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THE SKINNY ON HITTING 12 AGAINST

DEALERíS LOW CARDS

by Alan Krigman

Alan Krigman, and his poetic sidekick Sumner A. Ingmark, have been illuminating the dark recesses of casino gambling for more than a dozen years. Mr. Krigman is especially well known for sharing his insights into the mathematics underlying the various games (including blackjack), the influence of volatility and skewness as well as edge on bankroll during the course of a session, and the impact of betting as well as decision strategies on expected performance. A searchable archive of Mr. Krigman's prose and Mr. Ingmark's muse is online at http://www.iconworldwide.com/winningways/search.php.

Proficient blackjack players know that basic strategy says to hit a 12 against a two-or three-upcard. Many players, however, feel uncomfortable doing it. In fact, more than a few flout what the gurus dictate and stand on these combinations, hoping the dealer will go over 21 and they win.

Hands that total 12 versus low dealer upcards fall into that confounding class of conditions that call for a choice between the lesser of two evils. In short: these hands are underdogs no matter how you play them.

Your playing experience and qualitative reasoning may induce you to stand on them because you could bust if you hit, and might not win even if you donít. But, keep in mind that perception and memory are often unreliable. Gamblers tend to remember times they've seen victory snatched from the jaws of defeat by snooking "the book" and standing, as well as instances when they followed the letter of the law and lost anyway. Hereís the bottom line on these hands: Although standing looses more often than it wins, so does hitting Ė only to a lesser degree.

The precise figures for 12 versus low upcards depend on shoe size, the particular way the 12 is formed (i.e., the combination of cards that make up the 12), and whether or not the dealer must stand on soft 17. The average differences between numbers of losing and winning hands per thousand occurrences of the various combinations are shown in the accompanying table. The greater the difference of losing vs. winning hands, the more often the hand loses than wins.

Average excess of losses over wins per 1,000 hands hitting and standing on 12 vs. 2- and 3-up, when the dealer stands on soft 17

 

6-Decks 8-Decks

HAND

HIT

STAND

HIT

STAND

10-2 vs 2

252

295

252

296

9-3 vs 2

255

292

255

292

8-4 vs 2

254

291

254

291

7-5 vs 2

253

289

253

288

         

10-2 vs 3

232

254

231

254

9-3 vs 3

236

253

237

253

8-4 vs 3

233

248

233

247

7-5 vs 3

232

248

232

246

 

(For example, with a 9-3 against a dealer 2 upcard, if you hit the hand you will lose 255 more times compared to standing after 1000 hands, whereas, if you stand on 12, your losses are 292 times more than your wins.)

The values in the table lead to several conclusions. First, losses exceed wins by a wide margin regardless of the circumstances or how the hands are played. Second, the penalty is always less onerous by hitting than standing. Third, blackjack buffs are at less of a disadvantage when the dealer shows a three than a two. And, fourth, the distinction between six and eight decks for these hands is nearly negligible.

Enquiring minds might also want to know the skinny for 12 versus a dealerís 4 upcard. These are still uphill battles. However, there's a progression from two- to six-up along which the gradient drops. At four, the excess of losses over wins differs little between hitting and standing. For 10-2, the options are virtually equal; hitting is statistically better six times out of 100,000 in eight-deck games (hidden in the round-off of the data at 1,000), and one time out of 1,000 at six-deck tables. For all other two-card totals of 12 versus four, standing is slightly preferable.

Average excess of losses over wins per 1,000 hands hitting and standing on 12 vs. 4-up, when the dealer stands on soft 17

 

6-Decks 8-Decks

HAND

HIT

STAND

HIT

STAND

10-2 vs 4

211

211

210

211

9-3 vs 4

215

209

215

208

8-4 vs 4

214

208

214

207

7-5 vs 4

211

205

210

202

Since no sensible solid citizen would drink alcohol while gambling for money, then you should just cry in your Shirley Temple when you get a 12 against anything. Hit, of course, when the dealer shows a seven or above, and also when you're looking at a two or three. Stand otherwise, unless you get some satisfaction knowing a secret the bosses probably don't, in which case hit 10-2 versus four up.

You can tell the bezonians who scoff or groan that you have it on the highest authority hitting here is mathematically correct. But be braced to break then have the dealer do likewise. Or expect to get dirty looks (or worse) from your formerly friendly tablemates if your hit feeds the dealer a winning rather than a busting card. Fortunately for your fortunes and sang-froid, 10-2 versus four only occurs an average under four times every thousand hands. Nevertheless, as that maddening muse, Sumner A Ingmark, murmured:

Disastrous events may be rare, it is true,

But that's of no help when they happen to you.

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