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Thinking About the Game, What are the Odds?

You can win more when you correctly measure the chances for success

by Basil Nestor

I am reading my e-mail inbox. A company called British Web Lottery tells me I have won £2,543,170, the equivalent of $5,062,688. BWL wants me to contact someone in the UK to collect the prize. Funny, I don’t remember entering this particular lottery. I didn’t buy a ticket or give them an e-mail address. So why would someone want to give me $5,062,688? Am I just super-lucky, or is something else happening here?

Clearly, the e-mail is a scam. But before I hit the big delete button, let’s consider the strategic process that brought me to this conclusion. The same strategy can help you win more when playing legitimate gambling games such as video poker and blackjack. We’ll begin with lotteries.

Probable, Possible, and Impossible
It is sad to say, but some people believe these fake lottery notices. Naïve suckers pay money to the scammers to cover the cost of processing the supposed lottery claims, but the “lucky winners” never receive their prizes. There is always one more fee to pay and one more check to write until the sucker gets wise to the con or goes broke.

Note that the word “con” is synonymous with “swindle” in modern times, but it was originally slang for confidence. In other words, a lottery con requires the confidence of the victim; he has to believe that the impossible is possible. The odds say one thing, but the player concludes something else.

All gambling strategy is based on correctly knowing the odds, and all fatal blunders in gambling (and in life) usually involve not knowing the odds, or willfully ignoring them.

For example, what are the odds of winning a typical state lottery? In California, the Super Lotto odds are about one in 41 million. It’s an extremely slim shot, yet not impossible. But now consider the chances of winning the contest if you don’t buy a ticket. The odds are zero (with a few mega-millionths of a fraction added for the possibility that someone might buy you a ticket without your knowledge). In comparison, the earth has a much better chance of being hit by a giant asteroid in 2036; it’s 1 in 45,000.

So people who respond to scam e-mails are effectively cheating themselves because they incorrectly calculate the near-zero probability of winning a lottery without making a purchase. Duh! A similar situation often occurs in casinos, even though the games in regulated jurisdictions are squeaky-clean honest. Some players make needlessly bad wagers that create or aggravate a negative edge. They bet when the odds are extremely unfavorable, or they don’t bet when the odds are favorable.

Good Bets vs. Bad Bets
Let’s look at a few simple bets in blackjack. The first one is insurance. This bet is available when the dealer is showing an ace. If the dealer’s hidden card is a ten (giving him a natural 21), then the player wins 2:1.

Insurance is a very bad bet, unless you are counting cards. In a deck of fifty-two cards, only sixteen of them have a value of ten. That is 31% of the deck. So 31 times out of 100 you will win two bets, and 69 times out of 100 you will lose one bet. The net result is a deficit of seven bets. That’s a baaaaaad deal.

On the other hand, a double down in blackjack as per basic strategy is a very good deal. Every double down has a greater than 50% chance of winning. Or to put it another way, you always earn more on average than you risk when you double down as per basic strategy.

But some people don’t use basic strategy. Why? That’s a good question. Usually it involves a lack of knowledge or a superstition. Regardless of the reasons, the results are always the same. Players who ignore the odds and deviate from optimal strategies lose more over the long run compared to players who follow optimal strategies.

Poker Sneaks and Superstitions
A similar situation occurs in poker. We’ll use hold ‘em as an example. High pocket pairs such as ace-ace and king-king are consistent winners. Ditto for hands such as ace-king and ace-queen. Generally, these hands deserve a raise in the first round of betting before the flop. Yet people often do not raise with these combinations. Sometimes the player is trying to be sneaky, and sometimes he has a superstition about “always losing” with a particular hand.

Ironically, the lack of a raise encourages opponents to stay in the pot. This increases the probability that the good hand will be beaten. If the hand does win, the lack of a raise makes the pot smaller, and this often contributes to a net loss in the session.

So once again, ignoring the odds is an expensive indulgence.

Some Important Numbers
Another big advantage of knowing the odds is the peace of mind that comes when you know what to expect. It is easier to play through a dry spell when you know what the average should be. Likewise, knowing the odds gives you a sobering perspective during a hot streak so you won’t assume the game is always so generous.

Here are some odds for various casino games:

Event Odds (rounded) Average frequency
A pair or better in Caribbean Stud Poker 1 in 2 20 per hour
Two pairs or better in JOB video poker (after the draw) 1 in 4 100 per hour
Natural 20 in blackjack 1 in 11 5 per hour
Natural 21 in blackjack 1 in 21 3 per hour
Pocket pair in hold ‘em 1 in 17 2 per hour
AK in hold ‘em 1 in 83 1 every 2 hours
Pocket aces in hold ‘em 1 in 221 1 every 5.5 hours
Nine consecutive losses in blackjack 1 in 329 1 every 5.5 hours
Nine consecutive wins in blackjack 1 in 814 1 every 14 hours
Four of a kind in JOB video poker (after the draw) 1 in 423 1 per hour (when playing single hands)
Royal flush in JOB video poker (after the draw) 1 in 40,388 1 in 100 hours (when playing single hands)
Natural royal flush in Caribbean Stud Poker 1 in 649,740 1 in 11,000 hours (1,375 eight-hour days)
Megabucks jackpot 1 in 50 million 1 in 50 million 1 in 83,333 hours (10,417 eight-hour days)

Keep in mind that frequency calculations are based on the speed of each game, and some games (such as video poker) move quickly.

Also you’ll notice that some events may seem unlikely, but with enough trials, they inevitably happen. This is why it is more probable that you will see a royal flush than see the earth hit by an asteroid; the card game has more trials. Nevertheless, some events are so unlikely you shouldn’t expect to see them in a typical session. And one way or another, all gambling games require a bet. There is zero chance that you will win a prize without entering a contest.

The corollary to this is simple. If someone offers me a multi-million-dollar prize and I have not made a bet (or otherwise delivered a legitimate entry), then the odds are 100% that the offer is coming from a criminal. The odds have spoken. And so I will delete the e-mail.

Enjoy the game!

Basil Nestor is author of The Smarter Bet Guide to Blackjack, The Unofficial Guide to Casino Gambling, and other comprehensive gambling guides. Got a question? Visit and drop him a line.

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