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# So you want to count cards in blackjack

With the Oakland Raiders having packed up shop and relocated from Northern California to Las Vegas, it’s only a matter of time before fans of every NFL team have the opportunity to make a weekend trip out of heading to a game. And, of course, for most heading to Vegas doesn’t just mean getting to watch a football team play in a beautiful new stadium, it also means getting to spend the weekend on the Strip playing poker, blackjack and sitting at slot machines dreaming of sudden wealth.

In contrast, there are those who may forego the hopes of getting lucky at the slot machine by taking the time to learn to count cards at the blackjack table. In the weeks leading up to their trip they’ll read up on how to count cards, study what kind of games are the most likely to produce winnings and then upon arrival they’ll scour the casinos looking for the games with the best payout being played with the fewest decks. Some of them might even make a few dollars, but there’s no guarantee that they will.

The reason there’s no guarantee that they will win is because even experienced card counters, playing exactly by the book and going undetected by casino monitors have a not insignificant risk of losing money. The exact probability of a player losing all the money they’ve plopped down on the table is a function of several factors, including how much they started with, how much they’re betting on each hand, how religiously they’re following the count and a little bit of randomness as well. Ballparking things, if an individual sits down to count cards and play until they either double their money or lose all their money, roughly two thirds of the time they’ll double their money and a third of the time they’ll lose whatever they put down. Again, those numbers aren’t perfectly exact, but they’re close enough to get the point across.

So, with that knowledge, say a fan travels to Las Vegas for a three day weekend to watch a football game, and while there they play blackjack each day. Say they start out with \$200 each time, they count cards perfectly and play until they either double their money or lose it all, at the end of the weekend it would be expected that they’d have \$800, having doubled their money twice and lost their \$200 once. Obviously, it’s completely possible that they outperformed expectations and doubled their in money each of the three sittings, walking away with \$1,200. Alternatively, it’s possible luck didn’t go their way and they lost the full \$200 not just once, but two or possibly even all three times.

In any case, before diving too far into things, it may be prudent to take a step back and explain a few things about the math behind counting cards. The basic premise of counting cards is simple: bet big when the odds are in your favor, while betting small when the odds are in the casino’s favor. For most blackjack games, regardless of the number of decks in the shoe or payout, the probability of a player winning any given hand with a neutral (zero) count is roughly 49.5%, with the house having an inverse probability of somewhere in the 50.5% ballpark. For every step the count increases, the probability of the player winning increase by roughly 0.5% while the likelihood of the dealer winning decrease by about 0.5%.

On the flip side, for every step the count decreases, the probability of the player winning decreases by roughly 0.5%, while the probability of the dealer winning increase by that same amount. In short, here’s a ballpark, back of the envelope, rule of thumb rundown of what the likelihood of winning is for a player versus for the dealer on a handful of various counts for illustrative purposes.

• Count 5: probability bettor wins 52.0%, probability dealer wins 48.0%
• Count 4: probability bettor wins 51.5%, probability dealer wins 48.5%
• Count 1: probability bettor wins 50.0%, probability dealer wins 50.0%
• Count 0: probability bettor wins 49.5%, probability dealer wins 50.5%
• Count -2: probability bettor wins 48.5%, probability dealer wins 51.5%
• Count -3: probability bettor wins 48.0%, probability dealer wins 52.0%

Again, these are not precise numbers, they’re simply illustrative of the ballpark way in which the expected outcome of any give hand plays out. Now, the simple idea behind counting cards is that when the probability of the player winning is higher, to bet larger than when the probability of winning is lower. Here’s an imaginary example of ten hands dealt showing two different players using two different methods of betting, one with flat betting and one with a bet size that fluctuates as the count changes throughout the course of a game.

### Expected payout from sample blackjack game with two players of differing strategies

Hand Number Count Player A (Flat Bet) Player A: Expected Payout Player B (Swing Betting) Player B Expected Payout
Hand Number Count Player A (Flat Bet) Player A: Expected Payout Player B (Swing Betting) Player B Expected Payout
1 0 \$20.00 \$9.90 \$20.00 \$9.90
2 1 \$20.00 \$10.00 \$20.00 \$10.00
3 3 \$20.00 \$10.20 \$60.00 \$30.60
4 1 \$20.00 \$10.00 \$20.00 \$10.00
5 -4 \$20.00 \$9.50 \$10.00 \$4.75
6 -1 \$20.00 \$9.80 \$10.00 \$4.90
7 0 \$20.00 \$9.90 \$20.00 \$9.90
8 1 \$20.00 \$10.00 \$20.00 \$10.00
9 3 \$20.00 \$10.20 \$60.00 \$30.60
10 6 \$20.00 \$10.50 \$80.00 \$42.00
Total Expected N/A N/A \$100.00 N/A \$162.65

These are, of courses, hypothetical outcomes based solely on a very player friendly sitting. The outcomes are based on nothing more than the expectations of the outcomes, and not the real life outcomes. If these two players played a hundred or a thousand times rather than ten, it would certainly be expected that Player B would be far more likely to finish with more money than Player A, but it’s not guaranteed. There’s absolutely a possibility that luck could shine on Player A in terms of how the cards come out of the shoe, and that Player A walks away with more money. That’s randomness, and it happens all the time. However, the more the two players play the higher the expectation would be that Player B would wind up with more money when the two leave.

The question, obviously, then becomes what on earth does this have to do with the Seattle Seahawks, the NFL or anything even remotely related to football outside of the fact that the Raiders moved to Vegas?

That answer to that question is simple: Player B counting cards doesn’t guarantee he’ll wind up with more money. It doesn’t guarantee he won’t lose all the money he sat down at the table with. However, what he is doing is using the information available to him regarding the situation in order to best position himself for victory in an attempt to maximize his chances of success.

And in a word, that’s called Analytics.