Interesting. The author's central thesis is 'You can't win at betting.' A plethora of mathematical p-values, t-tests, graphs and anecdotes is evidenced to push this point home. The author does a cogent job and has me convinced it can't be done. And true, I keep trying, which is a paradox but it fulfils my craving for control. I get that.
A few issues. The book really seemed to lack organisational structure. It's very hard to delineate one chapter from another thematically. It's all thrown in. Buchdahl's main point ('You can't win at betting') is well worth telling but the book lacks structure. For me it went round in circles a lot. On the plus side, this did hammer the point home ('You can't win at betting'). It's quite a major change from the betting guides I grew up with - horse racing books that basically suggested if you study form hard enough you'll win. Crucially this book calls that out as a myth.
Prospective readers should note there is a lot of mathematics here. Much of the psychology and philosophy comes from popular works in the field (Daniel Kahneman, Nate Silver, even Malcolm Gladwell). There's quite a lot of Kahneman and Tversky stuff about the erroneous heuristics many gamblers apply. We see patterns that fit all the time ('What You See Is All There Is') and fail to register the influence of chance. Probably the strongest reason bettors will fail, however, is that of the 'wisdom of the crowd.' In the long-term the market's aggregated opinions will outperform the keenest of form students.
There are few tips here for methods to secure a profit through betting. Patrick Veitch, Haralabos Voulgaris and Warren Buffett (in the realm of stock market trading) are put forward as exemplars whose detailed knowledge can beat the market but the reasoning behind what makes this possible is sketchy at best. It's hard to see what reasoning the author could put forward since he has, by this point, applied 250 pages and a lot of heavy mathematical analysis to suggest that winning at betting is not possible; or at least that if you are a winner over the long-term it's actually just (extremely good) luck.
I enjoyed the final pages which provide a little coherence to the work as a whole. The intelligent gambler might reflect or at least consider that gambling derives from a desire for control. 'Having a healthy appreciation of uncertainty and a cognitive style geared towards probabilistic thinking' is encouraged to temper the errors that psychological drive will make.
I'm pretty happy to have purchased and read this entirely credible, if difficult, text, that adds something to the literature on gambling. As a player in sports betting markets the book you'd really want to read is the text that can reasonably dispute many of the strong arguments put forward here. I don't think I've read that yet.