drum
drum
Joined: Apr 10, 2015
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May 10th, 2015 at 6:08:14 AM permalink
Can anybody point me to any information on the odds of winning a game of blackjack before any cards are dealt. i.e. thats when we bet, so that what I'm interested in.

I've been trying to do the maths based on an 8 deck shore, stand on soft 17, split aces once, no double after split.

I've come up with a 37.1% chance of winning on a fresh deal, which is much lower than I thought it would be, anybody know if there is any figoure online I can check with?
RS
RS
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May 10th, 2015 at 6:12:20 AM permalink
I don't know how to do the math. But I believe/heard the chance of win is 43%. Chance of a push is 9%. Chance of a loss is 48%. Give or take 1% (maybe it's 42-10-48 or 43-8-49).

But that isn't the whole story, since double downs are counted as a "win", even though you're winning 2 units instead of a typical win of 1 unit. Same with splits. Oh and blackjacks, too.
drum
drum
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May 10th, 2015 at 6:43:56 AM permalink
That's a good point, I only count a black jack a 1.0 win, I guess it should be 1.5 wins, and similar maths for the split and Double as you say. shouldn't take me too long to reprocess, that lot once I've tweaked the code, let see what difference that makes.

I guess what I have could be the odds of winning, but the odds of "making a profit" a probably what I really want, and will get from these tweaks.
drum
drum
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May 10th, 2015 at 7:17:31 AM permalink
Thinking about this doubles and splits aren't strictly double because you are also doubling your investment. Need to think abit more about this.

I'm also counting a push as a half win, so on that basis, using your figures as a guide at expect something like 47% chance of a win, which is muc nearer what I'd expect.
drum
drum
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May 10th, 2015 at 1:30:44 PM permalink
Well I've stepped back a little bit, and my probabilities of winning for the relevant hands at


are with in about 0.001 which I reckon is probably rounding etc. So on that basis I reckon my basic maths is right. So I guess I need to think about doubles and splits, and also the difference between probability and expected return.
drum
drum
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May 11th, 2015 at 1:17:18 AM permalink
Okay I've now found the figures I remember they are in the Blackjack Blue Book II and it states that the odds before the deal are -

43.5% win
48.5% lose
8.5% push

However I still get odds well be 40% for a win, even though when I check out the individual hands the odds are correct for those hands.

So I say pre-deal odds for winning a game of blackjack are approx 37% and not 43% as stated in the book :-)
djl314
djl314
Joined: May 23, 2022
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May 28th, 2022 at 6:41:14 PM permalink
I think 43 is correct. I have a python simulator I just ran 120,000 hands playing perfect book strategy over 2 sims and they come up:

SIM 1
Win: 24358 41.39
Lose: 26172 44.48 51.48
Surr: 4121 7.00
Push: 4192 7.12
Bust: 2199 3.74
BJ: 2605 4.43

SIM 2
Win: 24637 41.85
Lose: 25967 44.11 51.16
Surr: 4151 7.05
Push: 4117 6.99
Bust: 2248 3.82
BJ: 2609 4.43


Anyone seeing major variations from this?
DogHand
DogHand
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May 29th, 2022 at 7:42:56 AM permalink
Quote: djl314

I think 43 is correct. I have a python simulator I just ran 120,000 hands playing perfect book strategy over 2 sims and they come up:

SIM 1
Win: 24358 41.39
Lose: 26172 44.48 51.48
Surr: 4121 7.00
Push: 4192 7.12
Bust: 2199 3.74
BJ: 2605 4.43

SIM 2
Win: 24637 41.85
Lose: 25967 44.11 51.16
Surr: 4151 7.05
Push: 4117 6.99
Bust: 2248 3.82
BJ: 2609 4.43


Anyone seeing major variations from this?
link to original post



djl314,

Your BJ numbers are too low.

For 120,000 rounds of an 8D game, the player (and the dealer) should get about 5700 BJ's:

120,000*2*(32/416)*(128/415) = 5694.16...

Are you perhaps counting only Ace-first natural as BJ's, so that AK is a BJ, but KA is not? However, even this would not account entirely for the discrepancy.

Did you forget that A-10 is also a BJ?

Hope this helps!

Dog Hand
djl314
djl314
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May 30th, 2022 at 8:16:31 PM permalink
It was a 6deck sim, and 58,000 hands for each sim…
But i see what your saying, and I’ll take a closer look…
DogHand
DogHand
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May 31st, 2022 at 3:55:08 AM permalink
Quote: djl314

It was a 6deck sim, and 58,000 hands for each sim…
But i see what your saying, and I’ll take a closer look…
link to original post



djl314,

I apologize for misreading your original post. I have rerun the numbers and now agree.that your BJ number results are reasonable.

For 58,000 rounds of a 6D game, the player (and the dealer) should each get about 2754 BJ's:

58,000*2*(24/312)*(96/311) = 2754.39...

But the player and dealer will BOTH get BJ's about 126 times in 58,000 rounds:

58,000*2*(24/312)*(96/311)*2*(23/310)*(95/309) = 125.66...

If we deduct the tied BJ's, then the player should get an untied BJ about 2628.7 times in 58,000 rounds. Your two sims averaged 2607, so your BJ numbers seem reasonable.

I shall have to consider your other results further.

Dog Hand

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