Probability Help Please!!

HI Wizard...just found your site and LOVE it!

What are the odds of winning a hand holding a 16 (10,6) when the dealer shows a 10 (not blackjack)? I know there are tons of variables here, just looking for some insight and how to go about figuring this one out.

I know holding a 16 has a 62% chance of busting and the dealer has just a 21% chance. If you stand, there are 26 cards the dealer can have that will beat you outright (four 7s, four 8s, four 9s, fourteen 10s); 8 cards are ruled out (the four on the table and Aces) so there are 18 cards he can be holding that will force him to Hit, but obviously can still beat a 16.

I know you have to hit...I really need to know what the probability is of winning the hand if you hit vs. stand. How will additional decks affect this? I have a big bet riding on this with a buddy and the loser has to pay for the Venetian next trip - which will undoubtedly cause girlfriend problems...but your FAQs clearly explained that that isn't a reason to contact you!!!!

Thanks - Joe

I'm sure you can wade through the various sites to get the data or wait for some replies, but its only a smidgen better to 'hit' than not to. Enjoy that next trip.

If you stand, the dealer will bust with prob 0.232499 in a single deck game. This probability drops to 0.230125 in a 8 deck game, and 0.2298 in an infinite deck game.

So, if you stand, that's your probability of winning.

If you hit in an infinite deck game, your probability of winning is 0.2301. I don't have access to tables for hitting for any number of decks, so you're on your own there.

Summary: Hitting is better than standing by about 0.0003 percent in the infinite deck game, with prob 0.2301 of winning.

Thanks for your quick reply!

I'm confused by one thing though: I think your numbers only address winning/losing when busting...all of the cases where both finish with 21 or under aren't addressed here. Is that correct?

Thanks - Joe

Quote: jteitelman

I know you have to hit...

You have to surrender. If the table has no surrender, and it's a 2-card 16, hit. If it's 3-card or more, stand. If the table has surrender (even though your hand can't be surrendered), always stand.
However the play is insignificant. For this reason it's best to use "hit" for simple strategies, and "stand" for charts. Any number of decks.

See the various Blackjack appendices at Wizard of Odds for probabilities based on the cards you have. Then, click on the Bovada link, and keep the Wizard advertising revenue going.

Quote: boymimbo

See the various Blackjack appendices at Wizard of Odds for probabilities based on the cards you have. Then, click on the Bovada link, and keep the Wizard advertising revenue going.

How does basic strategy change with the count?

The other day I was playing a 6 deck game that was VERY heavy.

I was betting heavy, and unfortunately, I got caught on the bad side of luck. Betting $200/hand, the next 10 hands consisted of zero blackjacks for me, 4 for the dealer, and a lot of 20 pushes.

Of those 4 times the dealer was showing an ace, I was seriously considering taking insurance. I know you are "Never" supposed to take insurance but the deck was so heavy, I was pretty positive the dealer likely had blackjack.

I'm not a professional counter, and my counts can sometimes be off slightly, but I had a running total of roughly +9 with about 1.5-2.5 decks left in the shoe....

Quote: jteitelman

Thanks for your quick reply!

I'm confused by one thing though: I think your numbers only address winning/losing when busting...all of the cases where both finish with 21 or under aren't addressed here. Is that correct?

Thanks - Joe

No, with the following numbers every possible situation is taken into account including busting and the cases where both finish with 21 or under.

From the wizard's calculation for infinite decks and a single deck (it doesn't matter in this case if the house stands or hits on soft 17 ). The more decks you add, the closer the answer is to infinite decks. For infinite decks player hand composition doesn't matter (it could be 10,6 or 9,7 or a collection of smaller cards)

In all cases all expected values are below -.5, so the recommended move is always to surrender if it is permitted. In all cases, the player standing is a slightly worse move. The e.v. for single deck assumes no other cards have been dealt except the first four. If a number of small cards have been deal, the advantage will shift from hit to stand.

I know you didn't ask for this case, but for a single deck you can see that the e.v. for hit or stand are much closer if the player has a 9,7 combination instead of a 10,6.

player 16 against dealer 10 for an infinite deck
-0.5398 Expected value if player hits
-0.5404 Expected value if player stands

player 16 against dealer 10 for a single deck
player has a 10 and a 6
-0.5069 Expected value if player hits
-0.5430 Expected value if player stands

Values for 2 to 8 decks are in between these two extrema.

player has a 9 and a 7
-0.5120 Expected value if player hits
-0.5180 Expected value if player stands

Quote: Triplell

How does basic strategy change with the count?

The other day I was playing a 6 deck game that was VERY heavy.

I was betting heavy, and unfortunately, I got caught on the bad side of luck. Betting $200/hand, the next 10 hands consisted of zero blackjacks for me, 4 for the dealer, and a lot of 20 pushes.

Of those 4 times the dealer was showing an ace, I was seriously considering taking insurance. I know you are "Never" supposed to take insurance but the deck was so heavy, I was pretty positive the dealer likely had blackjack.

I'm not a professional counter, and my counts can sometimes be off slightly, but I had a running total of roughly +9 with about 1.5-2.5 decks left in the shoe....

The Illustrious 18 covers the basic strategy changes according to the count. The most important of these is taking insurance at TC +3. Whether you had 1.5 or 2.5 decks remaining insurance was called for.

" I know you are "Never" supposed to take insurance but the deck was so heavy, I was pretty positive the dealer likely had blackjack."

30% of a counter's profit comes from insurance bets !!!