APS

Showing our working

The Sentence We Never Published

We wrote a line about our own subject that everyone in the room believed. We held it, measured it, and found it was backwards. It never reached a page — and this is the record of why not.

The line

It was going into a guide about basic strategy, and it said that the gap between playing the chart perfectly and playing casually is larger than the gap between playing the chart perfectly and counting cards.

It is a good sentence. It flatters the reader who has not learned to count yet, it makes the free material sound like the important part, and it matches what nearly everyone who plays this game will tell you. Nobody who read the draft objected to it.

It was also the strongest line in a batch of twelve, which is exactly why it was the one that got stopped.

Why it was held

This house has a rule that a claim has to trace to something on disk. The sentence traced to nothing. It was established knowledge — the sort of thing everyone knows — and established knowledge is not a source.

There are only three honest things to do with a claim like that. Measure it, if you own an instrument that can. Attach a name to it, so it becomes somebody's testimony rather than a floating assertion. Or cut it.

We own the instrument. So the sentence was held out of the shipment, and the software that would have printed it was told to work out whether it was true.

What the measurement said

Seven point two million rounds per arm, every arm dealt the same shoes so the comparison could not be an accident of the cards. Perfect basic strategy, a defined set of ordinary mistakes, and a counter, measured against each other.

Casual mistakes cost real money — more than twice what the house edge takes on its own. But counting was worth more than fixing them, not less. The sentence was backwards, and the difference was larger than the uncertainty in the measurement, so it was not a close call that could be argued either way.

The line does not appear anywhere on this site. What appears instead is what the measurement actually found, with its intervals, and with the three limits on it stated in the same breath rather than in a footnote.

Why we are telling you about a sentence that never existed

Because the interesting question about anyone teaching this subject is not whether they have ever been wrong. It is what happens to a claim between someone believing it and a reader seeing it.

For most published writing the honest answer is: nothing happens. It gets written, it reads well, and it goes up. There is no step in between, which is why so much of what circulates about this game is confident and unchecked.

We can show you our step. It caught the best sentence we had, and it cost us that sentence. We think that is the only kind of evidence worth offering, because it is the kind that costs something — anyone can publish a correction after being caught, and almost nobody can show you the thing that never got out.

What the measurement returned

Perfect basic strategy, flat bet

0.503% ± 0.069

dealer hits soft 17 · six deck · 3:2 blackjack · late surrender offered · double after split allowed

The defined casual-mistakes profile, flat bet

1.755% ± 0.087

dealer hits soft 17 · six deck · 3:2 blackjack · late surrender offered · double after split allowed

What counting adds

1.560 ± 0.174 percentage points

dealer hits soft 17 · six deck · 3:2 blackjack · late surrender offered · double after split allowed

The bet spread alone

1.392 percentage points

dealer hits soft 17 · six deck · 3:2 blackjack · late surrender offered · double after split allowed

Deviations alone, flat bet

0.453% ± 0.077

dealer hits soft 17 · six deck · 3:2 blackjack · late surrender offered · double after split allowed

The spread's share of the gain

89.2%

A share of the combined gain, not a measurement in its own right — so it carries no interval of its own.

dealer hits soft 17 · six deck · 3:2 blackjack · late surrender offered · double after split allowed

The deviations' share

3.2%

A share of the combined gain, not a measurement in its own right — so it carries no interval of its own.

dealer hits soft 17 · six deck · 3:2 blackjack · late surrender offered · double after split allowed