Every single game in the casino is driven by “Expected Value.”
When we are talking about the expected value of the entire game it is called payback or sometimes return to player (RTP). When we are looking at a single hand, spin or decision, it is called the expected value.
What percent of our wager can we expect to get back? We do not use percentages for expected value, but rather decimal form. So, an expected value of 1.00 means we expect to get back exactly 100% of our wager — or in other words, a push.
If we are dealt a Blackjack and the dealer does not have one, the expected value is 2.50 if the game pays 3 to 2. We wager one unit and get back 2.50 units. It does not matter if a unit is $1, $5 or $100, it is all the same as a percentage. Every decision we make should be based on the expected value of that decision. Why do we hit a 16 against a dealer 7, but not a 17? I mean it is only a one-point difference.
If we are dealt a Blackjack and the dealer does not have one, the expected value is 2.50 if the game pays 3 to 2. We wager one unit and get back 2.50 units. It does not matter if a unit is $1, $5 or $100, it is all the same as a percentage. Every decision we make should be based on the expected value of that decision. Why do we hit a 16 against a dealer 7, but not a 17? I mean it is only a one-point differencedean martin and frank sinatra playing blackjack, 1960 pic.twitter.com/g3O1u8Omqr— best of old hollywood (@oldhllywoods) October 11, 2020
Now, logically, there may be some of you who are trying to work this out a different way. When you have a 16, you have five cards that will improve your hand vs. only four with a 17. With a 17, there is a good chance the dealer may have a 10 underneath and at least you’ll tie. These are all valid reasons for hitting one and sticking on the other. But, in reality, they are just components of the math that really make the decision.
When we look at every possible outcome in Blackjack, we find that the expected value of a 16 against a 7 up-card is not very pretty. If we hit, the expected value is only about 0.59. On average, we’re going to lose about 40% of our wager. If we stand, the expected value is about 0.52 and we lose about 48% of our wager. So, we hit the hand because quite frankly, it is the lesser of two evils.
When we look at a 17 against a 7 up-card, the picture is not even close. If we hit, the expected value is only 0.53. Not surprisingly hitting a 17 is worse than hitting a 16. If we stick, the expected value is about 0.89. Our only hope of winning is the dealer busting. But the probability of a push is very high, and this greatly helps our case.
What if we take the ties out of the picture? What if is a 17 vs. an 8 up-card? Not surprisingly, the expected value of standing plummets. It goes all the way down to 0.62. We can still only win if the dealer busts, which is reduced with an 8 as the up-card. Additionally, the probability of a push has gone down significantly. If the dealer turns a 10, we lose.
These are extremely obvious (I hope) examples from Blackjack. But they show that the strategy decisions are not based on logic, but on actual math. I’m sure we’ve all sat a table while a player has either actually hit a 17 into a 10 or at least given it some thought. But it is a horrible decision that mathematically is not even close. It is not something to be thought about at all, yet alone done.