Thanks to a visionary and mathematically-inclined man by the name of Dr. Edward O. Thorp, we’ve now known for more than 50 years the beat-ability of Blackjack. Published in 1962, Thorp’s “Beat the Dealer” would forever change the way the world viewed the game of 21. What’s more, the book’s more than 700,000 copies sold instantly turned Blackjack into the most-played casino game in the U.S. – and possibly even the world.
What followed in the years immediately after – not unexpectedly – was a card-counting and advantage-play frenzy, which in turn prompted casinos to change the rules of the game in such a way that it ultimately became practically impossible for a player to beat the house in any way or by any per centage. Needless to say, Blackjack players responded by showing their displeasure in staying away.
All of which of course sparked casinos into trying to lure back their regulars by relaxing once more the rules of the game, and instead, resorting to beefed-up security systems so as to detect card-counting repeat offenders. And so was born a typical cat-and-mouse type of chase between casino operators and players.
Calculating Expected Value
Which now poses the question: exactly what is the expected value of a so-called “advantage Blackjack player”?
A good place to start would be to first define the term “advantage Blackjack player”. For our purpose here, such a player is one who practises counting cards in such a way that there does ultimately exist an ongoing advantage over the house.
It should also at this stage be mentioned that different sets of game-rules will have varying outcomes in terms of efficacy. For the purpose of our investigation we will consider the outcome of a typical simulation experiment running simulations on a standard game, i.e. Blackjack pays 3:2, dealer draws to 16 – stands on 17, player allowed to split, etc. Which simulation brings us right back around to Thorp and his Monte Carlo computer simulation software that mimicked a game of Blackjack.
The Numbers Never Lie
What Edward O. Thorp’s program essentially did was to run literally thousands of simulations of the expected return on a particular spread of cards. And what his computer simulator ultimately concluded was that, given a standard https://onlinebingoaustralia.org/progressive-jackpot/ game, the more hands a player played using the perfect basic blackjack strategy, the greater the anticipated value returned.
This, incidentally, is why some casinos have resorted to imposing minimum limits in terms of players playing against the dealer at any given time, no doubling down after splits, etc. All for the very reason that more hands played per hour potentially means more value gained by the strategic player.
On the other hand, whenever possible, even when playing shoes 6 or 8 decks large, when playing as many as 100 rounds per hour, the advantage player can expect to win up to $49 every 100 rounds played.
Blackjack always was, and even today, remains a mathematically beatable game.