scottygang
Joined: Jul 3, 2017
• Posts: 1
July 3rd, 2017 at 9:05:33 AM permalink
Hi,

I was wondering the chances of ever winning 4 times your bet on some sort of typical video BJ machine - say 6 deck continuous shuffle - with only 1 split allowed (e.g. 4x bet win could be from: split then 2 doubles). So like the chance you split * the chance you nail a 9 or 10 or whatever you need against the dealer up card for both hands * the chance you actually win both hands. I estimate its about 1/4000 hands. This analysis could have applications for players trying to limit their jackpot exposure and also for players trying to calculate the EV loss of having a short BR.
Romes
Joined: Jul 22, 2014
• Posts: 5490
July 10th, 2017 at 7:36:37 AM permalink
Hi scotty, and welcome to the forums.

I think you're a bit off on your thinking of individual events in a hand. First, to calculate a proper house edge you did not list all of the necessary rules we'd need to know. I'll refer you to the Wizards House Edge Calculator where you can see all of the different options: https://wizardofodds.com/games/blackjack/calculator/

Next, let's assume typical rules and a house edge of "around" .5% (this is somewhat trivial to the win rate of the hands assuming 'average' rules). The hand rates for blackjack are approx. as follows:

1) Win = 42%
2) Loss = 49%
3) Push = 9%

Thus on any given hand before its dealt you generically have approximately a 42% chance to win the hand. This doesn't take any counting/etc in to mind (though even counting doesn't drastically change the win rate). So the odds of winning 4 generic hands in a row is .42^4 = .03, 3%, or about 3/100... a bit better than 1/4000 hands =P.

When you get in to splits and doubles I believe your win rate should actually go up, as splits and doubles by basic strategy are player advantageous situations (for the most part... there are defensive splits such as 8-8 vs dealer 10 for example).
Playing it correctly means you've already won.
michael99000
Joined: Jul 10, 2010
• Posts: 2112
July 10th, 2017 at 7:46:21 AM permalink
I don't think he was looking for the odds of winning 4 separate hands in a row

It sounded to me like he's trying to find out how often you'll end up winning 4x your original bet on one individual hand , such as getting dealt two 3's against a drealer 6, splitting , getting doubles on both hands and winning everything
michael99000
Joined: Jul 10, 2010
• Posts: 2112
July 10th, 2017 at 7:46:21 AM permalink
I don't think he was looking for the odds of winning 4 separate hands in a row

It sounded to me like he's trying to find out how often you'll end up winning 4x your original bet on one individual hand , such as getting dealt two 3's against a drealer 6, splitting , getting doubles on both hands and winning everything
boymimbo
Joined: Nov 12, 2009
• Posts: 5994
July 10th, 2017 at 10:34:29 AM permalink
So a single split with a double after a split allowed on any card. Assuming that the dealer is single decking you and reshuffling after each deal? And hit soft 17.

That is easy enough to calculate. According to the Wizard's guide on single deck, you split on:

-pair of 2s against a 2 - 7
-pair of 3s against a 2 - 7
-pair of 4s against a 4 - 6
-pair of 6s against a 2 - 7
-pair of 7s against a 2 - 8
-pair of 8s always
-pair of 9s always except a 7 or 10
-pair of Aces always (but you can't double after a split so forget about that) s those are removed.

I then determined the cards you needed to get to double on both hands and then calculated the number of combinations where that was available. For example, if you have a pair of 2s against a 6 you have to draw a A, 3, 4, or 5 to double. There are 16 * 15 = 240 combinations of cards that will get you those two combinations out of 49 * 48 remaining cards (2,352) or a 10.204% probability that you can double both splits.

The total odds of you splitting a hand with the opportunity to double is 1.780773%.
The total odds of you doubling both hands after splitting is 0.08111%

Chart is below, using Wizard's combination blackjack analysis table 9.

DealerPlayerProbabilityCards to DAS# of CombsOdds of getting CombsTotal Probability
A8,80.000243793120.0051020410.0000012438
A9,90.000243792120.0051020410.0000012438
22,20.0001817 8 9 1320.0561224490.0000101582
23,30.000361996 7 81320.0561224490.0000203158
26,60.000361993 4 5 A2400.1020408160.0000369378
27,70.000361992 3 41100.0467687070.0000169298
28,80.000361992 3 420.0178571430.0000064641
29,90.00036199260.002551020.0000009234
32,20.000361997 8 91320.0561224490.0000203158
33,30.0001816 7 81320.0561224490.0000101582
36,60.000361993 4 5 A2100.0892857140.0000323205
37,70.00036199A 2 3 42100.0892857140.0000323205
38,80.000361992 3420.0178571430.0000064641
39,90.000361992120.0051020410.0000018469
42,20.00036199A 7 8 92400.1020408160.0000369378
43,30.00036199A 6 7 82400.1020408160.0000369378
44,40.000181A 5 6 72400.1020408160.0000184694
46,60.00036199A 3 4 52100.0892857140.0000323205
47,70.00036199A 2 3 42100.0892857140.0000323205
48,80.000361992 3560.0238095240.0000086188
49,90.000361992120.0051020410.0000018469
52,20.00036199A 7 8 92400.1020408160.0000369378
53,30.00036199A 6 7 82400.1020408160.0000369378
54,40.00036199A 5 6 72100.0892857140.0000323205
56,60.00036199A 3 4 52100.0892857140.0000323205
57,70.00036199A 2 3 42400.1020408160.0000369378
58,80.000361992 3560.0238095240.0000086188
59,90.000361992120.0051020410.0000018469
62,20.00036199A 7 8 92400.1020408160.0000369378
63,30.00036199A 6 7 82100.0892857140.0000323205
64,40.00036199A 5 6 72100.0892857140.0000323205
66,60.000181A 3 4 52400.1020408160.0000184694
67,70.00036199A 2 3 42400.1020408160.0000369378
68,80.00036199A 2 31320.0561224490.0000203158
69,90.000361992120.0051020410.0000018469
72,20.000361998 9560.0238095240.0000086188
73,30.000361997 8420.0178571430.0000064641
76,60.000361994 5560.0238095240.0000086188
77,70.0001813 4560.0238095240.0000043095
78,80.000361992 3560.0238095240.0000086188
83,30.000361997 8 420.0178571430.0000064641
87,70.000361993 4560.0238095240.0000086188
88,80.0001812 3560.0238095240.0000043095
89,90.000361992120.0051020410.0000018469
98,80.000361992 3560.0238095240.0000086188
99,90.0001812120.0051020410.0000009235
107,70.001329764120.0051020410.0000067845
108,80.001329763120.0051020410.0000067845
TotalsAll Cards0.017807730.0008111438

The odds of you winning?. I have to go back to work.
----- You want the truth! You can't handle the truth!