Peter Griffin made blackjack probabilities easier to study rigorously. His teaching and The Theory of Blackjack explain why decisions depend on rules and remaining cards, and why a counting-system rating is not a promise of earnings.
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A mathematics teacher who studied blackjack
Peter Griffin shared something significant with many of the blackjack card counters who revolutionized the game of 21. He was a mathematician. Many of the original advocates of card counting had a mathematical background. Peter Griffin was one of these men.
Born in 1937 in New Jersey, Griffin came from a well-educated family. His own grandfather had been a mathematics professor at Reed College and had actually written college textbooks on the subject of mathematics. It is no wonder that the young Peter Griffin grew up fascinated by numbers and probabilities, two things at the very heart of card counting.
After his formal education, Griffin joined the mathematics faculty at California State University, Sacramento in 1965. The university’s memorial archive records his service from 1965 to 1998. His academic career gave him a setting in which to investigate blackjack through probability and mathematical analysis.
Griffin’s interest in blackjack can be traced to 1970. In that year he proposed a class on the mathematics of gambling to the board of his university. Gambling provides useful examples of probability and decision-making, but those courses did not originate modern game theory. John von Neumann and Oskar Morgenstern’s Theory of Games and Economic Behavior appeared in 1944, well before Griffin’s blackjack work, as Princeton University Press’s account confirms.
In order to develop the curriculum necessary to teach his class, Griffin needed to research and test various theories of card counting and other blackjack probabilities. He sought practical experience in Nevada, alongside the theoretical work. John Lienhard’s University of Houston account describes early gambling losses that encouraged more analysis. Visiting a table can reveal how play is conducted, but a winning or losing trip cannot by itself validate a mathematical theory; calculation and simulation offer ways to test probabilities without risking money.
Out of defeat came progress. Peter Griffin was inspired to do more research and study. He immersed himself in every written work he could find on the subject. He practiced and analyzed the techniques he had learned while refining them to account for any inaccuracies. Griffin also took another approach. He began to compile a vast amount of statistics on professional blackjack players in Atlantic City while doing the same for players in Las Vegas and Reno.
Comparisons of play in different locations raise two separate questions: how the rules affect theoretical expectation, and how players’ decisions affect actual results. A city name does not determine a house edge. Games in Atlantic City, Las Vegas or Reno can differ in payout, decks, surrender and doubling rules; those conditions must be specified before comparing their mathematics.
In many respects, the work Peter Griffin was doing with statistics in blackjack was very similar to the work Bill James later did in the realm of baseball. Griffin’s findings did much to explain the theory of card counting. His analysis examined how particular decisions and card compositions change expected value. A quoted player disadvantage of 2% needs a defined game and a defined pattern of play; it is not a universal blackjack constant or the probability of losing a hand. Basic strategy selects decisions for specified rules, and the resulting edge must be calculated for that game. Earlier work, including Thorp’s, had already quantified blackjack probabilities.
Some of Griffin’s calculations require considerable mathematical preparation, but their central lesson is accessible: evaluate a decision by its expected result under the relevant conditions, rather than by whether the last hand won.
In Griffin’s day it was very popular to publish one’s card counting information in a book. Many authors were promoting their particular systems in books of their own, and Griffin followed suit. He wrote and published The Theory of Blackjack: The Compleat Card Counter’s Guide to the Casino Game of 21 in 1979.
The book became an important reference in blackjack literature. Its mathematical detail makes it a demanding read for a beginner, but also lets a reader follow the reasoning behind an answer. The UC Davis mathematics department’s 1998 memorial recalls both the book’s explanations and its humor. An accessible strategy guide can be a useful starting point before working through the more technical calculations.
It can be said that Peter Griffin’s great passion was teaching. This is what sets him apart from many other blackjack experts. His ability to analyze and count cards accompanied his career as an instructor. Other writers on the subject of blackjack and card counting actively sought to make a living from playing cards. Griffin’s enduring contribution was the study and teaching of blackjack mathematics, rather than a published promise that professional gambling would suit every reader.
He remained a mathematics educator through his academic career. UC Davis records that he died on October 18, 1998, at age 61, from prostate cancer. While his name may not be as familiar to blackjack players as Ken Uston, Edward Thorp, or Stanford Wong, it is worth remembering that many of the contributions made by Peter Griffin have enhanced the efficiency of many card counting methods.
One missing card changes a probability
Here is a simple illustration of the kind of composition question behind blackjack analysis, not a complete betting strategy. A fresh standard deck contains 16 ten-valued cards among 52 cards. Before any cards are identified, the chance that a randomly drawn next card is ten-valued is 16/52, or about 30.77%.
| Known card removed | Ten-valued cards remaining | Cards remaining | Chance of a ten-valued next card |
|---|---|---|---|
| None | 16 | 52 | 16/52 ≈ 30.77% |
| One 5 | 16 | 51 | 16/51 ≈ 31.37% |
| One king | 15 | 51 | 15/51 ≈ 29.41% |
The two removal examples describe separate deck states. Removing a known 5 leaves all 16 ten-valued cards; removing a king reduces that total to 15. Notice that the denominator changes in both cases. An unknown face-down card provides different information: do not simply subtract a ten or a low card when its value is unavailable.
That probability alone does not give the overall player advantage. A complete blackjack calculation also depends on the player’s cards, the dealer’s information, the available actions, payouts and other remaining ranks. A natural requires an ace as well as a ten-valued card; doubling, splitting and dealer outcomes cannot be reduced to the chance of drawing one ten.
Read counting ratings without confusing them with profit
QFIT’s counting-system definitions distinguish betting correlation, playing efficiency and insurance correlation. Those measures describe different tasks. A strong relationship to favorable betting situations does not tell you an hourly income, and a playing-efficiency figure is not the percentage of hands won. The published comparison also excludes side counts from its stated betting and playing figures.
For example, a hypothetical 2% expected loss applied to $1,000 in initial wagers gives an expected loss of $20. It does not mean the session must lose $20, that a $1,000 deposit loses only $20, or that the player loses 2% of hands. The same funds can be wagered repeatedly. To compare actual systems, specify the game, penetration, wager schedule, bankroll and execution assumptions, then examine variance as well as expected value.
Further reading
Blackjack involves financial risk. Set affordable limits before playing, and see the responsible-gambling policy if play stops being recreational.
