Statistical question

What are the chances of winning $3000 playing blackjack at a $10 level?

Quote: Mosca

What are the chances of winning $3000 playing blackjack at a $10 level?

It depends on your bankroll and the total duration of play over which you would like to give it a try. With infinite time, you can apply the first loss rebate theorem to answer this.


For example, if you have a bankroll of 1000 units ($10,000) then your bankroll x = 1000 units and your win goal is b = 1300 units (winning b-x = 300 units). Then with infinite time, h/a = -0.5% and sd = 1.15, plugging in to the first formula in the LRT, this chance is about 10.34%.

Of course, as M.S. (Mustang Sally, Michael Shackleford, etc. ...) will rightfully point out, this assumes a normal distribution, so the answer above is at best an approximation. The exact answer would require a Markov chain using the exact distribution for your BJ game.

Quote: teliot

It depends on your bankroll and the total duration of play over which you would like to give it a try.
With infinite time <snip> this chance is about 10.34%.

i agree too with BS and flat betting $10
and the rules of the game are important also (the lower the HE etc)

here is a table i made some time ago (it was in units so i changed it to $)
1.15 = SD
(this MAY not be correct for all the games that produce the edges)
win goal = $3000
values are "1 in"

bank / edge	-0.003	-0.004	-0.005	-0.006	-0.007
100	66.39	88.56	119.97	164.85	229.43
500	15.29	20.69	28.52	39.97	56.83
1000	8.95	12.32	17.33	24.83	36.14
3000	4.90	7.14	10.66	16.21	24.95
5000	4.24	6.40	9.87	15.37	24.06
10000	3.93	6.15	9.67	15.21	23.95

Quote: teliot

Of course, as M.S. (Mustang Sally, Michael Shackleford, etc. ...) will rightfully point out,
this assumes a normal distribution, so the answer above is at best an approximation.
The exact answer would require a Markov chain using the exact distribution for your BJ game.

the formula you and i use
is very accurate
ask BruceZ when you see him, he is a nice guy,
he remembers a BJ Q like this at 2+2 forum
MAYbe he does not want to remember

and another M.S. too
MathExtremist Stacy ;)

now for success within a number of trials (chances would be lower)
we need to look to Don Schlesinger for that answer
(it was in a later book of his and MAYbe QFIT has a calculator for that)

Quote: Mosca

What are the chances of winning $3000 playing blackjack at a $10 level?

Simple experience will tell you "not to hold your breath" waiting for a win of 300 units when flat betting. Common sense will tell you that anyone waiting for that isn't going to leave until it's all lost, anyway; and along with any other money that you have. Realization will tell you that $3,000 isn't going to change anything for you, especially compared to the loss of any other money you have. Finally, embarrassment will tell you to go right on supporting gambling. Because, the math will always tell you that "everything is possible", so you can get "your money" (and dignity) back.


Add on:

Quote: teliot

The exact answer would require a Markov chain using the exact distribution for your BJ game.

Good luck with that!

Add on #2: So what happened to GordonPayne, the latest guy around here who was going to "take blackjack by storm"?

Quote: Kerkebet

Good luck with that!

These are "close enough" to the distribution to be used in the Markov approach, or for a simulation like the one M.S. did:

https://wizardofodds.com/games/blackjack/appendix/4/

blackjack combinatorial analysis by simulation

Quote: teliot

These are "close enough" to the distribution to be used in the Markov approach, or for a simulation like the one M.S. did.

I meant just that the really important moments and meanings in life can not be met with simulation, or the stuff of advanced statistics.

It's not for me. I have a friend who says that he starts with $100, plays until he wins $100, then stops, and that he has won about $3000 a year this way. I don't believe him, but I'm not going to bother calling him out on it because there's no point to it. I only wanted to know the chance that it actually happened. He's been going on about it for maybe 10 years now.

I did mention that the concept of "sessions" is an illusion, but he didn't understand.

Quote: Mosca

It's not for me. I have a friend who says that he starts with $100, plays until he wins $100, then stops,

so to double a $100 bankroll flat betting $10 i gets abouts 47% chance of success for one session

this is way different from a start bank = $100 and play to $3000 or bust

it also depends on how many "sessions" are played in a year
example:
300 sessions played we can use a binomial distribution for 165 or more wins
that = abouts 1 in 302.57
200 sessions = abouts 1 in 540.85
seems it becomes more difficult with less sessions played per year

Quote: Mosca

and that he has won about $3000 a year this way.
I don't believe him, but I'm not going to bother calling him out on it because there's no point to it. I only wanted to know the chance that it actually happened. He's been going on about it for maybe 10 years now.

MAYbe the facts are messed up some place
1 in 302.57^10 i say is a very large number
6,430,705,965,877,197,611,591,917.08
1 in 540.85^10, oh, we not go there

Sally

It's more like 100-150 sessions a year. Thank you for your insight Mustang Sally, regarding the effect of bankroll. Like I said, there's no point calling him on it, if he wants to appear to be the expert it's fine with me. Life moves forward either way.