For me, there is as much satisfaction, and actually even more, in the process of “getting there†than in lending on the third base. I start by looking at what’s at play, then I am meandering my way to get to know it better, trying different approaches, appreciating details, recognizing mechanics, touching, stroking, and nudging until it yields and finally reveals its mystery. Yeah, I am still talking about tournament blackjack, and specifically: Dealer showing: 9 Player.......P1.........P2.........P3.........P4 Bnkrl......7,950.....7,450.....6,500.....11,400 Bet........2,300.....2,500.....2,500.......2,500 Cards.......6,5........5,4........10,6........10,2 Rank the best play for P1 against average players. A) Double down, B) hit once, C) hit to 15, D) hit to 17 Let me share my roundabout way to find the answer. At first we see two distinctly different plays: double down and hitting (we will get to whether to hit once, hit to 15 or hit to 17 later). Tournament blackjack play is about making a difference between bankrolls, our bankroll against other players’ -- and this can be achieved only by winning, pushing or losing our hand against dealer’s hand. What is the difference between hitting eleven to seventeen and doubling when dealer’s upcard is nine? Doubling 11 wins 52% (including 23% when dealer busts) and pushes slightly over 7% of the times. Hitting to 17 wins 53% (including 18% when dealer busts) and pushes exactly 10% of the times. Will the extra 6% hands won against dealer’s pat hands and extra 3% pushes outweigh the danger of not advancing when two opponents win their doubled bets (or one doubled and P4’s single win)? This will depend on their style of play, namely their doubling or hitting to 17, or hitting to the same score or better than our hand. If we decide to double down there is one sure thing: if we win our doubled bet– we are guaranteed to advance no matter what happens to the other players. Just this alone gives us 52% chance, and it is a lot. Now, let’s look at some extreme cases that will help us find ranges of our chances of advancing. If we double down and all other players also double down (P4 doesn’t have to but because of his lead of more than one max bet his play doesn’t make that much difference). We advance 52% by winning plus 6.7% when we push, and a staggering (to me) 22% when we lose but both P2 and P3 lose as well. The total chance is 80.7%. If we double down and all other players hit to win with us by one point we advance when we win (52%) and we still advance in most cases of pushes 5.6% (out of 7.3% pushes) but we will have virtually zero chances of advancing when we lose our hand. The total chance is 57.6%. If we hit to seventeen and all our opponents double down, while we win our hand 53% of the times it contributes only 11.4% toward our advancement, we push and advance 9%, and we lose the hand but advance 18.2%. The total chance is 38.6%. Seems like it is an absolute no-brainer to double down, or is it? If we hit to seventeen and all our opponents also hit to 17, we win our hand and advance 53% of the times, we push and advance almost 9%, and we lose the hand but advance almost 15%. The total chance is 76.4%. Okay, we have ranges: if we double down our chances to advance are from 58% to 81%, and if we hit to 17 our chances are from 39% to 76% --depending on our opponents’ style of playing. If we play against absolute novices, who stick to basic strategy, it is advisable to just hit as doubling gives away the chance of advancing if we lose the hand. It is a better play by a third (76% to 58%). If we play against players with some tournament experience, who know about “necessity†to win doubled bet on the last hand it is advisable to double down. It is twice as good play (roughly 80% to 40%). In most cases our opponents won’t belong to either of the groups and will act or rather react to our play and to final result of our hand. When it comes to P2 play we are most interested in finding out if he may be tempted to hit instead of doubling if P1 opts to hit, thus giving P1 both the low and the hi. Once P1 decides to just hit, hoping that P2 also hits, standing on a stiff is more likely to induce P2 to try to make a gain over P1 by hitting than if P1 hits until a pat or bust hand. If P1 busts or has a good hand P2 may realize that it is to his benefit to double down. This would be the reason to rate hitting once higher than hitting to 15 or hitting to 17. If P1 hits his success relies more on other players not winning their doubled hands than on P1 having a good hand. Even when P1 hits and ends up with a stiff he would have close to 50% chance to advance if P2 hits and P3 doubles and P4 hits. The real secret of this game is SURRENDER. This may be not obvious, as it does not apply to P1. However, note that P4 in many cases may redeem his evident overbet by surrendering, though, if other players double down and the second best opponents’ hand is 18 or less P4’s best bet is not hitting but standing on 12. Also P3 should surrender if P1 doubles and neither P1 nor P2 have 19 or better. P2’s best play is to surrender if…well, let’s leave a shred of unexplained to other people’s imagination. I hope I haven’t lost most of my readers on the way. Numbers are fun and in the right dose can be sexy, but then, sexy is in the eye of the beholder. S. Yama
