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.