Blackjack Win Goal

I have adopted a new goal in my BJ play: to stop after winning 2 units. I cash in (or put at risk) 20 units each time I sit down. Here's the question: Can you tell me what percentage of the time I would win 2 units (or 2 hands; 1 unit bet per hand) before I lost all 20 units?

I wanted to try this out because it seemed like an easier goal to achieve than to stop when I've won 50% of my bankroll, which I used to do.

And here's the results of my trial: I had 14 winning sessions in a row before I lost (70% of my bankroll or 14 units; I wasn't willing to throw it all away...). In the end I came out ahead 16 units. Each time I played, I would leave as soon as I was + 2 units. Here's the breakdown of the sessions:

1 time I played just 1 hand (got an 11, doubled, and won).
8 times I played 2 or 3 hands.
2 times 5-7 hands.
2 times played 1 shoe.
1 time I played 3 shoes.

The last session which I lost (14 units), I played about 4-5 shoes.

I'm trying to understand if this was just a streak of good luck or if choosing a winning goal that's easier to attain is a better strategy.

Then the question becomes how long do I stop for after winning the 2 units? In this case I left the casino and went home, except for the last 3 winning session, which I just moved tables and started in on a new shoe after each win. Would the outcome have been the same if I would have just played all those hands in all those sessions in a row?

Thanks for any advice you might have.

Why do people continue to add numbers to the letters as 'names' when they join the list?
Have we run out of letters? Are numbers after letters cool?
Confounded and confused.

Quote: acmd1633

I have adopted a new goal in my BJ play: to stop after winning 2 units. I cash in (or put at risk) 20 units each time I sit down. Here's the question: Can you tell me what percentage of the time I would win 2 units (or 2 hands; 1 unit bet per hand) before I lost all 20 units?

it depends on the game rules
but we can set an upper limit as if the game was fair (and BJ aint)
turning 20 into 22 is 20/22 or 90.9%
so we round down to 90% for a one-time success rate (probably still too high)

say you want to win 5 times in a row
ok
.9*.9*.9*.9*.9 = 0.59049
how about 7 times in a row
0.90^7=0.4782969

now that is less than a coin flip

Quote: acmd1633

I wanted to try this out because it seemed like an easier goal to achieve than to stop when I've won 50% of my bankroll, which I used to do.

yeps
20/30 or abouts 67% at the very best for ONE session win

Quote: acmd1633

I'm trying to understand if this was just a streak of good luck or if choosing a winning goal that's easier to attain is a better strategy.

well, if you just try to win 1 unit one time
that is at best
20/21 = 95.2% or with a house edge 94%

about as good as it will get for U

Quote: acmd1633

Then the question becomes how long do I stop for after winning the 2 units?

only you can answer that
unless you know how long IS long?

Quote: acmd1633

Would the outcome have been the same if I would have just played all those hands in all those sessions in a row?

i agree with that
others will not

have fun session winning!
Sally

Quote: TwoFeathersATL

Why do people continue to add numbers to the letters as 'names' when they join the list?

What does that have to do with the question I posed?

Quote: TwoFeathersATL

Have we run out of letters? Are numbers after letters cool?

Yes, and yes.

Quote: TwoFeathersATL

Confounded and confused.

Thanks for your valuable insight.

MustangSally,
I'm not sure if you are answering what I'm asking. It's not that I want to win 2 units in a row, I want to be +2 units before I am -20 units. For instance, if I go to a $50 table with $1000, I want to win $100 (two $50 hands) before I lose the $1000. What are the odds that that is possible? Not sure how to figure that out statistically.

Quote: acmd1633

I'm not sure if you are answering what I'm asking. It's not that I want to win 2 units in a row,I want to be +2 units before I am -20 units.

exactly
you want to win 2 units in one session
that probability is at best 20/22 or about a 90% chance of success for just one session

Quote: acmd1633

For instance, if I go to a $50 table with $1000, I want to win $100 (two $50 hands) before I lose the $1000. What are the odds that that is possible? Not sure how to figure that out statistically.

again at best
you want to turn 1000 into 1100 and stop that session at that point

1000 / 1100 = about 90%
so abouts a 1 in 10 shot of complete ruin



so say you want to win 10 sessions in a row
because that will be 20 unit total win over that many session wins
(at least hope for more)

that chance of that = 0.90^10 = 0.3486784401
about a 1 in 3 chance

not looking very good there i do say

need to play to win
so good luck and have fun

Quote: acmd1633

What does that have to do with the question I posed?


Yes, and yes.


Thanks for your valuable insight.

Welcome to the forum, acmd1633. I look forward to discussing blackjack with you.

Thanks,

My hope in posting this was to have the Wizard of Odds answer this question. How can I get that to happen?

Quote: acmd1633

Thanks,

My hope in posting this was to have the Wizard of Odds answer this question. How can I get that to happen?

No offence meant, but Mike ( Wizard) is not a private consultant to any of us. MustangSally is a highly respected and competent member to answer questions such as yours and you came over as somewhat ungrateful and lacking in respect.

Anyway... as Sally pointed out, your probability of getting from x units to x+y is, at best*, approximately x/(x+y)

I.e To get from 100 units to 110 units with fairly aggressive play, and putting all of your 100 units at risk, you stand about 90% probability of success and 10% probability of ruin. That is not probability of any two specific winning wagers, but is indeed what you asked for.

Also, as Sally pointed out, if you do this multiple times, you risk ruin more times and that ruin would probably wipe out your starting bankroll and your winnings to that point. You will lose your lifetime bankroll more often than you would double it !!! That's what matters whereas getting from $1,000,000 to $1,000,100 is a piece of cake if you desperately needed to increase your bankroll like that.

By aggressive betting I mean pushing as much to the table as is required to JUST hit your goal, such as maybe wagering your goal and then Martingaling till it's met. Actually, it's my experience that flat betting is as good, lasts longer and has similar outcome. Eg. if you want to get from 100 to 110, you could reasonably expect to achieve that if flat betting 5 till you succeed or bust. TINY bets would reduce your probability of success as you would then minimise the variance which would be your friend.

As others will tell you, the concept of starting and ending sessions is pretty meaningless because the cards don't know where sessions start and end.

Let the session be the period of entertainment that you consider to be value for money.

Quote: OnceDear

No offence meant, but Mike ( Wizard) is not a private consultant to any of us. MustangSally is a highly respected and competent member to answer questions such as yours and you came over as somewhat ungrateful and lacking in respect.

Anyway... as Sally pointed out, your probability of getting from x units to x+y is, at best*, approximately x/(x+y)

I.e To get from 100 units to 110 units with fairly aggressive play, and putting all of your 100 units at risk, you stand about 90% probability of success and 10% probability of ruin. That is not probability of any two specific winning wagers, but is indeed what you asked for.

Also, as Sally pointed out, if you do this multiple times, you risk ruin more times and that ruin would probably wipe out your starting bankroll and your winnings to that point. You will lose your lifetime bankroll more often than you would double it !!! That's what matters whereas getting from $1,000,000 to $1,000,100 is a piece of cake if you desperately needed to increase your bankroll like that.

By aggressive betting I mean pushing as much to the table as is required to JUST hit your goal, such as maybe wagering your goal and then Martingaling till it's met. Actually, it's my experience that flat betting is as good, lasts longer and has similar outcome. Eg. if you want to get from 100 to 110, you could reasonably expect to achieve that if flat betting 5 till you succeed or bust. TINY bets would reduce your probability of success as you would then minimise the variance which would be your friend.

As others will tell you, the concept of starting and ending sessions is pretty meaningless because the cards don't know where sessions start and end.

Let the session be the period of entertainment that you consider to be value for money.

Thanks for the clear explanation (and I totally endorse the flat betting strategy).

And thanks Mustangsally for your re-explanation. Appreciate the feedback.

Quote: acmd1633

And thanks Mustangsally for your re-explanation. Appreciate the feedback.

i think i did a better job of explaining in my 2nd post about the wins in a row thing

so here is a table calulated of %s of you winning at least 2 units starting with 20
looks to be at best 89.3% (so 90% was close to start)

looks to me you have a better than 50/50 chance to hit your target goal for the session by the 9th round

this was from data playing a 6 deck shoe

Round	by Round X	on Round X
1	6.202303	6.202303
2	22.257518	16.055215
3	28.539985	6.282467
4	35.10168	6.561695
5	39.450908	4.349228
6	43.283925	3.833017
7	46.353445	3.06952
8	49.005719	2.652274
9	51.282761	2.277042
10	53.279975	1.997214
15	60.519062	1.177815
20	65.170387	0.797988
25	68.480256	0.585781
30	70.988866	0.453201
35	72.974111	0.363946
40	74.595501	0.300522
45	75.951956	0.253571
50	77.108472	0.217673
60	78.987562	0.166912
70	80.460607	0.133149
80	81.654547	0.109283
90	82.645963	0.091577
100	83.483835	0.077907
200	87.666728	0.020549
300	88.830273	0.00587
400	89.163055	0.00168
500	89.258294	0.000481
1000	89.296406	1E-06

some sessions look to take many many rounds of play


Hmmm,
when you do win your session and pat yourself on the back
do you give Luck any credit too
or
do you give yourself all the credit?

I do not play BJ for real $$$ so i do not know
Sally

Quote: mustangsally

i think i did a better job of explaining in my 2nd post about the wins in a row thing

so here is a table calulated of %s of you winning at least 2 units starting with 20
looks to be at best 89.3% (so 90% was close to start)

looks to me you have a better than 50/50 chance to hit your target goal for the session by the 9th round

this was from data playing a 6 deck shoe

Round	by Round X	on Round X
1	6.202303	6.202303
2	22.257518	16.055215
3	28.539985	6.282467
4	35.10168	6.561695
5	39.450908	4.349228
6	43.283925	3.833017
7	46.353445	3.06952
8	49.005719	2.652274
9	51.282761	2.277042
10	53.279975	1.997214
15	60.519062	1.177815
20	65.170387	0.797988
25	68.480256	0.585781
30	70.988866	0.453201
35	72.974111	0.363946
40	74.595501	0.300522
45	75.951956	0.253571
50	77.108472	0.217673
60	78.987562	0.166912
70	80.460607	0.133149
80	81.654547	0.109283
90	82.645963	0.091577
100	83.483835	0.077907
200	87.666728	0.020549
300	88.830273	0.00587
400	89.163055	0.00168
500	89.258294	0.000481
1000	89.296406	1E-06

some sessions look to take many many rounds of play


Hmmm,
when you do win your session and pat yourself on the back
do you give Luck any credit too
or
do you give yourself all the credit?

I do not play BJ for real $$$ so i do not know
Sally

Sally,
Thanks for the in depth analysis. I feel like a dummy but I have no idea how to interpret that chart but I trust you know what you're talking about. And I don't want to waste any more of your time explaining this to me; you've been very generous with your time.

So, yes, at first I assumed it was skill (I play perfect basic strategy on an 8 deck shoe, dealer hits soft 17, double after split, re-split aces, no surrender) since my goal was seemingly so modest (how hard could it be to win just 2 hands more than you loose...). With my previous strategy of stopping after I won 50% of my bank roll (10 units in this scenario) I would stop, the most winning sessions in a row was no more than 4, and more like 2 or 3. But with this new goal I had 14 winning sessions in a row before the hammer came down. I figured at some point I would loose, but looking back on it, I have to assume some of the streak was due to luck but some must have been due to reaching a more easily attainable goal. But like OnceDear said, the cards have no memory of when you start and stop so who the hell knows... It would seem to me that you would have a significantly better chance winning 14 sessions in a row with a goal of 2 units vs winning 14 sessions in a row with a goal of 10 units. My brain is starting to hurt.

Quote: acmd1633

With my previous strategy of stopping after I won 50% of my bank roll (10 units in this scenario) I would stop, the most winning sessions in a row was no more than 4, and more like 2 or 3.

But with this new goal I had 14 winning sessions in a row before the hammer came down.

It would seem to me that you would have a significantly better chance winning 14 sessions in a row with a goal of 2 units vs winning 14 sessions in a row with a goal of 10 units. My brain is starting to hurt.

well that is true i do agree
to win 10 units 14 times in a row
64.6%^14 = 0.002204221
1 in 453.7

to win 2 units 14 times in a row
89.3%^14=0.2050786
1 in 4.9

but after winning 14 sessions in a row
that increases your unit bank at least 28 units (14*2)

if you win 3 in a row sessions trying for the 10 unit session win
increases your unit bank at least 30 units (10*3)

the chance i see of that is
64.6%^3 = 0.269586136
1 in 3.7

easier to a 30 unit 3 session win
than a 28 unit 14 session win

but the longer you do play
you can hit a high bankroll target but sooner or later
you will lose all your bankroll
that is what to expect

I love it when my Angels go OVER when I bet big
Sally

Play until you do not feel like playing anymore simple and easy.