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Impact on Expected Return in Common Casino

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The main idea behind the 2-1-2 system is supposedly to help you win more money during solid winning streaks and cut down your losses during choppier sessions. But does this strategy help you win more at gambling and can it improve your odds of beating the casino?

Gambling expert Michael Shackleford addressed these questions by analyzing the implementation of the system in several popular casino games like baccarat, roulette, and craps.

The analysis involves a hypothetical (and highly unlikely) winning streak capped at twenty one successful rounds. The probability of this occurring in baccarat is 1 in 2.8 million with wagers on the Player side.

Mr. Shackleford first calculated the average losses per session a system player can anticipate, along with the average number of wagers made per session. He then determined the theoretical expected return each casino game yielded with the 2-1-2 strategy in place.

1. Expected Return of Various Casino Games with the 2-1-2 System

To give you an example, a person systematically betting on the Player side in baccarat with this strategy can anticipate losing 0.053506 units during a single session, with the average number of wagers made standing at 4.332144. This would result in a negative expected return of -0.053506 / 4.332144 = -0.012350. Here are the figures for the other casino games and bets that were analyzed.

2. The 2-1-2 System = Negative Expected Value

If you look at the last two columns in the table, you will surely notice two things. First, the average theoretical return (or the ratio of money won to money wagered) is negative, which is to say you will end up in the red and lose rather than win when consistently implementing the 2-1-2 system.

Second, your expected return coincides with the exact house edge each of the analyzed wagers produces over the long run. In other words, the figures in the last column reflect what percentages the casino gets to keep per every dollar wagered at the tables in the long term.

If you perform several quick calculations, you will notice what we mean. The house receives 0.0136 cents (1.36%) per every dollar wagered on Don’t Pass bets, 0.0270 (2.70%) per dollar wagered on single-zero roulette, and so on.

3. So Is the System Efficient?

The short answer is no. Looking at the figures above, a reasonable person can arrive at one logical conclusion and it is that the 2-1-2 system does not help you win more at gambling. What is worse, it does not help you win at all. Your expected value will remain negative with or without this system.

4. Issues with the 2-1-2 System

The main flaw of the 2-1-2 system is that it is powerless when it comes to overcoming the casino advantage built into games like roulette, baccarat, and craps. As you previously saw, using this strategy does not even dent the house edge. Like all progressive systems, the 2-1-2 relies on bet sizing which has no effect on your winning odds whatsoever.

The casino games the system is applicable to are all based on chance. Each dice roll or spin of the roulette wheel is an independent event. As such, it remains unaffected by previous results and does not impact future outcomes. Switching from smaller to larger bets or vice versa does nothing to improve your odds of winning in the long run.

Like all positive betting progressions, the 2-1-2 system might yield some results and help you generate more profits in the short term. However, gamblers are doomed to lose money due to the house edge the longer they play, whether or not they are using the 2-1-2 system or another similar betting strategy.

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