Today I've been doing some research for an article for Blackjack Insider, and I've been examining the double-or-split decision when you must win both bets. Wong gives his advice on page 132 of CTS. To summarize his advice in a simpler format, here's a translation of what he says: Wong says: Split any pair, except for: Double (4,4) instead of splitting. Double (5,5) instead of splitting. Double (6,6) vs dealer 7,8,9,T,A. Double (7,7) vs dealer 7,8,9,A. I've been using infinite deck approximations in my research today, but the differences are usually small. But my results differ markedly from Wong's advice. I get even fewer appropriate doubles. Ken says: Split any pair, except: Double (4,4) vs dealer 6 & 7. Double (5,5) instead of splitting. Has anyone else done this analysis to confirm the accuracy of this list? (One more item: So far, I'm using Wong's advice of playing a no-bust strategy on both hands after a split. I know that's suboptimal. Later I'll check to see if more splits are appropriate with a better post-split strategy.)
How about (A,A) Ken, if DD after split is permitted we might get even more biased split with appropriate play, because (push - double win) is also 2-Bet Win. As to Aces (easiest case) let's consider (A,A) vs T: For Double Roughly we have total of: D(bust) ~ 23% D(17) x 4/13 = 12% x 4/13 ~ 3.7% D(18) x 3/13 = 12% x 3/13 ~ 2.8% D(19) x 2/13 = 12% x 2/13 ~ 1.8% D(20) x 1/13 = 37% x 1/13 ~ 2.8% Total 34.1% For Split we get the following picture: D(bust) ~ 23% D(17) x 7/13 x 7/13 ~ 3.5% D(18) x 6/13 x 6/13 ~ 2.6% D(19) x 5/13 x 5/13 ~ 1.8% D(20) x 4/13 x 4/13 ~ 3.5% Total 34.4% As you can see the main difference comes from D(20)'s multiplier because we have 1/13 vs 16/169, so the more D(20) is the better Split looks comparing to Double. Actually double is better for all other Dealer's up Cards, including an Ace(H17), which is really marginal. (32.25% vs 32%).
I think I've found one problem in my recent work. I don't think I prevented rehitting split Aces, which made splitting much more attractive. I'll check later tonight and recap. Thanks for the response tirle.
I found two problems with my code from last night, both significant. Once I fixed those issues, I agree with Wong's list with one exception. He says always split Aces, but my infinite deck results instead agree with tirle's: Split (A,A)vT, but double them against any other upcard. It's surprisingly close on every single Ace-split decision, and it's possible (likely actually) that this is a legitimate difference between infinite deck and 6-deck play. Wong also has a single deck exception, so I expect his results are fine, including the Ace splits. However, there's one more area to be explored... Does this list change with optimal after-split strategy? My guess is yes, it will change, and more splits will be appropriate. I'll update with that info later.
Effect of Removal Wong’s numbers, in my opinion, could use a lot of improvement when he writes about “tournament” situations. But I have faith in them when they are related to “standard blackjack game” situations. Tirle’s comments and example with Aces was clear and illustrative. However, in sentence:”… the main difference comes from D(20)'s multiplier because we have 1/13 vs 16/169, so the more D(20) is the better.” - one may come with impression that the more often dealer ends up with a total of twenty the better for splitting Aces. For analysis purpose dealer’s frequency of receiving twenty remains the same but the total cases of player winning against them is greater when player splits (and receives face cards on both hands) than doubling and getting a nine-value card. Ken, I don’t know the subject of your article but I would like to bring one interesting aspect of splitting versus doubling in tournaments to your and other readers’ attentions. It is “the key cards”. Often times when we encounter a close decision (and sometimes even not so close one) it is the deck composition of the remaining cards that determines the optimal play. Most of the time it is not a simple matter of the count. For example in most count systems fives and sixes are clumped together but when we are faced with a decision whether to double or not double a sixteen (pair of eights) fives and sixes play opposite function. It is the density of cards of specific values that’s important. There are cards that swing the scale toward one or the other decision only, but also there are cards that have a dual effect. For example, if you have a pair of eights versus dealer Ten – then, extra five-valued cards (and to a smaller degree a four-valued cards) improve chances for a good double down and at the same time increase dealer’s chances to bust. Lack of the key cards may call for a change of play as well. E.g. in situation sevens versus dealer nine if the seven- and six-valued cars are missing splitting not doubling may be called for. There are also groups of cards motivating change of usual play. For example, if we “exchange” enough cards from the group of middle cards (7, 8, and 9) for group of small cards (2 through 5) splitting sixes versus dealer six is the proper play. Players interested in the subject should take (another) look at Peter Griffin “The Theory of Blackjack” and his Effect of Removal tables. S. Yama
Revised edition coming Stanford talked to Swog and me a couple of weeks ago and he mentioned he wanted to make some revisions to his tournament book. He also mentioned another book in the works. I have been operating my casino company for over twenty years now and rarely hear anything new except for a new game now and then, after listening to Stanford just during dinner I learned several new things (mainly about dice). If you ever get a chance to talk to him, do so.
