Questions About LUCK

A blackjack player goes to Las Vegas twice per year for 30 years. Plays a 0.50% house edge game perfectly. Plays 5 hours each day for 3 days during these visits (assuming 60 hands per hour).

What is the probability that this player has a profit at the end of this timeline?

Out of 1 million players who play this way, how many will be lifetime winners? (or 1 out of how many)

What happens to these probabilities if this person goes 4x per year?

Quote: lucky13

A blackjack player goes to Las Vegas twice per year for 30 years. Plays a 0.50% house edge game perfectly. Plays 5 hours each day for 3 days during these visits (assuming 60 hands per hour).

What is the probability that this player has a profit at the end of this timeline?

Out of 1 million players who play this way, how many will be lifetime winners? (or 1 out of how many)

What happens to these probabilities if this person goes 4x per year?

Your numbers work out to 54,000 hands of blackjack. With a 0.5% house edge, the average loss would be 270 bets. The standard deviation is 232.4 bets. So to turn a profit, the bettor would need a +1.16 sigma condition or better. This has a likelihood of 12.3%, or about 1 in 8.

For four times per year, the numbers change to

108,000 hands
540 bets average loss
328.6 standard deviation
1.64 sigma condition
5.1% probability
about 1 in 20

edit: Oops, slipped a decimel point. Reworked the numbers.

Thank you Pappa. I have a very good friend who insists that he is profitable in all of his years of blackjack, without counting, and I thought it was just bluster, but your numbers seem to indicate that it wouldn't be all that unusual (1 in 8). I was guessing the figure would have been more like 3-4 in a million. Thanks again.

Yeah, it bugs me that conventional wisdom is that "since the house always has an edge, then the house must always win." This is simply not true. You are always less likely to be a winner than to be a loser. To maximize your chances of being a winner:

1) Play games with the smallest edge.
2) Play them as few times as possible.

There's an axiom on here that no system can overcome the house edge. This is absolutely true. But if you play few enough hands, you can minimize the impact of the house edge and give luck a chance to prevail.

One key point here is does your friend play perfectly? House edge goes up a lot if he's making a few mistakes here and there.

Quote: PapaChubby

to turn a profit, the bettor would need a +1.16 sigma condition or better.

never heard the WoO mention this sigma thing. I think Einstein wrote the page at Wikipedia [g]

Quote: PapaChubby

Yeah, it bugs me that conventional wisdom is that "since the house always has an edge, then the house must always win." This is simply not true.

I think here we all understand the house edge is a long term proposition, not a short term one and certainly not one that happnes evey hand. This emans, too, that some players will even score long term winnings, some players will rbeak even, most players will lose, and some players won't even win in the shrot term.

I'd say it all comes down in the end to luck, but my own Law (number 12) states there's no suh thing as luck. What I mean is that you may play perfect BJ basic strategya nd pick the lowest hosue edge possible, but unless you count well you're still likelier to lose in the long term. If yuo wind up a long term winner, then you were favored by random chance.

Quote: odiousgambit

never heard the WoO mention this sigma thing. I think Einstein wrote the page at Wikipedia [g]

Sorry, that's just my normal rocket scientist jargon. In longhand, I meant to say that the bettor needs a result which is at least 1.16 standard deviations above the mean to turn a profit.

Sigma is the greek letter used to represent standard deviation. Which is the square root of variance (conversely, variance is represented mathematically as sigma squared). Standard deviation is more intuitively useful than variance because the units are the same as the original population. In determining how much you might win or lose in a casino game, standard deviation gives you the answer in dollars. Variance gives you the answer in dollars squared. Who wants to deal with that?

For more information, look up the Wikipedia article on Normal Distribution.

Quote: PapaChubby

Sigma is the greek letter used to represent standard deviation. Which is the square root of variance (conversely, variance is represented mathematically as sigma squared). Standard deviation is more intuitively useful than variance because the units are the same as the original population. In determining how much you might win or lose in a casino game, standard deviation gives you the answer in dollars. Variance gives you the answer in dollars squared. Who wants to deal with that?

thanks. From this a light bulb came on and told me not to think of standard deviation linearly , since it is related to something that is squared. To go from one to 3 sigmas is no quick trip! [hey, notice I am picking up the jargon! give me my degree!]

.....

That just reinforces Pappa's ascertation that the less played, the higher the chance of being "lucky". What I was trying to get to was the casual player I described above who plays regularly over years and is a winner over time due to positive variance. I still find it astounding that 1 in 8 in my given scenario could be a winner.

Your numbers work out to 54,000 hands of blackjack. With a 0.5% house edge, the average loss would be 270 bets. The standard deviation is 232.4 bets. So to turn a profit, the bettor would need a +1.16 sigma condition or better. This has a likelihood of 12.3%, or about 1 in 8.

I would have thought that one standard deviation would be the square root of total hands played (232.4) times the standard deviation of one hand, say 1.15 or 1.16 or so?

1 in 6 or so?

And for 108000 hands, 1 in 13 or so? No?

Quote: Curiousguy11

Your numbers work out to 54,000 hands of blackjack. With a 0.5% house edge, the average loss would be 270 bets. The standard deviation is 232.4 bets. So to turn a profit, the bettor would need a +1.16 sigma condition or better. This has a likelihood of 12.3%, or about 1 in 8.

I would have thought that one standard deviation would be the square root of total hands played (232.4) times the standard deviation of one hand, say 1.15 or 1.16 or so?

1 in 6 or so?

And for 108000 hands, 1 in 13 or so? No?

Yes, you're right. I based my answer on a standard deviation of 1. Didn't consider splits, doubles and blackjacks.