This strategy is very similar to the Martingale (betting system).
Only difference is the starting point. The outside betting strategy start betting after waiting for 3 same results come out in a row. Then starting the bet. To reduce losing probability, player needs to bet other place same time whenever he or she sees when 3 same results comes out in a row like odd 3 times, even 3 times, red 3 times, black 3 times, 1-16 3 times, abd 17-36 3 times. The important rule you must keep is cash out when you reach $300.00 gain.
Starting money: $300.00 (change to $5 chips: outside bet is requred to stack all chips as one)
Please check the concept of the Marktingale system below first.
Originally, martingale referred to a class of betting strategies popular in 18th century France. The simplest of these strategies was designed for a game in which the gambler wins his stake if a coin comes up heads and loses it if the coin comes up tails. The strategy had the gambler double his bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake. Since a gambler with infinite wealth will with probability 1 eventually flip heads, the Martingale betting strategy was seen as a sure thing by those who advocated it. Of course, none of the gamblers in fact possessed infinite wealth, and the exponential growth of the bets would eventually bankrupt those who chose to use the Martingale. It is widely believed that casinos instituted betting limits specifically to stop Martingale players, but in reality the assumptions behind the strategy are unsound. Players using the Martingale system do not have any long-term mathematical advantage over any other betting system or even randomly placed bets.
Effect of variance
As with any betting system, it sometimes happens that one achieves a better result than the expected negative return, by temporarily avoiding a losing streak. Furthermore, a straight string of losses is the only sequence of outcomes that results in a loss of money, so even when a player has lost the majority of his bets, he can still be ahead overall, since he always wins 1 unit when a bet wins, regardless of how many previous losses.[1]
Intuitive analysis
When the expected value of the stopping time is finite (which is true in practice), the following argument explains why the betting system fails: 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 each bet does not depend on 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.
The martingale strategy fails even with unbounded stopping time, as long as there is a limit on earnings or on the bets (which are also true in practice). It is only with unbounded wealth, bets and time that the martingale strategy can succeed.
In plain English, this means that a player will either exceed the house betting limit after only a small series of losses; run out of money after a small series of losses; or will have to eventually leave the casino.
Mathematical analysis
The impossibility of winning over the long run, given a limit of the size of bets or a limit in the size of one’s bankroll or line of credit, is proven by the optional stopping theorem.
Mathematical analysis of a single round
Let one round be defined as a sequence of consecutive losses followed by either a win, or bankruptcy of the gambler. After a win, the gambler “resets” and is considered to have started a new round. A continuous sequence of martingale bets can thus be partitioned into a sequence of independent rounds. We will analyze the expected value of one round.
Let q be the probability of losing (e.g. for roulette in America, with two zeroes, it is 20/38). Let B be the amount of the commencing bet. Let n be the finite number of bets you can afford to lose.
The probability that you lose all n bets is qn. When you lose all your bets, the amount of money you lose is
The probability that you do not lose all n bets is 1 ? qn. If you do not lose all n bets, you win B amount of money (the initial bet amount). So the expected profit per round is
Whenever q > 1/2, the expression 1 ? (2q)n < 0 for all n > 0. That means for any game where you are more likely to lose than to win each bet (e.g. all chance gambling games) you are expected to lose money on average per round. Furthermore, the more times you are able to afford to bet, the more you will lose.
As an example, suppose you have 6,300 available to bet. You bet 100 on the first spin. If you lose, you bet 200 on the second spin, then 400 on the third, 800 on the fourth, 1,600 on the fifth, and 3,200 on the sixth.
If you win 100 on the first spin, you make 100, and the martingale starts over.
If you lose 100 on the first spin and win 200 on the second spin, you make a net profit of 100 at which point the martingale would start over.
If you lose on the first five spins, you lose a total of 3,100 (3,100 = 100 + 200 + 400 + 800 + 1,600). On the sixth spin you bet 3,200. If you win, you again make a profit of 100.
If you lose on the first six spins, you have lost a total of 6,300 and with only 6,300 available, you do not have enough money to double your previous bet. At this point the martingale cannot be continued.
In this example the probability of losing 6,300 and being unable to continue the martingale is equal to the probability of losing 6 times or (20/38)^6 = 2.1256%. The probability of winning 100 is equal to 1 minus the probability of losing 6 times or 1 – (20/38)^6 = 97.8744%.
The expected amount won is (100 x .978744) = 97.8744 . The expected amount lost is (6,300 x .021256)= 133.9118 . So overall you can expect to lose (133.9118 – 97.8744) = 36.0374 .
An alternative mathematical analysis
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.
As before, this depends on the likelihood of losing 6 roulette spins in a row assuming we are betting red/black or even/odd. 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 200 coin tosses, they often do not add streaks of more than 5 because they believe that these streaks are very unlikely[citation needed]. This intuitive belief is sometimes referred to as the representativeness heuristic.
The odds of losing a single spin at roulette are q = 20/38 = 52.6316%. If you play a total of 6 spins, the odds of losing 6 times are q6 = 2.1256%, as stated above. However if you play more and more spins, the odds of losing 6 times in a row begin to increase rapidly.
- In 73 spins, there is a 50.3% chance that you will at some point have lost at least 6 spins in a row. (The chance of still being solvent after the first six spins is 0.978744, and the chance of becoming bankrupt at each subsequent spin is (1-0.526316)x0.021256 = 0.010069, where the first term is the chance that you won the (n-6)th spin – if you had lost the (n-6)th spin, you would have become bankrupt on the (n-1)th spin. Thus over 73 spins the probability of remaining solvent is 0.978744 x (1-0.010069)^67 = 0.49683, and thus the chance of becoming bankrupt is 1-0.49683 = 50.3%.)
- Similarly, in 150 spins, there is a 77.2% chance that you will lose at least 6 spins in a row at some point.
- And in 250 spins, there is a 91.1% chance that you will lose at least 6 spins in a row at some point.
To double the initial bankroll of 6,300 with initial bets of 100 would require a minimum of 63 spins (in the unlikely event you win every time), and a maximum of 378 spins (in the even more unlikely event that you win every single round on the sixth spin). Each round will last an average of approximately 2 spins, so, 63 rounds can be expected to take about 126 spins on average. Computer simulations show that the required number will almost[clarification needed] never exceed 150 spins. Thus many gamblers believe that they can play the Martingale strategy with very little chance of failure long enough to double their bankroll. However, the odds of losing 6 in a row are 77.2% over 150 spins, as above.
We can replace the roulette game in the analysis with either the pass line at craps, where the odds of losing are lower q=(251:244, or 251/495)=50.7071%, or a coin toss game where the odds of losing are 50.0%. We should note that games like coin toss with no house edge are not played in a commercial casino and thus represent a limiting case.
- In 150 turns, there is a 73.5% chance that you will lose 6 times in a row on the pass line.
- In 150 turns, there is a 70.7% chance that you will lose 6 times in a row at coin tossing.
In larger casinos, the maximum table limit is higher, so you can double 7, 8, or 9 times without exceeding the limit. However, in order to end up with twice your initial bankroll, you must play even longer. The calculations produce the same results. The probabilities are overwhelming that you will reach the bust streak before you can even double your bankroll.
The conclusion is that players using Martingale strategy pose no threat to a casino. The odds are high that the player will go bust before he is able even to double his money.
Table limits are not specifically designed to prevent players from using Martingale strategy. The table limits exist so that the casino is not gambling more money than they can afford to lose. Statistics[citation needed] as of January 2009 show that the 29 roulette wheels in Downtown gaming Las Vegas average a win amount of $1,114 per day for the last year. Most casinos have a $500 dollar table limit[citation needed] so that they are not risking too much money on a few spins. A casino is a business; and, like any other business, it has to worry about cash flow. Casinos are required to keep enough cash on hand to pay off a reasonable expectation of a gambler’s windfall. A small casino with a pit that normally takes in $12–$15 thousand a day doesn’t want to keep enough cash on hand to pay off a $10,000 bet that hits 36:1 on roulette. A major casino on the strip earns over $3000 per day on a roulette game and can have over 20 roulette games. They can risk no-limit tables. A smart pit boss would welcome a Martingale strategy player and comp him heavily so that he returns.
