I am reading casinology and they state that?

Divide By Zero, there are plenty of hands where the player has a positive expectation. It's the whole "if a tree falls in the forest and no one is around to hear it, does it make a noise?" argument.

There are absolutely times when the player has a positive expectation. The difference is the card counter knows when he has the edge and increases his bet. The casual gambler doesn't realize when he has the edge, so he won't change his bet accordingly. READ THIS: Just because he doesn't know about the edge doesn't mean he doesn't have the edge.

Divide By Zero's comment: "It could mean that the count is in the player's favor 16.5% of hands instead of 32.5% of hands," is right even though this comment directly contradicts his first comment that "[t]here are 0 hands where the player has a positive expectation unless the player is counting cards."

OP's source is claiming that over the course of normal blackjack play, 32.5% of the hands are advantageous to the player (meaning 67.5% are not advantageous to the player). This isn't enough information to calculate the house edge, however.

For example, 32.5% of the hands are advantageous but doesn't say advantageous by HOW MUCH.

If I had a 32.5% chance to win a million dollars and a 67.5% chance of losing one dollar, I would still play the game. I'll likely walk away having lost a little, but the small possibility that I might win big is worth it.

OP's source is claiming that paying 6:5 on blackjacks reduces the number of advantageous hands to 16.5% (meaning that 83.5% of hands are disadvantageous). But by how much? It turns out that if the player has an advantage, he stands to win a lot of money whereas if he doesn't have an advantage, he stands to lose only a little.

As a result, in the 16.5% of the time he has an advantage, he'll recoup almost all of his losses (all but 1.39%) from the 83.5% of the time he didn't have an advantage.

There are 0 hands where the player has a positive expectation unless the player is counting cards. A positive expectation requires a positive edge. So I'd need more context to know what that quote is talking about.

It could mean that the count is in the player's favor 16.5% of hands instead of 32.5% of hands. I wouldn't know if that sounds right or not.

Edit -- something I just thought of.

>>"How does that happen it gives the house advantage gain is only 1.39 percent?"

They say a card-counter's edge is only in the 1% to 2% range. So a difference of 1.39% house edge is a huge difference.

** Edit #2 **

Eddie, I'm aware of what you're saying and I even thought of that before posting. But on any given hand if you don't know the count of the deck, then your EV (by your knowledge) is negative.

We can be as technical as you want. By your logic, we can say that about 42% of hands have a deck arrangement that favors the player. So in 42% of hands, the player has a 100% edge!

Also by that logic, if we flip a coin, on some of the flips there's a 100% chance it's heads and on other flips there's a 0% chance. Therefore I can say, "in 50% of all coinfliips, the player betting Heads has a positive expectation".

In both examples (which are just valid extensions of the same exact reasoning as yours and the author's), it's pure nonsense. Expectation is based on the bettor's knowledge, not on what an omniscient being knows or what someone with more information (like the count of the deck) knows. When flipping a coin for even money, your EV is 0 on every flip -- both losing flips and winning flips (because you're not able to predict any of the flips). When playing blackjack and not counting, your EV is negative every hand you play, because you don't know which hands have a favorable count. This is just EV 101, and the author should be ashamed for phrasing it the way he did. He should have just said, "The count favors the player __ % of the time" instead of making a misguided statement about EV.

Just based on that, I would question everything in that book. Someone who doesn't understand the basic theory of EV shouldn't be writing a book on gambling.