Ever corect to double 5, 6, or 7 vs 6?

A travelling salesman was driving down a dirt road to a farm when he passed a pig with a wooden leg. He knocked on the door of the house and when the farmer appeared he asked him about the pig.

"That's a very special pig", the farmer said. "About 2 years ago I was tilling the fields and the tractor hit a ditch and turned over on me. The pig ran 3 miles down the county road to my neighbor's farm, squealed at the door and when they answered he grabbed Jim by the sleeve and pulled him all the way back to the ditch where I was laying under that tractor. That pig saved my life".

"Just last year me and the missus were upstairs sleeping when a fire broke out downstairs. That pig smelled the smoke, ran into the house from the barn, ran up the stairs through all that fire and smoke and kept squealing until we woke up. Then he led us bsck downstairs through the smoke and fire and outside to safety".

"I agree that's a very special pig", said the salesman, "but that doesn't explain the wooden leg".

"A pig like that", answered the farmer, "you don't eat him all at once".

what is the index to double 9 vs ace?
what is a nt/t threshold?

Perhaps you shouldn't have mocked him.

The reality is that extreme disproportions in card content, the disproportions responsible for important shifts in player expectations [ of eight percent or slightly better ] and the disproportions mathematically justifying radical departures from basic strategy play, only occur(red) in what Peter Griffin had called "pathological" situations; that is, the compositions existing in the stub of the pack when all, or almost all, of the cards within that pack are dealt.

These conditions were standard at the time that Thorp's early analyses were published in the magazine articles that preceded the first edition of BTD thru the mid to late sixties. Old-time players didn't like it when the clubs began shuffling some dozen cards before the fifty-first or fifty-second card was dealt, but Thorp had clearly shown that the deck-casing players' advantage sky rocketed within the stub. The clubs felt they had little choice.

It was precisely because of:

(1) This phenomenon of spiraling end-of-deck advantage.

(2) The fact that the game used to be dealt without a discard holder [ the discards were collected face-up upon the bottom of the deck - there was no cut-card ], and

(3) That analysis of the game was greatly simplified when there were only two ranks to be considered [ Tens and Others ]

that the first published card counting method was the Ten Count. As a ratio count, the exact number of undealt cards was known. With the discards placed upon the bottom of the deck, the number of undealt cards was not obvious. Discard trays were added to alert the dealers to the need to shuffle. Until the late seventies, the games in Northern Nevada had all the cards, undealt and dealt, in the dealers' left hand, meaning there were occassional mid-hand shuffling of the discards, regardless of the clubs' dissapproval.

And using the NT/T ratio as the guidance for betting and basic strategy departure was simplified because only the quantum of Tens need be varied to reach the desired deck content. If you compare the NT/T departure thresholds between the first and second editions of BTD, you see are many differences. They are different for two reasons. Julian Braun had recalculated the indices using less of the crude approximations Thorp had employed and he had accounted to the two-card combinations which constitute the arithmetic hand totals. I assume he then weighted the resulting NT/T ratios derived thereby, but I cannot confirm this as he is inconveniently dead.

Included in the second edition of BTD were Braun's original departure figures for the count promulgated by Harvey Dubner, now identified as the High Low. In the Thorp/Braun version, the difference between 2 thru 6 and Aces and Tens was divided by the number of cards remaining. Therefore, the user of this original version of a blackjack point count (so called because it resembled the point count methods used to fine tune the bidding process in the game of bridge) knew the number of undealt cards. But there were problems.

Keeping these two counts wasn't easy; Revere wrote that he struggled for a year to perfect keeping both the running count and the number of cards undealt. Also, the predictive power of the point count regarding player versus house advantage tails off in the stub of the deck, just as the Ten Count's power to depict advantage and present departures is picking up. Also there were errors in the published indices. The manner of determining undealt subset compositions should have had the uncounted cards, 7s 8s and 9s, present as 3/13 of the undealt pack. But they were over represented, distorting some common decisions, like standing versus drawing on 12 or standing on 16 [ FWIW, the Ten Count never indicates standing on 16 v 7 ]. It was several years before properly balanced undealt subsets were constructed to generate reliable departure indices for point count systems. And then they were sold and not cheaply; $200 was a standard price tag.

Also, FWIW, it was Braun who did the work for the pre-Stanford Wong system sellers, Revere and the Canadian psychology professor with the Slavic name who peddled the Hi-Opt strategies under the name Lance Humble.

If anyone else would like to add to this bit of [ useless? pointless? ] blackjack history, I'd appreciate it.