Probabilities and Variance of Two-Sided Bets in Blackjack, Roulette, Baccarat
In this article, I’m exploring the differences between the two-sided “coin flip” bets available in games of Blackjack, Roulette, Baccarat and Sic Bo to try and answer the question – which is the best bet?
To give this some context, I’ll talk about the varying degrees of volatility between these games, as they all offer two-sided bets that act like coin flips. Even though the chances to win any of these bets are similar, the outcomes are decided differently.
If you are in any way excited by odds and probabilities, this page should make for an interesting read.
Coin, Wheel, Dice or Cards?
Coins
A coin with two sides, a roulette wheel with 37 pockets, three dice with 216 outcomes, and eight decks of 52 playing cards with millions of results all have varying degrees of randomness.
This isn’t easy to describe in either layman’s or mathematical terms, but I’ll give it a go.
A flip of a coin is a single event, and therefore only one event you’re concerned with. The chance is 50-50, but seeing consecutive Head results in a row wouldn’t be surprising. The odds of flipping 10 Heads in a row are 1/1024.
Wheel
Roulette is quite similar to a coin flip, although it’s an expanded version because instead of two “pockets” of Heads and Tails, you’ve got 37 pockets 0-36. Because of the Zero (which is green), the chance of seeing 10 Reds in a row is 1/1376.
Dice
Dice results also behave in roughly the same manner, though it further expands the “pockets”. Three dice only have 16 possible total outcomes (3 to 18), but there are 216 ways in which the three dice can show them.
Since that number is more significant than in Roulette, we can safely assume the High/Low bet on dice will have less variance than the High/Low bet on Roulette.
In other words, you should be prepared for longer losing or winning streaks in Roulette.
The same bet will feel gentler in Sic Bo, even if the mathematical probabilities per roll are similar.
Cards
This is further expanded in the game of Baccarat. This entire game is designed to act like an elaborate coin flip, with special rules such as the Third Card Rule and the requirement of a knowledgeable dealer who can handle the game. It’s an elaborate charade that acts as a coin flip.
There are roughly 5,000,000,000,000,000 – five quadrillion – possible combinations in an 8-game deck of Baccarat. That’s a lot of pockets. While the odds and probabilities remain in the usual coin flip range, the outcome distribution feels more life-like and not as out of control as Roulette.
Blackjack is an order of magnitude more complex than Baccarat because the dealer and the Player make choices. Various table rules affect the chance of winning and the house edge. An 8-deck game of Blackjack has less variance than an 8-deck game of Baccarat.
This is because, in Blackjack, you make choices, which makes all the difference. This is the only two-sided casino game that lets you do that instead of you simply being a casual observer of outcomes.
Blackjack
Blackjack is essentially a two-sided bet. You either win 1 unit when you win or lose 1 unit when you lose, with a caveat that you can win 3:2 if you get a Blackjack.
If you’re playing the game, you’ll want the one with the most favourable table rules to reduce the house edge as much as possible, and you’ll want to follow the basic blackjack strategy.
Some of the best live dealer blackjack games to play are:
Roulette
Roulette has two-sided bets: Red/Black, Odd/Even and High/Low. All three behave the same in mathematical terms. The house edge comes from the existence of Zero; otherwise, Roulette would be a fair game.
An important thing to note here, perhaps crucial, is that a version of Roulette (French Roulette) cuts the house edge in half, to 1.35%, when you lose on a two-sided bet because the ball landed on Zero. The rule is called “La Partage”, where you get half of your bet back in the described scenario.
However, even with the house edge reduced to half, the game has a significant house edge. There is no question that French Roulette is the best version of Roulette to play for two-sided bets. Read these articles for more information:
- French Roulette overview
- Live Casinos with La Partage rule
Baccarat
Unlike Blackjack, Baccarat is a simple betting game requiring no skill. You observe what happens after you bet on either the Banker or the Player winning.
There is a long list of available Live Baccarat games, some of which include win multipliers, so the best thing to do is to visit one of these pages and find your perfect game:
Sic Bo
Sic Bo is a game that uses three dice to generate randomness. There are numerous betting options available, and the ones I’ll be talking about here are the two coin flips: Big/Small and Odd/Even. Both have a probability of 48.61%, with a house edge of 2.78%. These are the Sic Bo side bets with the lowest house edge.
All live dealer versions of Sic Bo have the same payouts, even the win multiplier versions, as the Big/Small and Odd/Even bets can’t get multipliers.
The four live dealer Sic Bo multiplier games I’m talking about are as follows:
- Super Sic Bo (Evolution)
- Sic Bo Deluxe (Playtech)
- Mega Sic Bo (Pragmatic Play)
- Ultimate Sic Bo (Ezugi)
As Sic Bo uses three dice, the range of possible outcomes is greater, and the variance is a bit steadier than, say, a game with two dice.
Two-sided Bets Compared
| Game | Bet | Probability | House Edge | Variance |
|---|---|---|---|---|
| Roulette | Red/Black | 48.65% | 1.35% | Extreme |
| Roulette | Odd/Even | 48.65% | 1.35% | Extreme |
| Roulette | High/Low | 48.65% | 1.35% | Extreme |
| Sic Bo | Big/Small | 48.61% | 2.78% | High |
| Sic Bo | Odd/Even | 48.61% | 2.78% | High |
| Baccarat | Banker | 45.86% | 1.06% | Moderate |
| Baccarat | Player | 44.62% | 1.24% | Moderate |
| Blackjack | 42.22% | as low as 0.50% | Low to Medium |
The house edge of 1.35% applies to playing two-sided bets on French Roulette only. On regular European Roulette without either La Partage or En Prison rules, the house edge would be 2.70%.
The chance of winning any hand of Blackjack is roughly 42%, though this varies with the table rules and the strategy used.
The house edge can be as low as 0.50% with the perfect rules and strategy where the correct decision is made every time.
Conclusion
If you’ve read until the end, congratulations and thanks.
You should now be able always to ask yourself – how is this game generating its randomness? – when you play any casino game.
Remember, the more “pockets” the game has, the more natural the results will appear.
Roulette is the wildest game for long losing and winning streaks, which explains why it is the epitome of gambling fallacies and the betting systems that lead to ruin.
What you’ve read in this article is the reason for that.
You don’t hear such stories about Blackjack, do you?
This is because Blackjack is a game played by a different profile of gamblers, of course, but also because it doesn’t prompt doubling up after a loss, and, last but not least, because the likelihood of entering a long losing streak is lower than in Roulette.
On the other hand, if you’re looking to benefit from wild randomness and want to turn your £10 into £10,240 with a 10-game winning streak, then Roulette is the game.