Question for the Wizard - Does the odds of being dealt a blackjack vary with # of players at table?

Is there any difference in the probability of getting dealt a blackjack playing heads up against the dealer vs. playing with multiple players at the table?
Let's say with 5 other players at the table with a 6 deck shoe for this question.

I thought there was no difference, however one thing that has been pointed out to me is that as players hit their hands they are more likely to use up Aces since they are more often counted as 1 than 11 when hitting since it is more likely to be dealt an initial total of 12 or greater than a total of 8 or lower. However they are less likely to use many tens. Or non aces used up can increase the odds of getting an Ace later.

I am not trying to answer my own question since I am looking for a mathematical solution from the Wizard, but just pointing out the reason for asking the question.

If the dealer starts the shoe with 5 Black Jacks in a row, "geriatric mechanic" comes to mind.

Quote: pjsatz

Is there any difference in the probability of getting dealt a blackjack playing heads up against the dealer vs. playing with multiple players at the table?
Let's say with 5 other players at the table with a 6 deck shoe for this question.

I thought there was no difference, however one thing that has been pointed out to me is that as players hit their hands they are more likely to use up Aces since they are more often counted as 1 than 11 when hitting since it is more likely to be dealt an initial total of 12 or greater than a total of 8 or lower. However they are less likely to use many tens. Or non aces used up can increase the odds of getting an Ace later.
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The answer is no, the number of players doesn't make a difference.

We could get into a discussion about the cut card effect, but the number of players doesn't affect that as far as I can tell.

Quote: Wizard

Quote: pjsatz

Is there any difference in the probability of getting dealt a blackjack playing heads up against the dealer vs. playing with multiple players at the table?
Let's say with 5 other players at the table with a 6 deck shoe for this question.

I thought there was no difference, however one thing that has been pointed out to me is that as players hit their hands they are more likely to use up Aces since they are more often counted as 1 than 11 when hitting since it is more likely to be dealt an initial total of 12 or greater than a total of 8 or lower. However they are less likely to use many tens. Or non aces used up can increase the odds of getting an Ace later.
link to original post

The answer is no, the number of players doesn't make a difference.

We could get into a discussion about the cut card effect, but the number of players doesn't affect that as far as I can tell.
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heh? i know you know more than me but...

lets say im playing heads up with 1 deck

my first card dealt to me is an ace...

your saying the dealer still has the same probability to get an ace even though there is one less ace in the deck than there was before?

Quote: heatmap

your saying the dealer still has the same probability to get an ace even though there is one less ace in the deck than there was before?
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No, I'm not saying that.

And if your first card is not an ace the dealer does not have the same probability of getting an ace.

A quick simulation looked at head to head but did count how often each hand number (from a 8 deck shoe 83% penetration) received a winning Blackjack. Until you reach the cut card effect, when you can see when the number of hands drop, there is no obvious difference. (Shoes which get to have more hands tend to use up the large cards, so the later hands in those shoes are worse than average. This can be seen in hands No. 64 and above.)

Thus there is no significant difference between your luck playing the first few hands in a shoe. (Obviously if you were capable of tracking every card, later hands have the slight advantage of knowing more cards that have gone so you could technically adjust your strategy!) In this simulation the player sticks to infinite deck strategy, although for counting Blackjacks that doesn't matter much.

Hand No	Blackjack	Delta to Av	Hands:
1	4.527 273%	0.004 955%	100 000 000
2	4.523 709%	0.001 391%	100 000 000
3	4.526 372%	0.004 054%	100 000 000
4	4.526 633%	0.004 315%	100 000 000
5	4.527 199%	0.004 881%	100 000 000
6	4.524 199%	0.001 881%	100 000 000
7	4.524 818%	0.002 500%	100 000 000
8	4.529 540%	0.007 222%	100 000 000
9	4.527 267%	0.004 949%	100 000 000
10	4.529 778%	0.007 460%	100 000 000
11	4.524 374%	0.002 056%	100 000 000
12	4.527 451%	0.005 133%	100 000 000
13	4.527 571%	0.005 253%	100 000 000
14	4.525 329%	0.003 011%	100 000 000
15	4.525 057%	0.002 739%	100 000 000
16	4.526 783%	0.004 465%	100 000 000
17	4.528 095%	0.005 777%	100 000 000
18	4.527 946%	0.005 628%	100 000 000
19	4.524 399%	0.002 081%	100 000 000
20	4.528 764%	0.006 446%	100 000 000
21	4.528 600%	0.006 282%	100 000 000
22	4.523 421%	0.001 103%	100 000 000
23	4.529 179%	0.006 861%	100 000 000
24	4.526 573%	0.004 255%	100 000 000
25	4.529 587%	0.007 269%	100 000 000
26	4.525 521%	0.003 203%	100 000 000
27	4.526 827%	0.004 509%	100 000 000
28	4.523 636%	0.001 318%	100 000 000
29	4.524 505%	0.002 187%	100 000 000
30	4.527 779%	0.005 461%	100 000 000
31	4.526 110%	0.003 792%	100 000 000
32	4.524 719%	0.002 401%	100 000 000
33	4.523 522%	0.001 204%	100 000 000
34	4.523 719%	0.001 401%	100 000 000
35	4.527 838%	0.005 520%	100 000 000
36	4.525 274%	0.002 956%	100 000 000
37	4.525 108%	0.002 790%	100 000 000
38	4.525 959%	0.003 641%	100 000 000
39	4.528 292%	0.005 974%	100 000 000
40	4.523 463%	0.001 145%	100 000 000
41	4.525 072%	0.002 754%	100 000 000
42	4.527 305%	0.004 987%	100 000 000
43	4.528 898%	0.006 580%	100 000 000
44	4.525 885%	0.003 567%	100 000 000
45	4.524 903%	0.002 585%	100 000 000
46	4.525 703%	0.003 385%	100 000 000
47	4.527 693%	0.005 375%	100 000 000
48	4.524 171%	0.001 853%	100 000 000
49	4.528 463%	0.006 145%	100 000 000
50	4.523 812%	0.001 494%	100 000 000
51	4.524 019%	0.001 701%	100 000 000
52	4.529 995%	0.007 677%	100 000 000
53	4.523 343%	0.001 025%	100 000 000
54	4.528 317%	0.005 999%	100 000 000
55	4.524 587%	0.002 269%	100 000 000
56	4.530 508%	0.008 190%	100 000 000
57	4.525 408%	0.003 090%	99 999 997
58	4.522 696%	0.000 378%	99 999 965
59	4.525 307%	0.002 989%	99 999 669
60	4.526 286%	0.003 969%	99 996 417
61	4.529 139%	0.006 821%	99 965 158
62	4.525 759%	0.003 441%	99 728 450
63	4.527 007%	0.004 689%	98 384 298
64	4.503 455%	-0.018 862%	93 015 978
65	4.466 778%	-0.055 540%	78 659 633
66	4.389 949%	-0.132 369%	53 945 775
67	4.280 372%	-0.241 945%	27 250 130
68	4.130 394%	-0.391 923%	9 434 378
69	3.947 212%	-0.575 106%	2 139 941
70	3.823 881%	-0.698 437%	311 516
71	3.417 792%	-1.104 526%	28 732
72	3.349 001%	-1.173 316%	1 702
73	6.451 613%	1.929 295%	62
74	0.000 000%	-4.522 318%	1

Can you run a simulation with multiple players or multiple hands being played? Not expecting to see any real difference but just wanting to verify. Thank you.

Everyone here is going to tell you no, but I'm going to tell you YES,

but... only in a specific situation

If another player at the table is counting cards, and he sits out some hands when the count is negative, your chances of getting blackjack is lower. Your chances of winning is also lower.

So what other player do, does affect you. But only if they're card counting.

Watch everyone else on this forum burn me at the stake now... it's coming...

Lemme explain my point further.

Suppose you're buying pokemon cards.

You were going to take the booster pack in the front of the shelf, but another kid took it instead. Do you might as well just take the next pack in line? Are they the same?

Every mathematician is going to say it's the same.

But imagine...

If a 30 year old pokemon card AP brings an x-ray device to scan which pack has the holofoil charizard, and buys that pack. He also buys all the packs with holofoil blastoise and mew.

Do you now have the same chance getting your dream cards now?

No.

Quote: VladPutin

Do you now have the same chance getting your dream cards now?

No.
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What is your point?

Quote: Wizard

Quote: VladPutin

Do you now have the same chance getting your dream cards now?

No.
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What is your point?
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Other people's plays at the table may affect your EV.

Quote: VladPutin

Quote: Wizard

Quote: VladPutin

Do you now have the same chance getting your dream cards now?

No.
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What is your point?
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Other people's plays at the table may affect your EV.
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Absolutely, sometimes they increase your EV, and sometimes they decrease it. I’ll give you 3 guesses as to the net change to your EV…