profit. If you win the bet, you cross off the two end numbers and move on to the next wager. But if you lose the bet, you add the total number of units to the end of your number string. The nice thing about this blackjack strategy is that it gives you a lot of freedom.

Basically, you could either make this a negative or positive progression betting system based on the string of written numbers. If a player were to play any one of the above propositions, there are eighteen individual results which result in a win for that player and for an American Roulette wheel twenty individual results that result in a loss for that player.

Theoretically, because the player is cancelling out two numbers on the list for every win and adding only one number for every loss, the player needs to have his proposition come at least For example, if the list starts with seven numbers and the player wins five times and loses three An obvious downfall to the system is bankroll, because the more losses sustained by the player, the greater the amount being bet on each turn as well as the greater the amount lost overall is.

Consider the following list:. Consecutive losses, or an inordinate number of losses to wins can also cause table limits to come into play. Occasionally, a player following this system will come to a point where he can no longer make the next bet as demanded by the system due to table limits. One work-around for this problem is simply to move to a higher limit table, or a player can take the next number that should be bet, divide it by two and simply add it to the list twice.

The problem with the latter option is that every time a player commits such a play, it will infinitesimally increase the percentage of spins a player must win to complete the system. The reason this is so is because the player is adding two numbers which both will be crossed out in the event of wins where only one loss was sustained. However, there is no guarantee that the player will reach the desired goal before the bankroll is lost. This is referred to as risk of ruin. The recursion of the algorithm terminates when the sequence is empty or when the player possesses insufficient funds to continue betting.

When the function is called, the size of the bet made is equal to the sum of the first and last numbers of the sequence. If the length of the sequence is one, then the bet is equal to the sole member of the sequence.

If the bet is won, then the first and last members are spliced from the sequence and the next round begins. However, if the bet results in a loss, then an integer equal the size of the lost bet is appended to the sequence and the next round begins. As determined by the parameters for termination of recursion, the only cases in which the algorithm will terminate are those in which the player has either won an amount equal to the summation of the original sequence or has lost all of their available capital.

In this version after a win, instead of deleting numbers from the line, the player adds the previous bet amount to the end of the line. After a loss, the player deletes the outside numbers and continues working on the shorter line. The player starts their line again if they run out of numbers to bet. It is with this that a player with a bankroll of x can create their own line, or lines, representative of the maximum amount that they can sustain in losses.

Additionally, a player does not necessarily have to continue the system until the table limit is met or exceeded, but could instead pick a single bet that the player does not wish to exceed and make that bet their own personal limit. For example, if a line of:. In the line immediately above, it would take an opening streak of six consecutive losses for the line to be completed.

This volume, on the probabilistic aspects of gambling, is a modern version of those classics. While covering the classical material such as house advantage and gambler's ruin, it also takes up such 20 th -century topics as martingales, Markov chains, game theory, bold play, and optimal proportional play.

In addition there is extensive coverage of specific casino games such as roulette, craps, video poker, baccarat, and twenty-one. Skip to main content Skip to table of contents. Advertisement Hide. This service is more advanced with JavaScript available.

Authors view affiliations Stewart N. Front Matter Pages Review of Probability. Pages Conditional Expectation. Markov Chains. Game Theory. House Advantage. Betting Systems. Active 1 year, 7 months ago. Viewed 5k times. WarreG WarreG 2 2 silver badges 10 10 bronze badges. For example, betting on black or red in roulette is not because of that pesky green spot.

But I'm not sure I understand your question exactly. Why do you think that one could win long term in a game where each play is and importantly, each play is independent? I try this because everyone thinks it is impossible, but who knows. With negative progression systems you can make profit with more losses than wins which means that if for a large amount of bets you could make a profit IF you don't go on a big losing streak or have unlimited funds.

My idea was that if you could somehow get a broke percentage of zero this could work! Just always bet an amount equal to your total cumulative previous losses, and play until you win a bet. But, of course, it's quite silly to consider betting games with unlimited funds. Add a comment. Active Oldest Votes. GEdgar GEdgar Are there any processes that are not martingale? Of course. The easiest one is: bet only if you will win.

There are also some interesting studies on "prophet" theorems, which compare your outcome this way, with your outcome if you do not know the future. Google "prophet theorem" or "prophet inequality". Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.

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