# Quasi martingale betting

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As stochastic integration preserves the local martingale property , such processes are guaranteed to be at least local martingales. However, this is not enough to conclude that they are proper martingales. Whereas constructing examples of local martingales which are not martingales is a relatively straightforward exercise, such examples are often slightly contrived and the martingale property fails for obvious reasons e.

The aim here is to show that the martingale property can fail for very simple stochastic differential equations which are likely to be met in practice, and it is not always obvious when this situation arises. Consider the following stochastic differential equation 1 for a nonnegative process X. Here, B is a Brownian motion and a,b,c,x are positive constants. This a common SDE appearing, for example, in the constant elasticity of variance model for option pricing.

Now consider the following question: what is the expected value of X at time t? The obvious answer seems to be that , based on the idea that X has growth rate b on average. A more detailed argument is to write out 1 in integral form 2 The next step is to note that the first integral is with respect to Brownian motion, so has zero expectation. Therefore, This can be differentiated to obtain the ordinary differential equation , which has the unique solution.

In fact this argument is false. For there is no problem, and as expected. However, for all the conclusion is wrong, and the strict inequality holds. I would play "never bust" - always force the dealer to make a hand AND beat mine. First, what are the odds of losing 9 straight hands where you never bust. The odds of winning with the "never bust" strategy are approximately equal to the odds of being dealt either a or and upgrading to , plus the odds of dealer busting.

The odds of losing 9 hands in a row are 0. I've been told this calculation for the risk of a losing streak is oversimplified, and seems to double-count longer streaks. Here is a post I recently wrote elsewhere about martingale, I'll repost it here, tweaked a bit for context.

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By following the strategy precisely gamblers can ensure that they profit the same amount every single time they get a win. How to Use the Martingale Strategy Using the strategy is very simple to do. The strategic Martingale betting strategy starts off with wagering a small base amount that gamblers can afford to wager and it adjusts from there depending on whether the wager is successful or not. Each time the gambler places a winning bet, they should place the base bet the next round.

The system is reliable, but can be risky during major losing streaks. So, before you start betting, it makes sense to thoroughly weigh all the pros and cons. Martingale on totals strategy Unlike in regular Martingale, in Martingale on totals also called double Martingale , you alternately bet on opposite outcomes of the same event. Let us look at it more closely. If your bet lost, you would have to double it until you get the desired result.

Now the second part of the strategy comes into play. Everything is quite simple. It should be noted that, to successfully use the strategy, you should have a will of iron and not be afraid to bet big money. Because, ridiculous as it may sound, most bettors simply do not have the patience to wait for their chance. Limited Martingale Limited Martingale is considered to be a more reliable strategy than classic one. However, your bet amount will have to be considerably higher, too.

Previously, you have already lost a number of bets and the total amount of your loss is dollars, while the amount you plan to win is dollars. To calculate the bet amount automatically, use my calculator given above If you bet this amount and the bet wins, your net winnings will be dollars. If you are unlucky again, you will be able to easily calculate the amount of your next bet. With limited Martingale strategy, you can bet with any odds which significantly raises your chances to win.

In this article , I described its flat-based variation which allows to avoid the basic problem of limited Martingale — the fast increase of bet amounts. Quarter Martingale Strategy in Basketball According to statistics, one in four quarters of a game between a favorite and an underdog results in a win of the latter. That is why, by increasing the bet amount you may easily reach the desired outcome. Typically, the odds for outsiders are rather high, often higher than 2.

If they are lower, you need to calculate the bet amount using the formula from the previous paragraph. Remember that a losing series can leave you completely bankrupt, so your main allies should be good judgement and thorough analysis.

Martingale Strategy in Tennis As is well known, a tennis match consists of sets which, in their turn, consist of games. For every score, players are awarded 15, then 30, and finally 40 points. After that, no more points are given, and the player that scores wins the set. With this strategy, bets are made in a live mode.

Suppose, you bet on the score. Why this score? Because statistically, it is the most common score in tennis. The odds for this event are usually around 2. If you follow this sport and are well informed about the current tennis players, you will have no difficulty predicting the results. This strategy is especially useful in matches where equally strong players are involved.

Martingale Strategy in Hockey Let us look at the Martingale strategy in the example when a period ends with a draw. As you know, a hockey game consists of three periods each of which may end with a draw. Typically, bookmakers offer rather high odds for this outcome, which allows to not only cover the losses arising during the cycle, but also receive good profit.

When betting on a draw, you need to choose low-scoring teams. Can You Win with Martingale System? It may seem that using this strategy is a piece of cake. Just double the stake and wait for your bet to win. However, it is not at all that easy. As you can see from the examples given in the beginning of the article, when you start with dollars, your fifth bet is 1, dollars, and the seventh is 6, dollars.

At this point, the total turnover is already 12, dollars. So, having a bankroll of 10, dollars is certainly not enough, even if the first bet is only dollars. Another major downside of the strategy is that you have to raise your stake all the time. If you quickly reach the maximum bet amount, your bookmaker will simply cut your limit and not let you finish the cycle. Reviews According to internet forum posts on Martingale strategy, there are people who made profit with it and those who had a negative experience.

In my opinion, Martingale system is both one of the best and most dangerous strategies today. If you calculate everything right, it may bring you good income. But you can also lose all your money. So, it makes sense to only bet the money that you have already mentally let go of. Tips on Betting with Martingale System Betting on sport events requires a lot of analyzing.

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