Expected value for blackjack In the game of blackjack, the odds of winning each hand are slightly less than 50 percent. As you play an infinite amount of hands, you would always lose money because you would win less than 50 percent of the time. By this rationale, wouldn't your highest odds of winning be if you only played one game?

You are correct in that a typical "house edge" falls just below 50 percent in most casinos.
Note that probabilities of winning fluctuate as cards are constantly being dealt, due to ratio of high cards (good) to low cards (bad) remaining in the deck fluctuates. The study of these changing probabilities is what lead to the birth of card counting. 
If one becomes a skilled counter, they can place higher bets during stages in which the player has the probabilistic advantage over the casino. If played correctly, card counters generate a positive EV using strategic betting, and actually generate a profit over a long period of time. 
