# Blackjack: What are the odds of me starting with £200 and leaving with £10,000? That's a 1 in 50 chance right?

### 7 Answers

- The_Doc_ManLv 74 months ago
Odds don't work that way, and by the way, the odds are ALWAYS slanted towards the house making all the money.

To REALLY compute the odds, you have to start with the realization that the odds of winning overall in blackjack are based on the odds of winning on one hand multiplied by however many hands you would play. The odds ALWAYS favor the house, so to win one hand, you have to be on the low-probabily side of things. To win for the evening, you have to be on the low side of the odds that entire time. And that is the problem with cumulative probability. The numbers usually catch up.

- Anonymous4 months ago
Dunno,

I would venture to say somewhere btwn the

odd's of living past I00 & growing beyond 7'

tall which aren't that likely @ all my dude-cuz!

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- zman492Lv 74 months ago
The odds cannot be calculated without knowing what the house rules are for the game, how well you play, and how you determine the size of each bet.

Remember the dealer will win over half of blackjack hands played, even if you play perfectly, because you can win more than your original bet on some hands.

- Divide By ZeroLv 74 months ago
Re-edit: gah I forgot Y!A doesn't let me do single-spacing. Fixed.

Cliff notes: 1.88% or 1/53 in Baccarat

Edit - alright I'll just do some math.

I said blackjack would be a bad choice primarily because you'd either have to sacrifice EV by going all-in each hand (thus giving up your option to split or double down), or probably worse, bet half your stack. So instead I'll do some math for a different game.

Baccarat banker bet would be a good choice. It has a low house edge and a >50% chance of winning a non-tied hand. The payout is slightly under 1:1 but your goal of 50x isn't a power of 2 anyway.

Idk how many decks is typical but let's say you're playing 8 decks. Using the chart at wizardofodds, I see that the chance of winning a non-tied hand is .50682624. Call that p, and call the chance of losing q.

If you win 5 all-ins, you'll be at $5639. The chance of that is p^5. Your next bet will be (10k-5639)(2/1.95) = 4473. If you win that, you're at 10k. If you lose it, you're down to 1166 and then if you win your next 3 bets, you're up to 8646. And so on, the process can potentially continue for a very long time. However, long sequences have negligible chances, so we can get very close to the answer without an infinitely long calculation.

The sequence will be:

200

^5=5369, bet=4473

1166^3=8646, bet=1389

7257, bet=2813

4444

8666, b=1368

7298, b=2771

4527

8828, b=1202

7626, b=2435

5191, b=4932

259

^5=7302, b=2767

4535

8843, b=1187

7656, b=2404

5252, b=4870

I stopped there, which is further than I needed to go. Your chance is:

p^5(p + qp^3(

p + q(

p + qp(

p + q(

p + qp(

p + q(

p + q(

p + qp^5(

p + qp(

p + q(

p + qp )))))))))))

= 1.88% or about 1/53

- PyrusLv 64 months ago
Not even close. It actually is a random variable that follows a certain probability density function. What you did with the 1 in 50 chance is multiply the outcome from the income. 200 x 50 = 10000. Unless the probability distribution happened to be EXACTLY uniform and you were winning 200 pounds with the probability of 1 / 50th root of 50, (which we all know is impossible), then you would have a 1 in 50 chance to win.

To learn more about it, study what Stochastic processes is, and start with what is known as the Gaussian Distribution.