The double or nothing feature in video poker is the only other casino bet, besides the odds in craps, with no house edge. Whether or not you take it depends on your reason for playing. If you are playing a negative-expectation game, for purposes of entertainment, then I think you should accept the double-up option in moderation, depending on on. In betting, a 'double or nothing' bet is an even money wager in which you either double your money or lose your entire bet. For instance - let's say that you decide to wager with a friend on a Manchester City game and lose. You may say to him - 'I'll bet you that Man City wins next week at home against Manchester United - double or nothing?' The Double or Nothing game consists of a standard playing deck of 52 cards and 2 jokers. It’s up to you to bet on whether the randomly overturned card will be a Red Card or a Black Card. Guess right, and you double your money. Guess the wrong color or land a joker and you lose.

Gambling is defined by the relationship between risk and reward. Put something on the line, fade a bit of variance to beat the odds, and collect a little something in return. Sounds simple enough, right? But what about the ultimate gamble, putting it all on the line for a single double or nothing bet?

Ideally, a savvy gambler exercising sound bankroll management would never find themselves in a true double or nothing spot. It’s much more feasible to break a bankroll into pieces that can be deployed safely and strategically over a series of bets. Nonetheless, even the most proficient players on the planet can find themselves dabbling in a bit of double or nothing action. Just ask Jake Cody, one of the top professional poker players on the planet.

Cody has already captured poker’s elusive “Triple Crown,” winning titles at the World Series of Poker (WSOP), World Poker Tour (WPT), and European Poker Tour (EPT) during the Brit’s storied career on the felt. And with over $4.5 million in live tournament earnings to his credit, not to mention millions more won playing online, Cody certainly has cash to burn.

Even so, it was a strange sight to see Cody – fresh from winning a £2,200 buy-in tournament at the 2018 U.K. Poker Championships in February – take his £42,670 (just under $60,000) in prize money straight to the roulette table for a daring double or nothing bet.

After a bit of prompting from his pals, and a healthy dose of liquid courage at the bar, Cody decided to have a bit of fun. He plunked down the entire stack of $60,000 in casino chips on Black and hoped for the best. You can watch the scene play out here (scroll midway down page for video), but suffice to say, Cody’s bold bet on Black paid off in spades.

After scoring the five-figure double up, Cody later told PokerNews exactly how a poker pro who prides himself on skillful play wound up playing a true game of chance for big bucks:

I mainly did it for the story to be honest. It sounds kind of silly, but I base a lot of my life decisions based on how good of a story it would be. I thought it would be a good story.

It might sound ridiculous too, but I genuinely didn’t even contemplate that I was going to lose. I was just completely convinced I was going to win.”

On the opposite end of the spectrum from Cody’s roulette escapades, small stakes gamblers down on their luck might use a double or nothing bet as their last stand. They’ll either score a sweet 100 percent profit on a single bet, or go busto to end their session, but both alternatives beat the arduous effort involved in rebuilding slowly from the ground up.

Whatever the reason, gamblers often find themselves contemplating which double or nothing scenario offers the biggest upside. Fortunately, the casino floor offers several variations of the double up wager, ranging from the relative safety of blackjack to the roller coaster of a roulette spin.

To help you make up your mind, check out the following five double or nothing bets to see which one is the best for you:

1 – Base Bet in Blackjack – (House Edge = 0.50 percent)

The classic casino card game, blackjack incorporates skill and strategy to separate winners from losers. Thus, a good old-fashioned hand of “21” sure does seem like the best bet for your double or nothing dollar. After all, a player using basic strategy enjoys a tiny house edge of 0.50 percent on average, depending on various gameplay rules and provisions.

But a skillful player’s advantage in blackjack can only be realized over the long run, with a large enough sample size to balance out variance. In the span of just a single hand, anything can happen. To wit, check out the overall probabilities behind a single random hand of blackjack:

As it turns out, ties or “pushes” occur far more often than one might imagine – players wind up deadlocked with the dealer on more than 8 percent of hands. If ties are removed from the equation, blackjack players who apply basic strategy will only collect wins on 42.43 percent of their hands. Of course, with juiced up payouts on blackjacks, coupled with the opportunity to double down when favorable spots arrive, skillful blackjack players can turn that 42.43 percent win rate into enough profit to beat the game over the long run.

This double or nothing scenario doesn’t afford the advantage of a long run though, so blackjack – despite a low house edge that’s among the best on the floor for players – isn’t an ideal candidate for a “win or go home” wager. And blackjack’s flaws – at least when this one-off bet exercise is concerned – are even more pronounced than meets the eye.

Remember those blackjack payouts (6 to 5 in bad games, 3 to 2 in good games) and double down plays mentioned earlier? Well, those are the tools winning blackjack players use to level the playing field given the house’s higher win rate. Splitting paired hands is another weapon in the arsenal, as it allows players to “break” bad totals like 16. Over the course of an extended session, landing plenty of blackjacks, doubling down at the right time, and splitting when the situation calls can pad a competent player’s profit margin.

But when you’re playing a single contained hand, one which sees your entire bankroll put at risk, both doubling down and splitting are taken off the table. You need to match your original bet with a second chip or stack of equal value in order to double down or split. That means a double or nothing play leaves you without the necessary ammunition to fire that second barrel.

Famed gambling expert and author John Grochowski described the blackjack dilemma as follows in his analysis of double or nothing bets:

The blackjack payoffs don’t increase the frequency of winning hands, and you can’t double down or split pairs if you have your entire stake on the table at once.

What you’re left with is a game in which a basic strategy player wins a tad less than 48 percent of decisions, and average players will win a little less often than that. Somewhere between 52 and 53 percent of the time, the double-up player will walk away with nothing.”(Quote)

Grochowski’s stated win rate of 48 percent actually includes ties and wins, but even so, as he observes, double or nothing players will lose their blackjack bet 52 times out of every 100 tries.

2 – Banker Bet in Baccarat – (House Edge = 1.06 percent)

Despite their apparent similarities – two-card starting hands, face cards lumped together at the same value, and a set total to try and achieve – baccarat is blackjack’s polar opposite. Blackjack players must memorize the basic strategy guidelines for hundreds of unique scenarios, and their skillful play helps to counter the game’s natural variance.

Baccarat players, on the other hand, don’t even need to know the rules. After placing a bet on either the Player or Banker hand, all they have to do is sit back and let the dealer decide their fate. Two cards will be dealt to each hand, and then a third when warranted, before the final totals are compared. The hand closest to 9 wins, with players who backed that hand collecting an even money* payout.

*Banker bet payouts are slightly less than even money, which you’ll learn more about below

Players don’t get to act on the cards or affect the outcome in any way, making baccarat the very definition of a game of chance. Due to a quirk in the rules that sees the Banker hand draw last, it holds a slight statistical edge over the Player hand, as you can see below:

With those win probabilities in mind, the house edge on a Banker bet stands at 1.06 percent, while the Player bet offers a 1.24 percent rate. At this point you’re probably wondering why anybody would ever bet on the Player hand at all. Well, they wouldn’t if the payouts were identical, but baccarat institutes a 5 percent commission policy on winning Banker bets. This fee paid to the house counteracts the Banker hand’s inherent advantage, putting in on even ground with the Player hand from a probability versus profit perspective.

In other words, a gambler betting $100 on the Banker hand would collect $95 on a win, while winning Player bets would receive the full $100 even money return. Knowing this, you can’t literally go for a double or nothing win by betting the Banker in baccarat, but it’s close enough for this page’s purposes.

Grochowski offers the following insight into how the 5 percent commission fee on Banker bets can impact its double or nothing prospects:

Well, it depends on whether you’re willing to settle for 195 percent of your bankroll instead of the full double-up. The casino gets its edge by charging a commission, usually 5 percent, on winning banker bets.

When you win, you win 95 percent of your bet. When you lose, you lose the whole thing.”

As he reveals, when ties are factored in as wins – or put more accurately, ignored for the sake of the double or nothing exercise – a Banker bet in baccarat will win slightly more than it loses. And compared to the 2 percent hole you’d face putting it all on one hand of blackjack, a 0.7 percent edge on the Banker bet seems like a steal.

3 – Pass Line or Come Bet in Craps – (House Edge = 1.41 percent)

The base bet at a craps table is the Don’t Pass Line wager, which is placed before the first roll (the “come out” roll) of a round. When betting on the Don’t Pass Line, you’re simply hoping to see the shooter roll a 7 or 11 before a 2, 3, or 12 hits. When 7 or 11 arrive on board first, you’ll double your bet. And when a 2, 3, or 12 shows up, you’ll “crap out” and lose it all.

Technically, you can also bet on the Don’t Pass Line, which just flips the Pass Line dynamic on its head. And while the Don’t Pass Line does indeed offer a slightly lower house edge of 1.36 percent, most craps players avoid this wager, as it has you betting against the shooter and the table. For that reason, we’ll avoid what craps enthusiasts call the “dark side” and stick with Pass Line betting.

If you’ve never played craps, you’re probably wondering what happens when that come out roll lands on a 4, 5, 6, 8, 9, or 10. When these numbers show up before a 2, 3, or 12 for a crap out, or a 7 or 11 for an immediate win, the game continues onward. The six numbers above will be established as the “point” if rolled first on a come out roll. From there, Pass Line bets remain in play, and a new sort of game begins.

Now, you’re hoping to see the same point number appear to collect an even money payout. But if the shooter rolls a 7 at any point, they’ll “seven out” and your initial Pass Line bet is claimed by the house. Thus, the Pass Line in craps offers two ways to collect a double up payout.

First, you can simply score a 7 or 11 on the come out roll to receive an immediate even money payout. From there, once a point number has been set, a repeat roll of that same number before a 7 shows up is good for even money.

You aren’t limited to betting on the come out roll either, so if a shooter is in mid-session, you can place a Come bet to achieve the same effect. Here’s how Grochowski describes the similarities between the Pass Line and Come bets:

If the next roll is a comeout when you arrive at the table, bet pass or don’t pass. If not, make it come or don’t come.

On pass or come, you’ll win 49.29 percent of decisions. That’s a double-up number that beats blackjack.”

And as the veteran casino gaming analyst reveals, Pass Line and Come bettors enjoy a win probability of 49.29 percent – with no ties to gum up the works. That means the casino will still beat you slightly more than you’ll beat them, but the margin of 0.71 in their favor is actually three times better for you than blackjack.

4 – Base Bet in Casino War – (House Edge = 2.88 percent)

An odd little carnival contest masquerading as a table game, Casino War looks for all the world to be a “sucker” bet. This is the card game War, after all, just like you played at home on rainy days. Two players face off – well, a dealer and a player in this case – each taking one card face up. The high card wins the round, and when a tie occurs, it’s settled by a “war” – or yet another high card contest, just with more on the line.

At its essence, Casino War is basically just a streamlined version of baccarat. Both games rely purely on random chance, but Casino War simply strips down the two-card totals, drawing round, and other minutiae of baccarat. On its surface, Casino War seems like a much worse game than blackjack or baccarat by virtue of its 2.88 percent house edge. And while that is much higher than the other two card games, house edge rates really only apply to long run sessions.

Judged within the one off structure of a double or nothing bet, Casino War is actually a great play. Check out the following win / war / loss probabilities so see for yourself:

That’s right, yet another game that gives players a better than 50/50 shot to win a single hand. Based off that fact alone, only the Bet in baccarat is a better option among the wagers discussed so far. One issue facing double or nothing bettors, however, is the need for an additional bet when you go to war. If the initial cards dealt out are tied in value, Casino War calls for a second bet to be placed in order to wage war. The war itself is yet another high card contest, but unless you have the second bullet, you’ll turn a tie into a loss.

Even with this limitation though, Grochowski deems the base bet in Casino War to be perfectly acceptable for double or nothing warriors:

While the base game of Casino War isn’t that bad, the tie bet is something to avoid like the plague. Playing with a six-deck shoe, the house has a stunning 18.65 percent edge on the tie bet, and if you happen to find a single-deck game, you are giving the house an edge of more than 30 percent on the tie bet.

Sticking to the basic game will make your money go a lot further while you chat and have fun.”

5 – Red/Black or Odd/Even Bet in Roulette – (House Edge = 5.26 percent)

Bringing this page full circle, the even money bets on a roulette table are among the most entertaining offered on the casino floor.

Sure, the house edge of 5.26 percent on double-zero American wheels is rather high, but as we know by now, it only matters in the long run. For a one-time shot at glory, like Cody proved in the clip from earlier, betting on Black or Red – along with the other even money bets in roulette, Even / Odd and First 18 / Last 18 – is a great way to go for the gusto as a gambler.

Grochowski certainly agrees, as he proclaims even money wagers on the roulette wheel to rank alongside blackjack in terms of viability:

On a double-zero wheel, you’ll win those even-money payoffs 47.37 percent of the time, and on a single-zero wheel, it’s 48.65 percent.”

When wagering on any even money roulette bet on an American double-zero wheel, you’ll have 38 spaces in play, including 18 winners. The other 18 spaces opposite your pick are direct losers, along with the green “0” and “00” house spaces.

Thus, with odds of 18/38, your chances of winning on a single spin stand at 47.36 percent. And as Grochowski alluded to above, when you can locate a European style single-zero wheel, your win probability on even money wagers climbs to 48.64 percent.

For beginning gamblers finding a simple double or nothing wager is a good place to start. You can find the 5 double or nothing bets listed on this page in most casinos and they’re easy to make.

A martingale is any of a class of betting strategies that originated from and were popular in 18th-century France. The simplest of these strategies was designed for a game in which the gambler wins the stake if a coin comes up heads and loses if it comes up tails. The strategy had the gambler double the 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 will almost surely eventually flip heads, the martingale betting strategy is certain to make money for the gambler provided they have infinite wealth and there is no limit on money earned in a single bet. However, no gambler possess infinite wealth, and the exponential growth of the bets can bankrupt unlucky gamblers who chose to use the martingale, causing a catastrophic loss. Despite the fact that the gambler usually wins a small net reward, thus appearing to have a sound strategy, the gambler's expected value remains zero because the small probability that the gambler will suffer a catastrophic loss exactly balances with the expected gain. In a casino, the expected value is negative, due to the house's edge. Additionally, as the likelihood of a string of consecutive losses occurs more often than common intuition suggests, martingale strategies can bankrupt a gambler quickly.

The martingale strategy has also been applied to roulette, as the probability of hitting either red or black is close to 50%.

Intuitive analysis[edit]

The fundamental reason why all martingale-type betting systems fail is that no amount of information about the results of past bets can be used to predict the results of a future bet with accuracy better than chance. In mathematical terminology, this corresponds to the assumption that the win-loss outcomes of each bet are independent and identically distributed random variables, an assumption which is valid in many realistic situations. It follows from this assumption that the expected value of a series of bets is equal to the sum, over all bets that could potentially occur in the series, of the expected value of a potential bet times the probability that the player will make that bet. In most casino games, the expected value of any individual bet is negative, so the sum of many negative numbers will also always 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 is also true in practice).^[1] It is only with unbounded wealth, bets and time that it could be argued that the martingale becomes a winning strategy.

Mathematical analysis[edit]

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.^[1]

However, without these limits, the martingale betting strategy is certain to make money for the gambler because the chance of at least one coin flip coming up heads approaches one as the number of coin flips approaches infinity.

Mathematical analysis of a single round[edit]

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. Following is an analysis of the expected value of one round.

Let q be the probability of losing (e.g. for American double-zero roulette, it is 20/38 for a bet on black or red). Let B be the amount of the initial bet. Let n be the finite number of bets the gambler can afford to lose.

The probability that the gambler will lose all n bets is qⁿ. When all bets lose, the total loss is

${\displaystyle \sum _{i=1}^{n}B\cdot 2^{i-1}=B(2^n-1)}$

The probability the gambler does not lose all n bets is 1 − qⁿ. In all other cases, the gambler wins the initial bet (B.) Thus, the expected profit per round is

${\displaystyle (1-q^n)\cdot B-q^n\cdot B(2^n-1)=B(1-(2q{)}^n)}$

Whenever q > 1/2, the expression 1 − (2q)ⁿ < 0 for all n > 0. Thus, for all games where a gambler is more likely to lose than to win any given bet, that gambler is expected to lose money, on average, each round. Increasing the size of wager for each round per the martingale system only serves to increase the average loss.

Suppose a gambler has a 63 unit gambling bankroll. The gambler might bet 1 unit on the first spin. On each loss, the bet is doubled. Thus, taking k as the number of preceding consecutive losses, the player will always bet 2^k units.

With a win on any given spin, the gambler will net 1 unit over the total amount wagered to that point. Once this win is achieved, the gambler restarts the system with a 1 unit bet.

With losses on all of the first six spins, the gambler loses a total of 63 units. This exhausts the bankroll and the martingale cannot be continued.

In this example, the probability of losing the entire bankroll and being unable to continue the martingale is equal to the probability of 6 consecutive losses: (10/19)⁶ = 2.1256%. The probability of winning is equal to 1 minus the probability of losing 6 times: 1 − (10/19)⁶ = 97.8744%.

Double Or Nothing Betting Odds

The expected amount won is (1 × 0.978744) = 0.978744.
The expected amount lost is (63 × 0.021256)= 1.339118.
Thus, the total expected value for each application of the betting system is (0.978744 − 1.339118) = −0.360374 .

In a unique circumstance, this strategy can make sense. Suppose the gambler possesses exactly 63 units but desperately needs a total of 64. Assuming q > 1/2 (it is a real casino) and he may only place bets at even odds, his best strategy is bold play: at each spin, he should bet the smallest amount such that if he wins he reaches his target immediately, and if he doesn't have enough for this, he should simply bet everything. Eventually he either goes bust or reaches his target. This strategy gives him a probability of 97.8744% of achieving the goal of winning one unit vs. a 2.1256% chance of losing all 63 units, and that is the best probability possible in this circumstance.^[2] However, bold play is not always the optimal strategy for having the biggest possible chance to increase an initial capital to some desired higher amount. If the gambler can bet arbitrarily small amounts at arbitrarily long odds (but still with the same expected loss of 10/19 of the stake at each bet), and can only place one bet at each spin, then there are strategies with above 98% chance of attaining his goal, and these use very timid play unless the gambler is close to losing all his capital, in which case he does switch to extremely bold play.^[3]

Alternative mathematical analysis[edit]

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 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.^[4] This intuitive belief is sometimes referred to as the representativeness heuristic.

Anti-martingale[edit]

In a classic martingale betting style, gamblers increase bets after each loss in hopes that an eventual win will recover all previous losses. The anti-martingale approach, also known as the reverse martingale, instead increases bets after wins, while reducing them after a loss. The perception is that the gambler will benefit from a winning streak or a 'hot hand', while reducing losses while 'cold' or otherwise having a losing streak. As the single bets are independent from each other (and from the gambler's expectations), the concept of winning 'streaks' is merely an example of gambler's fallacy, and the anti-martingale strategy fails to make any money. If on the other hand, real-life stock returns are serially correlated (for instance due to economic cycles and delayed reaction to news of larger market participants), 'streaks' of wins or losses do happen more often and are longer than those under a purely random process, the anti-martingale strategy could theoretically apply and can be used in trading systems (as trend-following or 'doubling up'). (But see also dollar cost averaging.)

How Does Double Or Nothing Work

See also[edit]

References[edit]

1. ^ ^abMichael Mitzenmacher; Eli Upfal (2005), Probability and computing: randomized algorithms and probabilistic analysis, Cambridge University Press, p. 298, ISBN978-0-521-83540-4, archived from the original on October 13, 2015
2. ^Lester E. Dubins; Leonard J. Savage (1965), How to gamble if you must: inequalities for stochastic processes, McGraw Hill
3. ^Larry Shepp (2006), Bold play and the optimal policy for Vardi's casino, pp 150–156 in: Random Walk, Sequential Analysis and Related Topics, World Scientific
4. ^Martin, Frank A. (February 2009). 'What were the Odds of Having Such a Terrible Streak at the Casino?'(PDF). WizardOfOdds.com. Retrieved 31 March 2012.