Observed this last week on a semi-final (1 advance) table last hand and thought it would be a good tournament teaser. 6 deck shoe, dealer stands on any 17, minimum bet $100, no max bet, no surrender. 4 players left, you are BR3, last to bet and act. BR4 2,300 bets 2,300 BR1 5,100 bets 100 BR2 4,800 bets 500 BR3 (you) 3,600 bets 2,200 BR4 9,3,10 busts BR1 10,4 stands BR2 8,4 stands BR3 (you) 10,7 Dealer upcard Q A push does not advance you, do you hit to 18, 19, 20, 21 risking a bust or stand with 17?
Rookie's teaser said that the dealer has Q up. First of all, the hero in the teaser (BR3) bet $100 less than optimal as he has opened up the chance for BR2 to DD for a tie. In this particular situation, with one advance and betting last, there is no reason for our hero to keep back any chips at all. Since there is no need to win a full swing and he's got the high already because BR2 didn't realize what was going on and failed to DD his 12, hitting the 17 would not be the move. Not having any idea what has come out of that shoe before this hand, I see two 4's and one 3 on the felt so three cards that could help him are gone. Stand on the 17 and pray.
Good catch LeftNut regarding the additional $100 bet by (our Hero) BR3 to avoid the possibility of BR2 doubling for a possible tie which would involve a play off to advance. In defense of BR3, a 10 second rule for decisions was in effect. Hitting hard 17 will bust 62%. Catching a 2,3 or 4 = 23%. Dealer bust with 10 up = 23% The math appears close with a 10 second evaluation but a bust by BR3 eliminates his chance to advance and hitting to 18, 19 or 20 may push which would not advance BR3. BR3 stood with his hard 17, dealer turned a 10 for 20 total and BR1 advanced with his minimum $100 bet. I agreed with BR3 standing on H17 but welcome the "Math Guys" to enlighten me, c'mon Ken, Yama and BlueLight. Two opinions are requested, 10 seconds and 10 minutes evaluation time.
It is important to correctly recognize the situation. Since BR1 bets small we can’t lose our bet, even push does us no good. It is “must win” hand, do or die. When we must win the hand and have no time for finer dissecting -- betting all-in (or max bet) is the right think to do. If we have some time to spare for thinking then we should look if betting half of our bankroll is enough to cover main opponent winning double bet. There are other benefits, but not as important, if we bet no more than 1/3 of the bankroll for splitting to three hands, or 2/7th for “masonuc maneuver”, or even ¼ for splitting to four hands. It is more important to cover opponent’s winning double or triple bet without us being able to split. When we can cover opponents triple bet with one of the above mentioned fractions of our bankroll only then we don't bet maximum allowed. Right, standing on 17 advances us only when the dealer busts – about 23%. And by hitting we improve our hand about 23%, but some of the improved hands will still lose, we win with dealer only 18.5%. S. Yama
My instincts were to hit to 18, but that does appear to be the wrong option by quite a margin. [On reflection, I'm not sure why my instincts were leading me in this direction. It's entirely wrong. The 'Push is as bad as a loss' strategy variations tend towards standing rather than risking a bust. In particular: 'stand on fifteen or more against 10'.] It would require software to calculate precise figures for 6 decks with the known cards removed, but I doubt there would be much difference from the infinite deck approach : Stand Rely on dealer bust = 22.98% Hit to 18 (i.e. take exactly one card) Using the dealer outcome chart from here: http://www.blackjackinfo.com/bjtourn-dealercharts.php#TIDS17 - Code: [B]Player Prob of Prob of beating Total reaching dealer with this total[/B] 18: 1/13 * (22.98 + 12.07) = 2.7% 19: 1/13 * (22.98 + 12.07 + 12.07) = 3.62% 20: 1/13 * (22.98 + 12.07 + 12.07 + 12.07) = 4.55% 21: 1/13 * (22.98 + 12.07 + 12.07 + 12.07 + 37.07) = 7.4% ------ 18.27%
Just for fun Just for fun Colin, In a six-deck game we roughly need to add 12 Aces, deuces, treys and fours (total extra 48 cards) – cards that help person wishing to hit 17 against dealer Ten - to make it a better play. In such case we advance 22% of the time but dealer bust just short of 22% so it is better to hit. Funny, it still would be worse than standing while playing regular decks. If we double Aces to fours (total 96 extra cards) hitting wins 26% of the times and standing succeeds about the same as in the above alteration – 21.7%. S. Yama
Stand If you need to win a hand against a dealer up card of 10 you stand with 16. For infinite deck by hitting you gain the push and lose a little on the win probability. However a push does you no good in the situation as posted. In fact if you need to win you would stand with a total of 15. Therefore standing with 17 is the best play here. If you hit and don't bust there is still no guarantee you will win. Your best chance is to hope the dealer is stiff and busts. For infinite deck with dealer 10 up and you with 17 and standing totals : H17....... .2298 H18....... .1828 H19....... .1678 H20....... .1387 H21....... .0925 For a 6 deck game with the cards on the layout removed from the pack. (remove 9,3,10; 10,4; 8,4; 10,7; Q) then the exact figures for hitting and standing are: H17....... .23127 H18....... .18069 .................................BlueLight
Thanks for the shoutout Yama -- but yeah, my trick doesn't work here. Pretty much only works when you are a close BR2 in a two-man situation and betting second, and BR1 bets minimum. I definitely push all in here 10 seconds to think about it. No question. And as BlueLight alludes to, you stand here even with 16. Actually, even with 15. So definitely with 17.
