Introduction

This document is meant to serve as a source for playing strategy for the game of Roulette. Betting strategies along with mathematical odds are presented here. Basic rules for playing Roulette can be found at:

http://www.DotComCasinoGuide.com/info/rules/roulette.html

Odds

The main thing to look for when looking for a Roulette Wheel is the type of wheel. The two versions are the European Wheel with a green 0, and the American Wheel which has both a green 0 and green 00. The house edge for the European Wheel version is 2.70%, while the house edge for the American Wheel version is 5.26%. These percentages will be derived below. Obviously, you want to look for the sites which offer the European Wheel Roulette game. Another thing to look for is those that offer the En Prison rule or the La Partage rule. With the En Prison rule, the house “holds” the bet for another spin on even money bets (Red-Black, High-Low, Odd-Even) when the wheel lands on the 0 or 00, thus essentially giving you another chance to win, and cutting their edge in half. The play may also choose to option the La Partage rule. This entails the house only taking half of the losing 0 bets, which also essentially cuts the house edge in half. Atlantic City casinos employ the La Partage rule only.

European Wheel

37 slots; 1 Green 0; Even Money Bets: House edge of 2.70%

Derivation: 18 / 37 = 0.486; Bets pay at 1:1; 2 * 0.486 = 0.973; 1 – 0.973 = 0.0270; Converted to % = 2.70%

American Wheel

38 slots; 2 Green 0; Even Money Bets: House edge of 5.26%

Derivation: 18 / 38 = 0.474; Bets pay at 1:1; 2 * 0.474 = 0.947; 1 – 0.947 = 0.0526; Converted to % = 5.26%

European Wheel-En Prison Rule in effect

37 slots; 1 Green 0; Player loses half their even money bet on Green; Even Money Bets: House edge of 1.35%

Derivation: From base 37 slots: 37 even money bets will yield 18 winners, 18 losers, and half retained on the Green 0 landing. This gives 36.5 money units left out of 37. 36.5 / 37 = 0.986; 1 – 0.986 = 0.0135; Converted to % = 1.35%

American Wheel-La Partage Rule in effect

38 slots; 2 Green 0; Player loses half their even ** Togel Singapore **money bet on Green; Even Money Bets: House edge of 2.63%

Derivation: From base 38 slots: 38 even money bets will yield 18 winners, 18 losers and half retained on the 2 Green 0 landings. This gives 37 money units left out of 38. 37 / 38 = 0.974; 1 – 0.974 = 0.0263; Converted to % = 2.63%

Regardless of the Wheel type and whether the En Prison rule is used, the types of strategy and betting methods described in this document still apply, they just work a lot better on European Wheel games with the En Prison rule in effect!

What you should know at this point, and always keep in your mind for the rest of your life when you are playing Roulette, is that nothing in the long run can overcome these house edges. For every single bet, the odds are that you are going to lose. Most Roulette strategies involve some type of adjusting of your bets after you win or lose to try and compensate for your overall balance. For example, with the European Wheel, no En Prison Rule, the odds of you winning on an Even Money bet is 18 / 37 = 48.6%. But, if you place two bets in a row, the odds of you winning one of those two is 73.6%! (Odds of house winning on one is 1 – 48.6% = 51.4%; Odds of house winning 2 in a row is 51.4% * 51.4% = 26.4%; 1 – 26.4% – 73.6% that house loses). So Roulette strategies try to use this to the player’s advantage by increasing the amount of the bet after a lose to try to make up for the previous bet.

Let’s take a moment now to talk about the statistics principle called the Law of Independent Trials. The European Wheel will be used for all statistical numbers. The Law of Independent Trials basically applies whenever the domain you are looking to analyze the probability of, has no dependence on previous outcomes of that domain. The Roulette Wheel falls into this category. The odds of the house winning is 51.4%. (19 / 37). The odds of the house winning 2 bets in a row is 51.4% * 51.4% = 26.4%. So from the outside perspective before the first bet is made, the odds are the house won’t win 2 bets in a row against the player. However, after the house wins the first bet, the Roulette Wheel doesn’t have a memory, and could care less what the first spin was. Therefore we are back to the odds being in the house’s favor of 51.4% that they will win the 2nd bet as well. This should not frighten you at all from playing Roulette. (Actually it should frighten you if you think you’re going to walk into a casino with a foolproof strategy and leave with lots of money). Part of gambling is the excitement and the risk! With a mindset going in of how much money you are going to bet, the strategy you are going to use, and what your personal limits are, you will have a blast! I will attempt to describe below some of the “famous” strategies thought of in the past, and just what mathematical probabilities you are dealing with. Try to decide what might best be for you, in terms of what you can risk financially.

All of the strategies below involve the Even Money bets. (Red-Black, Even-Odd, High-Low). The statistics can be transferred to other bets on the table as well, but bets on single numbers only win 1 out of 37(38) times, so it’s just not as practical or as fun to keep repeating those bets and trying to find a strategy to hit the jackpot.

Strategies

The Martingale

One infamous betting strategy is what is called the Martingale. This type of betting method is used on outside bets where the payout is even money. To briefly describe this, it entails doubling your bet after each losing bet so that your next bet will “make up” for all the lost bets up to this and your profit is your initial bet. For example, if you bet $1 and lose, you can make your next bet $2 so that if you win then you’re still a $1 in the profit. If you bet $1, lose, double this bet to $2 and still lose, your next bet would be $4. If you win this bet, then you win the $4, but have only lose the total of $1 + $2 = $3. So your $1 in the profit margin.

Two problems with the Martingale. #1 there are house table limits, so even if you had a lot of money, at some point you will not be able to double your bet. Many online casinos we have reviewed at .com Casino Guide offer a range of $1 to $100 for example. Have in mind the table range of your favorite casino when you are looking at the odds charts we post below. And #2, very quickly this can lead to extremely high bets, all to profit at $1. If you lose 7 bets in a row: $1, $2, $4, $8, $16, $32, and $64, all of a sudden your next bet would be $128 in an attempt to make an end profit of $1 to cover your 7 losing bets. Granted, the odds of losing 7 bets in a row are low, as will be derived below, but it WILL happen. And on that 8th bet, that wheel could care less if the last 7 spins have come up all black for example and you’re betting on red. Below is charted the odds and amounts to be bet if you choose to use the Martingale.

European Wheel-No En Prison Rule-Martingale

Bet # Bet ($) Odds Losing(%) Total ($) Total Profit at this point if you win

1 $1 51.35% -$1 $1

2 $2 26.37% -$3 $1

3 $4 13.54% -$7 $1

4 $8 6.95% -$15 $1

5 $16 3.57% -$31 $1

6 $32 1.83% -$63 $1

7 $64 0.94% -$127 $1

8 $128 0.48% -$255 $1

9 $256 0.24% -$511 $1

10 $512 0.12% -$1023 $1

That’s probably several bets further than you should even consider going if you plan to use this strategy. Let alone that I don’t think I’ve seen a site that offers a table range of $1 to $500+ on outside bets. You see the trend on the right column that you only profit $1 at the point you win due to all your previous loses. Who wants to risk a bet of $512 that will for all practical purposes only profit you $1? You’d have to be insane!

But, let’s look at the Martingale and see if it’s useful for you at the lower end of the scale. Let’s draw our sanity check at using a maximum of 4 bets in a row at this method. The odds of you losing 4 bets in a row is 6.95%. So therefore a 93%+ chance that you will have your $1 profit by this point. The largest risk you are facing is losing that 4th bet at $8, which puts you at -$15 for that 4 bet sequence. Not fun to be out $15, but $15 is not hundreds of dollars either. You shouldn’t have dark thoughts being out the price of a few beers.. Perhaps at this point you call that a lose, and start the system anew. Placing a $1, and going through the sequence again. All the while keeping in mind the odds are really 93% that you’re going to keep getting that $1 profit at some point. So then you see here that it becomes a balance. How many of those $15 sequences can you afford to lose? Set limits for yourself as to how much you can financially lose.

Let’s look at the math. 93% of the time you are going to win with this sequence. For a 100 sample, that’s $93 profit. However, 7% of the time you are going to lose your 4 bet sequence. With your total loss for each one being $15, that around $105 lost. Therefore your total loss is $12 on average if you do the sequence 100 times. If the odds are with you that night and you get lucky enough to only lose that sequence 6 times, you actually make a profit of $3! And that’s what gambling is about, playing the game for fun because you love it, and hoping that lady luck is with you that night.

The Pyramid System

Another system thought of is what is called the Pyramid System. This system doesn’t let you get out of control with your betting, as it is not based upon doubling. The system works where for every bet you lose, you increase your next bet by some unit, let’s say $1 for example purposes, and for every bet you win you decrease it by $1. This way each winning bet you have is $1 greater than your previous losing bet. Let’s chart an example using the European Wheel again.

European Wheel-No En Prison Rule-Pyramid System

Bet # Bet($) Result Tally ($)

1 $1 L -$1

2 $2 L -$3

3 $3 W 0

4 $2 W $2

5 $1 L $1

6 $2 L -$1

7 $3 L -$4

8 $4 L -$8

9 $5 W -$3

10 $4 W $1

Final 4W 6L $1

You can see that even though we’ve only won 4 spins compared to 6 loses that we’re still up $1! And our highest bet was only $5. With 4 loses in a row on the Martingale system, we’d be up to $16 bets trying to make that $1 profit. The Pyramid system can give you longer sustained play at lower risk than versions of the Martingale. But as you can see from the above charts with 10 bets to make $1 profit, this system doesn’t afford you large gains either as you can make your $1 profit from one winning spin.

Let’s combine the two for a moment. We can set our strategy to double our bet up to $4, then use the Pyramid system to slow try to get back our loses while in turn minimizing future loses if we keep losing. We can set this threshold to be 2 additional spins, so the bets would be $5 and $6. Our chart would look like this:

Combination

Bet # Bet ($) Odds Losing(%) Total ($) Total Profit at this point if you win

1 $1 51.35% -$1 $1

2 $2 26.37% -$3 $1

3 $4 13.54% -$7 $1

4 $5 6.95% -$12 -$2

5 $6 3.57% -$18 -$6

You can see here that at our worse case scenario, at odds of happening 3.57%, we lose $18. Even before we get to this point however, at a clip of 6.95% we have a chance to get bailed out with only a $2 lose. All other times, we benefit from a 100% – 13.54% = 86.46% chance that we are going to show a profit. So let’s see what happens for 100 theoretical cycles: 86.46% of the time we can take our $1 profit, so we’re up $86.46. Of the remaining 13.54%, we will win 48.65% of the time on the next spin, netting a $2 lose. So that’s 13.54 * 48.65% = 6.59. 6.59 * -$2 yields a loss of $13.18. (decimal places carried out on calculations).

Therefore we are now at $86.46 – $13.18 = $73.28.

There is now a 6.95% chance that we will have to make that 5th spin, and if we win that, we have a net loss of $6. Therefore with a win we have 6.95 * 48.65% = 3.38. 3.38 * -$6 yields a loss of $20.30.

Therefore we are now at $73.28 – $20.30 = $52.98

And now let’s compute the bad news, with a 3.57% chance we will lose that 5th bet in a row, we would net an $18 lose. Thus we have 3.57% * $18 = $64.27.

Therefore we are now at $52.98 – $64.27 = -$11.29

So what good is this method if you lose $11? Well guess what, nothing mathematically can give you a complete mathematical edge over Roulette as the house has their 2.70% edge for each spin. But like the Martingale, all you need is 1 less worse case scenario and you’ve only lost $6 instead of the $18, which gives you a $12 difference and now you’re in the black! With our worse case of 96% chance of not happening, you can bet that some nights will be your lucky night. And that’s what winning on most games comes down to, getting on that hot streak!

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