Red And Black Casino Game

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Introduction

We've already discussed betting on Red or Black which is the most popular of the outside bets. Another is 'Low' or 'High' which involves betting on 1—18 (Low) or 19-36 (High). You can also bet Even numbers or Odd numbers which gives you the same odds at the High/Low and Red or Black wagers. Roulette is a casino game named after the French word meaning little wheel.In the game, players may choose to place bets on either a single number, various groupings of numbers, the colors red or black, whether the number is odd or even, or if the numbers are high (19–36) or low (1–18).

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Trente et Quarante is French for 'thirty and forty.' It is an old European casino game still found in Monte Carlo and other major French casinos. When I went to Monte Carlo, I didn't knowingly see the game, but I wasn't specifically looking for it either.

The game can be most closely compared to baccarat. There are two hands, and players bet on which one will have the better score. In this case, the lower the score the better.

Rules

1. Six 52-card decks are used.
2. Aces are valued as one point, 2s to 10s according to pip value, and face cards as 10 points.
3. There are four bets available: Black, Red, Color, and Inverse. In addition, an Insurance wager is available on each of these four bets.
4. After players have made their wagers, the dealer will deal cards to determine the value of the 'black' hand. A running total will start at 0 and go up as the cards are dealt from the shoe. The dealer will stop when the total points is 31 or more. The maximum possible score is 40.
5. Next, the dealer will do the same thing but for the 'red' hand.
6. The Black wager shall win if the black hand has fewer points than the red hand. If the red hand has fewer points, then the result is a loss. If there is a tie at 32 to 40 points, then the result is a push. If there is a tie at 31 points, then the player may choose to lose half, or 'imprison' his bet, which I explain below.
7. The Red wager is the opposite of the Black wager, winning if the red hand is less and losing if it is more. The tie rules are the same.
8. The Color wager acts like a Black wager if the first card dealt to the black hand is black, and like a Red wager if that first card is red.
9. The Inverse wager is the opposite of the Color wager, acting like a Black wager if the first card is red, and a Red wager if the first card is black.
10. The player may take out Insurance on the Black, Red, Color, or Inverse wagers. The Insurance wager must equal 1% of the primary wager and pays the loss if the outcome is a 31 tie. If the primary wager wins or loses the full amount, then the Insurance wager loses. A 32-40 tie results in an Insurance tie. In other words, Insurance pays 49 to 1 on a 31 tie, pushes on any other tie, and otherwise loses.
11. If the player imprisons a wager after a 31 tie, then it is blocked off somehow. Then the next hand is played out. If that next hand results in a win for the blocked off wager, then it is returned to the player. If the next hand results in a loss for the blocked off wager, then it is lost. Any tie, including on 31, results in the blocked off wager remaining on the table until there is a win or loss to resolve it.

Odds

The following table shows the probability of each number of points for each hand.

Points Distribution

Points	Probability
31	0.148177
32	0.137900
33	0.127618
34	0.116876
35	0.106136
36	0.094963
37	0.083814
38	0.072255
39	0.060751
40	0.051510
Total	1.000000

The next table shows the probability of each possible outcome between the Black and Red hands.

Points Distribution

Event	Probability
Black wins	0.445184
Red wins	0.445184
Tie (32-40)	0.087705
Tie (31)	0.021927
Total	1.000000

The next table shows the return table for the Black, Red, Color, and Inverse bets. The lower right cell shows a house edge of 1.10%.

Return Table for Black, Red, Color, and Inverse

Event	Pays	Probability	Return
Win	1	0.445184	0.445184
Push	0	0.087705	0.000000
Lose half	-0.5	0.021927	-0.010964
Lose all	-1	0.445184	-0.445184
Total	1.000000	-0.010964

The next table shows the return table for Insurance, assuming the player chooses to lose half on a 31 tie. The lower right cell shows a player advantage of 18.41%!.

Return Table for Insurance

Event	Pays	Probability	Return
Win	49	0.021927	1.074436
Lose	-1	0.890367	-0.890367
Push	0	0.087705	0.000000
Total	1.000000	0.184069

The above Insurance table shows that Insurance is indeed a great bet. Aside from some Super Bowl proposition wagers, the best bet I've ever known. Unfortunately, as stated in the rules, Insurance is limited to 1% of the primary wager. The next table shows the combined effect of betting 100 units on Black, Red, Color, or Inverse and 1 unit on Insurance. The lower right cell shows an expected loss of 0.912295 units. The combined expected value between the two bets is thus -0.912295/101 = -0.00903262.

Combined Return Table on 101 Units Wagered

Primary Wager Event	Primary Wager Pays	Insurance Pays	Total Win	Probability	Return
Win	100	-1	99	0.445184	44.073184
Push	0	0	0	0.087705	0.000000
Lose half	-50	49	-1	0.021927	-0.021927
Lose all	-100	-1	-101	0.445184	-44.963551
Total	1.000000	-0.912295

Strategy

• It doesn't matter what you bet on between Black, Red, Color, and Inverse.
• Always take insurance.
• The odds between losing half and imprisoning a bet after a 31 tie are the same.

In other words, do whatever you want, as long as you take Insurance.

Methodology

This analysis was based on a random simulation of over 26 billion hands. A cut card was used in the simulation, placed after 271 cards.

Links

• montecarlocasinos.com has a page on the game rules.
• The Doctrine of Chances: Probabilistic Aspects of Gambling by Stewart N. Ethier. This book has a chapter on Trente et Quarante. My house edge for the game is 0.000018 higher than Ethier's. I believe this is due to cut card effect, which would not have played a role in Ethier's method of an exact combinatorial analysis.

Written by:Michael Shackleford

Roulette – in movies, on TV, and in literature, it’s often depicted as glamorous, exciting, and ridiculously lucrative for whichever character is playing. While winning big at the spinning wheel seems like a fantasy reserved for James Bond and other fictional high rollers, it is possible to minimize risk and win big at the same time by knowing the best roulette bets. It all comes down to the numbers, and how you want to play them.

In American Roulette there are 38 numbers – 1 through 36, a single zero, and a double zero. Besides the latter two, half the numbers are red, half are black, half are even, and half are odd. The 0 and 00 are green and obviously not even or odd. Betting on those will earn you a payout of 35:1 – but more on all that later.

Now that we’ve got the bare bones of the Roulette wheel and the felt laid out, let’s flesh out only some of the best roulette bets you have to choose from.

Roulette Bet 1 : Red/Black, Evens/Odds, 1-18/19-36

No other game on the casino floor gives players the chance of close to 50/50 odds on a single bet. With the red/black, evens/odds, or 1-18/19-36 bets, you’re giving yourself the chance of hitting almost half the options on the Roulette wheel – the 0 and 00 aren’t counted – which gives you a pretty nice chance of winning. Granted, that means that the payout ratio is lower (1:1, bet $10 win $10) but by the numbers, it’s one of the safest and best roulette bets you can go with when playing the wheel.

Payouts for this can be surprisingly rewarding if you’re willing to risk more money on each bet. Take Ashley Revell – he once bet $136,000 on a single spin of the Roulette wheel. If throwing down that sum of money on a single bet doesn’t sound impressive or at least make you sweat a little, know that the sum was the entirety of Revell’s life savings and the entire event was televised. So if Revell won, he’d double his money and evoke envy and admiration from his spectators; if he lost, he’d lose everything and earn deserved pity.

Revell laid all his loot on red, and the wheel delivered – the ball landed on the red 7, and Revell walked away having doubled his life savings. However, we can’t honestly recommend betting your entire net worth on a single spin of the wheel since we wouldn’t exactly characterize that as successfully minimizing risk.

Roulette Bet 2 : Columns

If a 1:1 payout isn’t exciting enough to motivate you to lay down some chips, you can slightly up the ante and the payout to 2:1 by betting on the columns. By going with this second best roulette bet, you’re bringing your option of numbers down to a little under a third, but betting on a column still covers a significant chunk of the felt while doubling your winnings – a $10 bet will win you $20.

Columns don’t contain consecutive numbers – for example, the first column has 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, and 31 – and the number of red and black numbers differs between each column, a fact that we’ll cover in a moment. And remember, the 0 and 00 aren’t included in any of the columns because they’re special and too good for all the other numbers.

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Roulette Bet 3: Black and third column/Red and second column

This third best roulette bet was specifically designed for people who like to hedge their roulette bets, or at least attempt to. The Roulette board is an interesting creature and when studied thoroughly, it may help you score big bucks. On the third column of the board, there are 8 red numbers and 4 black, whereas the second column is reversed, holding 8 black numbers and 4 red.

You, the savvy Roulette player, can take advantage of this layout for some slow but steady gains. If you bet on the red-rich third column and double your bet on the black ($10 on the third column, $20 on the black), you give yourself a solid chance of breaking even or making gains.

Here’s why: the third column contains more red numbers than any other column, giving yourself a good chunk of red on the wheel. At the same time, you’re betting on black, which gives you a little under half the wheel. The third column has a payout of 2:1, and the black has a payout of 1:1, so your column bet should be half the black bet to break even. This is because if a red number shows up on the third column, you win double your bet, but lose your black bet, which is the same amount – it’s considered a push, since you’re even. It’s the same when a black number comes up: you win your black bet, but lose your column bet. But when a black number on the third column comes up, you pull ahead. This system of betting minimizes the risk while giving you a solid chance of steadily padding your bankroll.

The same thing applies to the combination bet of red and the second column – red gives you just under half the numbers, and the second column has 8 black numbers. Be patient, and this roulette bet could help you earn big gains.

Roulette Bet 4: Straight up

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If you care way more about the payout than you do about minimizing risk, your best option is to go with the straight roulette bet. This involves betting on a single number and hoping that Lady Luck is on your side. The risk is extremely high, but the payout – 35:1, $350 for a $10 bet – is pretty freakin’ sweet. Plus, this is the only category that includes the 0 and 00 tiles.

If you’ve got a bankroll of $350, you could technically go through 35 $10 bets in a row before you’re out of the game. And if you win once, you’re up $350. The chances of you hitting the exact number you’re going for is about 2.7% or 1 in 37, but what’s a big reward without bigger risk?

Roulette Bet 5 : Split bet

If you want to go big but the straight bet gives you the cold sweats, you can still go for a higher reward with a lower risk and choose the split bet instead. This involves placing chips on any two numbers that are next to one another on the felt. This can be either horizontal or vertical placement, and to place the bet you put a chip on the line between the two numbers.

The payout of 17 to 1 is lower than the straight bet, but the chances of hitting your numbers are 1 in 18, which is way better than the 1 in 37 the straight roulette bet offers.

The 5 best roulette bets summarized:

1. Red/Black, Evens/Odds, 1-18/19-36
2. Columns
3. Black and third column/Red and second column
4. Straight up
5. Split bet

Put these winning roulette bets to the test

So you’ve read and digested all the best roulette online real money bets we’ve laid out here, and now you want to put them to the test. Great! Try these roulette bets at our online casino real money usa and see how they work out for you, or come up with your own winning combination bets and let us know how it goes!