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Martingale betting system mathematical analysis wikipedia ferrer tsonga betting on sports

Martingale betting system mathematical analysis wikipedia

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Is this encyclopedic? I'm not sure of exactly how the Wikipedia stands on howtos Question: who invented the Martingale system, and when? Is there any reason why this should not be merged into the main Martingale article? This seems pretty POV to me.. Like warning to some gambling addicts that this will not work. This is one of the best betting strategies on roulette and works pretty good if you find a high limit table somewhere..

But does the strategy really require that the gambler has an infinite wealth? I would easily try this out once as soon as I have a companion that could lend me any amount of money for a very short period of time without interest. I would pay him back everything within a minute or so—guaranteed. It's risk free for him and it's risk free for me—and yet I know I will win the amount I want. Am I really an idiot then? I believe that this betting strategy is a sure method of not losing money and possibly winning money, just not very much relative to what you've already got.

You don't need complicated stat equations to prove to yourself that this does indeed work. There are basically two main factors in determing how much you'll win. Roulette is a game of pure chance - there is no skill - every number has an equal chance of coming up but the payouts are made at under the odds. NO method works. In practice casinos couldnt care less about Martingale or any other theory.

It is proposed to merge this "with" martingale probability theory. It would be more plausible to merge this into that article. There is a "mergeinto" template for that purpose. I'd keep it as is. I found this article in searching this exact topic. I had not heard of the name of the theory, only the method of essentially doubling one's bet upon sequential losses.

Had it been merged with the other topic, I likely would not have found it, much less realized the correlation between the two. I agree that the analysis is completely incorrect - so incorrect that it should be removed until it is re-written correctly. Would it make sense to add a bit here about Nick Leeson , who destroyed the Barings' Bank with what was in effect a martingale series of bets of the Nikkei index? On an unrelated note, does anyone know the origin of the term "martingale", and how it's related to this betting system?

The math here still looks incorrect. It claims that the expected profit is The formula only assumes that the player wins once and stops playing. As an example, note tha the current formula shows the correct payoff if there are consistent losses on all x plays, but does not show the correct payoff if there are consistent gains on all x plays. The correct way to show the expected payoff of a martingale involves combinatorics and the series of corresponding payoffs and probabilities.

Luckily, the series can be reduced to a closed-form solution. We should also show a graph that illustrates the Martingale payoff. The example is misleading. It is comparing a loss per round with a loss per roll and indicating that there is a difference in the edge. Martingale makes no difference to edge. Objective talk , 18 April UTC.

Added for the obvious: an article shouldn't be calling anyone 'foolish', etc. It's unlikely that you'll lose any money by withdrawing it at profit at some point if you have a lot of money and play with smaller bets. This is just stupid absolutistic idealistic analysis of a situation where you play for an infinite amount of time. Well, duh, Einstein, how is that possible in real life? Gambling is by definition not risk-free.

I was wondering if there is a modified martingale system that would let you gain on a bet by more than doubling the new bet after a failed bet. It would have similar risks and would risk the catastrophic failure point quicker, but adds the possibility of reward rather than just breaking even.

That's five billion dollars. I was thinking about the same thing; I think that if one did indeed have infinite available cash and no table cap you could always be 'up' if following a martingale strategy. However I can't prove that this is true mathematically, is anyone here an expert who can tell me if I'm wrong?

Could someone explain me how to get the value for probability of 6 concesutive losses within e. If you were able to give me some general formula for it I would be very thankful. Or just link me some site with explanation how to count it. I found it hard to deduce some formula on my own. Thank you very much. I acctually thought of this theory without any help when i was 12 years old, was planning on trying it out today then looked it up and it seems to be v well known.

Anyway, why is everyone using examples of loosing 6 times in a row. Now i havn't thought about this alot but the only reason i can think for not doing this is you will be winning tiny stakes :S. No: With lots of small bets, you will over time approach closer and closer to an outcome reflecting the real odds which of course are against you. It's still stupid to bet against the house, of course, but the odds do not become so decisive to the house's advantage, of course until you make lots of bets.

The system not only requires the player to have an unlimited bankroll, it also requires the casino to have unlimited solvency so it can keep paying off possible wins as the stakes increase. Since expectation is linear, the expected value of a series of bets is just the sum of the expected value of each bet. Since in such games of chance the bets are independent, the expectation of all bets is going to be the same, regardless of whether you previously won or lost.

In most casino games, the expected value of any individual bet is negative, so the sum of lots of negative numbers is also always going to be negative. This reasoning, "intuitive" though it might be, is actually incorrect unless the stopping time has finite expectation. I removed this with a reason in the edit summary, but User:Objective undid it without one "revert".

Oh well. A continuous sequence of martingale bets can thus be partitioned into a sequence of independent rounds. Following is an analysis of the expected value of one round. Let q be the probability of losing e. Let B be the amount of the initial bet. Let n be the finite number of bets the gambler can afford to lose.

The probability that the gambler will lose all n bets is q n. When all bets lose, the total loss is. In all other cases, the gambler wins the initial bet B. Thus, the expected profit per round is. Thus, for all games where a gambler is more likely to lose than to win any given bet, that gambler is expected to lose money, on average, each round.

Increasing the size of wager for each round per the martingale system only serves to increase the average loss. Suppose a gambler has a 63 unit gambling bankroll. The gambler might bet 1 unit on the first spin. On each loss, the bet is doubled. Thus, taking k as the number of preceding consecutive losses, the player will always bet 2 k units.

With a win on any given spin, the gambler will net 1 unit over the total amount wagered to that point. Once this win is achieved, the gambler restarts the system with a 1 unit bet. With losses on all of the first six spins, the gambler loses a total of 63 units. This exhausts the bankroll and the martingale cannot be continued.

Thus, the total expected value for each application of the betting system is 0. In a unique circumstance, this strategy can make sense. Suppose the gambler possesses exactly 63 units but desperately needs a total of Eventually he either goes bust or reaches his target. This strategy gives him a probability of The previous analysis calculates expected value , but we can ask another question: what is the chance that one can play a casino game using the martingale strategy, and avoid the losing streak long enough to double one's bankroll.

Many gamblers believe that the chances of losing 6 in a row are remote, and that with a patient adherence to the strategy they will slowly increase their bankroll. In reality, the odds of a streak of 6 losses in a row are much higher than the many people intuitively believe. Psychological studies have shown that since people know that the odds of losing 6 times in a row out of 6 plays are low, they incorrectly assume that in a longer string of plays the odds are also very low.

When people are asked to invent data representing coin tosses, they often do not add streaks of more than 5 because they believe that these streaks are very unlikely. This is also known as the reverse martingale. In a classic martingale betting style, gamblers increase bets after each loss in hopes that an eventual win will recover all previous losses. The anti-martingale approach instead increases bets after wins, while reducing them after a loss. The perception is that the gambler will benefit from a winning streak or a "hot hand", while reducing losses while "cold" or otherwise having a losing streak.

As the single bets are independent from each other and from the gambler's expectations , the concept of winning "streaks" is merely an example of gambler's fallacy , and the anti-martingale strategy fails to make any money. If on the other hand, real-life stock returns are serially correlated for instance due to economic cycles and delayed reaction to news of larger market participants , "streaks" of wins or losses do happen more often and are longer than those under a purely random process, the anti-martingale strategy could theoretically apply and can be used in trading systems as trend-following or "doubling up".

But see also dollar cost averaging. Martingale betting system For the generalised mathematical concept, see Martingale probability theory. Dubins ; Leonard J. February Retrieved 31 March


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