Why Blackjack Buffs Rightly Respect those Terrible Twos

All good blackjack players know that some dealer upcards are easier to beat than others. Everybody hates to face 10s and aces. Sevens, eights, and nines are deemed dicey if not downright dangerous as well, if only because Basic Strategy says not to stand with a hand below 17 against any of these li'l devils.

Lower upcards are "stiffs" with which dealers appear to be at least vulnerable. The gurus tell you to stand even if you're unfortunate enough to start with most totals below 17 against them. You have better prospects when you depend on the dealer to bust than to try for a higher tally and risk going over yourself.

But, what about those terrible dealer twos? They're an exception to the "stand against stiffs" rule because the wallet-sized crib sheets recommend hitting rather than sticking with a total of 12 against a two. This, despite nearly universal intuition about the next card out of the shoe being a 10 and knocking a bettor out of the box immediately. Twos are also taboo vis-a-vis soft doubles.

Such considerations have lead many solid citizens to wonder, if they haven't convinced themselves of it outright, whether two-up isn't really as bad as or worse than seven-up. What do you think?

Dealers do bust when they start with two-up, of course. Perhaps by flipping over a 10 then pulling another for a quick 22. Or with some other happy combination of cards. Statistically, this will happen about 36 percent of the time -- although it's easy to get the impression that the law of averages must work because of what happens at someone else's tables, yours being those at which twos always mature into high non-breakers. In comparison, dealers are expected to bust with seven-up only 26 percent of the time. Were this the only criterion, twos would be weaker dealer upcards than sevens. And misconceptions that the opposite may be true could easily be attributed to the difficulty in perceiving the difference between 26 and 36 percent of events that each only occur in under 8 percent of all rounds. Especially during the heat of the action when nobody's keeping accurate records.

But blackjack is a more complex game than you thought when you were a kid and played it around the kitchen table for buttons or matchsticks. Meaningful comparison of two- and seven-up goes beyond just the relative likelihoods of the dealer breaking.

One key additional factor involves the chance that a dealer who doesn't bust will finish with a hand at various levels from 17 through 21. Clearly, the more apt dealers are to end with higher totals, the tougher it will be for players to win the round. The relevant information is shown in the accompanying chart. Note that dealers are more likely to finish at 19 through 21 starting with two- than seven-up, so the corresponding completed hands are accordingly more difficult to beat.

Probability that the dealer will finish at various levels starting with two-up and seven-up

upcard	17	18	19	20	21
two	14%	13%	13%	12%	12%
seven	37%	14%	8%	8%	7%

Another factor in comparing two- and seven-up involves player starting totals with positive expectations. That is, which dealt hands have better prospects of winning than losing, even if not by much, against either upcard? The totals or combinations with an advantage over both are 9, 10, 11, 18, 19, 20, A-2, A-3, A-6, A-A, 8-8, and 9-9; there are 12 in all. This is the complete list for twos. But totals or combinations with positive expectation against seven-up also include 8, A-4, and 2-2. That is, three more starting hands are projected to beat seven than two.

The bottom line is that players following Basic Strategy have an overall advantage against two-up exceeding 9 percent. When the dealer's upcard is a seven, players have an overall advantage above 14 percent. So, players are favored either way. But bettors have greater edge against the seven. If your gut told you that twos were the more treacherous, it was right. Or, as the instinctive inkslinger, Sumner A Ingmark, impressively inscribed:

Though intuition's not reliable,
And you want facts quite undeniable,
At times, a guess proves wholly viable.