Odds Of Losing 6 Blackjack Hands In A Row

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You Probably Mean “Probability”

First off, let’s change the question from one about “odds” to one about “probability”. Most people who are asking this question want a simple answer expressed as a single digit or as a simple percentage. Odds mean something different, so we will not be going there. That’s because, though gamblers tend to use these two phrases interchangeably, they are not.

Odds Of Losing: Your Question Is Incomplete

Now there’s a crucial piece of information missing from your question. And that’s how you intend to play. For example, if we were seated together at the blackjack table. I lean over to you and say, “Hell, I’m having an awful game. In fact, my luck is so crap, I’ll bet you $100 that I lose the next 6 hands in a row”. If you were that stupid to bet me, then, of course, I’d make sure to lose the next 6 hands! I would show you that the probability/odds of losing 6 hands in a row were 100%!

Finally, An Answer?

If you’re playing a typical shoe game, then the basic strategy will tell us that the player will win 43.3% of hands, lose 48% and push the other 8.7%. So then, what are the odds of losing the next 6 hands at blackjack using basic strategy?

Since each hand has a 48.0% chance of being a loss, the answer is 0.48 ^ 6 = 0.012 = 1.2%.

But what if you lose the first and push the second? And then lose the next 5 hands? We’re guessing that you want us to ignore all pushes. We should only count hands won or lost. Of non-pushed hands, the player will win 47.4% and lose 52.6%. So, let’s re-phrase the question once again. What is the probability of losing the next 6 hands at blackjack using only basic strategy and ignoring all pushes? The answer is, the odds of losing are 0.526 ^ 6 = 0.021 = 2.1%. That is roughly 1 in 47 attempts.

What About Other Length Losing Streaks?

Here are the relevant numbers for losing streaks in a row:

n Probability One in
1 loss 52.6% 1.9
2 losses 27.7% 3.6
3 losses 14.6% 6.9
4 losses 7.7% 13
5 losses 4.0% 25
6 losses 2.1% 47
7 losses 1.1% 90
8 losses 0.59% 170
9 losses 0.31% 323
10 losses 0.16% 614
11 losses 0.08% 1168
12 losses 0.04% 2219
13 losses 0.02% 4217

The Sad Underlying Reason For This Question

Really the only reason for asking this question is if you’re considering going down the road of progressive betting. Especially a negative progressive system. Of course, these systems would fail miserably if they encountered a losing streak. Hence the initial question. And the most common system they’ve found is the dreaded Martingale. This is where you double up your bets for each loss, thereby hoping to break even at some point.

The Martingale is the most basic of all the negative progressive betting systems. The idea behind the Martingale system is very simple. If you lose a hand, just double your wager for the next hand. Eventually, you’ll win and therefore make back all your losses as well as your initial bet. Yep, it’s that simple. And it sounds doable. The real problem with it is that gamblers fail to take into account just how likely those unlucky streaks can be. Looking at the table above we can see that the probability does get smaller and smaller. But just not small enough to mitigate the odds of losing.

Odds Of Losing: Why You Should NOT Bet The Martingale

Don’t for one second think that the martingale system is a good idea. What it does, is give you a high percentage chance of winning a small amount of money, but it totally fails to take into account long term outcomes. Think about this: for a $10 better who needs to be able to handle 7 losses in a row, then he’d be needing a bankroll of $2550, and also you’ll need to be able to bet $1280 on the 8th hand. And all this for a $10 each way bet! Now you can see just how crazy that would be.

Aside of the above, using the martingale system with blackjack is a pretty bad idea. Keep in mind that you have doubles and splits, which can sometimes happen in the same hand. In that case, you’re going to need a much bigger bankroll in order to play basic strategy. Of course, you could very well choose to ignore basic strategy, in which case you’ll need to take a substantially higher loss on all of your bets as your odds on losing go up.

Odds Of Losing: It’s Not Only The Martingale

All negative progressive betting systems are doomed to fail. Unfortunately, any series of negative betting expectations will lead to a negative expectation overall. We suggest that if you’re playing for fun, then you just stick with the tried and tested flat betting. And if you’re playing for profit, then you’ll need to play with basic strategy at online jackpot sites or count those cards.

From my video poker appendix 3 we can see the standard deviation for 1-play jacks or better is 4.417542. The standard deviation for 4-play jacks or better is 5.041215. Keep in mind these figures are per hand and relative to the betting unit. Adjusting for bet size and number of hands the standard deviation of $5 bet in 1-play jacks or better is 1^1/2*5*4.417542 = 22.08771. The standard deviation of 4 bets of $2.50 in 4-play jacks or better is 4^1/2*$2.50*5.041215 = 25.20608. So you are better off betting the smaller total amount in 1-play. Interestingly you can double the total amount bet in 4-play and the standard deviation only goes up by 14.12%.

Actually I get a player return of 101.62%. Buried within their rules is this statement, 'Please note that all games share the same mechanism which determines the jackpot win. Thus, with card games, the probability of hitting the jackpot combination is not natural but controlled by this shared random mechanism in the same way as slot machines' wins.' It is my understanding that they offered this game for quite a while before posting this warning. I just don't trust any casino that would rig a card game, even if they admit it in the fine print.

For the sake of simplicity let’s stay with your example and say the probability of winning is 70% and losing is 30% if you hit. The expected value of hitting would be 0.3*1 + 0.7*-1 = -0.4. This is greater than the expected value of -0.5 by surrendering.

No, these exceptions should not be used for 4-8 decks. There are a few exceptions in 4-8 deck games but they are so border line that it isn’t worth the bother to learn them. An interesting rule of thumb for all numbers of decks is that with 16 vs. 10, where the 16 is composed of 3 or more cards, in general the odds favor standing.

The name for this system is the Martingale. Ignoring ties the probability of a new loss for a hand of blackjack is 52.51%. So the probability of losing 8 in a row is .5251⁸ = 1 in 173.

No. If your goal is a small win then you should be playing low volatility, high hit frequency games. I can’t suggest any particular games but look for ones with comparatively small jackpots. These will also help you to play longer.

The Martingale is dangerous on every game and in the long run will never win. However it is better to use in baccarat than roulette, just because of the lower house edge. The probability of the player winning 8 times in a row is 0.493163^8 = 1 in 286. Also keep in mind you could win a hand late in the series and still come out behind because of the commission. For example if you started with a bet of $1 and you won on the 7th hand you would win $60.80 ($64*95%), which would not cover the $63 in previous loses.

I’ve been asked about these North Carolina slot machines so many times I’m tempted to fly there just to see them for myself. Yes, if they did give the probability of each symbol for each reel then an optimal strategy and a return could be fairly easily calculated. However I have never actually seen such a table and have never worked out the odds.

The probability of any hand less than a pair is the product of the number of ways to pick 3 different ranks out of 13, less 12 for the consecutive ranks that result in a straight, and the number of ways to pick a suit 3 different times, less 4 for picking the same suit each time. So the total combinations for ace-high or less is (combin(13,3)-12)*(4³-4) = 16,440.

Odds Of Losing 6 Blackjack Hands In A Rowing

Now let’s look at the combinations for a jack high or less. We have omitted 3 ranks so there are 3 ranks to choose from among 10. However 8 of these combinations result in a straight (2/3/4 to 9/10/J). Again there are 4³-4 ways to pick the suits. So the total combinations is (combin(10,3)-8)*( 4³-4) = 6,720. The total combinations for Q-A high is simply 16,440-6,720=9,720. For an explanation of the combin function please see my probabilities in poker section.