Calculating Probability of Push on 12 vs 2

Hi Everyone,

I know, by wrote, that we are to hit on 12 vs 2 because of the 5%~ probability of a push.

I'm curious as to how this is calculated... does anyone know?

thanks,
empy

You will never push on a 12 or any other total less than 17. You will either win if the dealer bust or lose if the dealer makes a 17 through 21.

Hi SplittingAA,

maybe i didn't explain myself correctly, or maybe more likely; i'm out to lunch.

i got that 5% chance of push on 12 vs 2 from sources such as:

is this article wrong in your opinion?

thanks,
empy

or;

I think the OP is referring to the probability of a push after hitting a 12. Meaning the two conditions making a hand of 17-21 by hitting and then the dealer getting the same total (5%), vs any other result (95%). Like many other figures in the analysis of blackjack the probability is calculated by looping through every possible way the cards can fall.

The odds are calculated by taking your probable total versus the dealer's probable total based on the cards drawn. This is completed by probability analysis in that you take all of the combinations multipled by the combinations available.

In the case of 12 vs 2, to stay, you are dealing with the dealer's probability of making a hand based on their 2.

In the case of 6 decks stay on soft 17, the odds are that the dealer has 17 is .139656, 18 .134389, 19 .13002, 20 .124019, and 21 .118413 with odds of busting at .353504.

So quite simply, the expected value of standing on 12 is .353504 - (1-.353504) = - .29299
When you hit a 12, the orders are to stand no matter what on your next card,

At this point, your odds of busting are 4/13 = .307692.
Your odds of hitting 13 to 16 are 4/13 = .307692
Your odds of you making each of a 17 through 21 are 1/13 = .076923 per card.

Player	Player	Dealer Bust	Dealer 17	Dealer 18	Dealer 19	Dealer 20	Dealer 21
Total	Odds	.35350	.13966	.13439	.13002	.12402	.11841
13-16	0.30769	0.10877	(0.04297)	(0.04135)	(0.04001)	(0.03816)	(0.03643)
17	0.07692	0.02719	-	(0.01034)	(0.01000)	(0.00954)	(0.00911)
18	0.07692	0.02719	0.01074	-	(0.01000)	(0.00954)	(0.00911)
19	0.07692	0.02719	0.01074	0.01034	-	(0.00954)	(0.00911)
20	0.07692	0.02719	0.01074	0.01034	0.01000	-	(0.00911)
21	0.07692	0.02719	0.01074	0.01034	0.01000	0.00954	-
Bust	0.30769	(0.10877)	(0.04297)	(0.04135)	(0.04001)	(0.03816)	(0.03643)

Forgive my table formatting. So you multiply the player probabilities by the dealer probabilities and add them all together to get the EV of hitting to be -.24464 units.

So the EV of hitting vs staying favors staying by .04835 units or $.4835 on a $10 bet.

Hi boymimbo,

Thank You! this is what I was looking for...

At the same time, it raises the question of why the BS chart i'm using tells me to Hit on 12 vs 2....

any ideas on that one?

boymimbo actually meant to say it favours hitting. The EV for hitting is less negative, as calculated, so you should hit 12 vs 2

Thanks!

The only part i can't figure out now is how to calculate the dealer probabilities for 17,18,19,20&21...

I'm able to figure out how to get the player probs, but not the dealer ones..

can you provide a formula?