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Reason I like Bovada #3:

One-stop shopping

Let me share my experience at another online casino whose name I won't mention:  I wanted to try out their free-play games, and they made me sign up for an account.  That was annoying, just for free-play, but actually most casinos make you register, so they can annoy you by email to pressure you into depositing real money.

I didn't get to choose my own username, they assigned one, and it was long! An astounding twelve digits of mixed numbers and letters.  There was no way I'd be able to memorize it, I'd have to write it down.

After trying out the free-play games I decided to deposit money and play for real.  And guess what? I had to register a separate account to play for real.  They assigned me a brand-new twelve-digit username.  Great.

Shortly thereafter they started offering play-in-browser games.  That's convenient, so I wanted to get in on that.  Guess what?  Yet another username.

And guess how they handle they money they give you as a matching bonus on your deposit?  You guessed it, another account.

Okay, now let's fast-forward to Bovada: One account gets you everything.  And I mean everything.  Real money, fake money, bonuses, you name it.  I didn't get to choose my account name, but at least it's easy to remember.

And if you want to play for free with fake money, you don't even need an account at all.  For example:

Play for free, no B.S.
One click and you're in.

All in all, I think Bovada is the best bet for U.S. players.


Gambling problem?
  1. Call the 800-522-4700 hotline or get online help
  2. See these horror stories.
  3. Know that Parkinson's drugs encourage gambling.
Play these
free slots now

Gambling problem?
  1. Call the 800-522-4700 hotline or get online help
  2. See these horror stories.
  3. Know that Parkinson's drugs encourage gambling.

"Expected Value" is useless when applied to the lottery

Here's a lesson about how sometimes you have to put the math into perspective.

As they say, a little knowledge is a dangerous thing.

Some people learn about the house edge and expected value, which are important for understanding casino games.  They then try to apply those concepts to figuring out when it's a "good" time to play the lottery, where those concepts are all but useless.

First, let's have a refresher on those concepts. 

  1. The house edge is the casino's average profit per bet, in percentage terms.  For example, the house edge in roulette is 5.26%.
  2. Expected loss is the average loss of your bets.  If you bet $100 on roulette, then $100 x the 5.26% house edge is $5.26.  That's how much you'd lose on average on each $100 bet if you made $100 bets forever.  Of course, on a single bet, you're either gonna lose your whole $100, or win some more.  "Expected loss" is poorly named, since it's not the amount you actually expect to lose.  A better term is "average loss", which is what I use sometimes.
  3. Expected value is the flip side of expected loss.  It's how much you wind up with after your bets, on average.  If you bet $100 on roulette, and lose an average of $5.26, then what you wind up with is $94.77.  That's your expected value (aka, average value).

Let's see a practical example.  Here's how we calculate expected value for roulette:

  Expected Value of $100 Roulette Bet 
Outcome Result Odds Expected Value
Win $200* 0.4737 $94.74
Lose 0 - -



$94.74

*$200, not $100, because when we win we get our original bet back.

And here it is for the Texas Lottery's "Lotto Texas":

Expected Value of $1 Lotto Texas Ticket
Prize Odds Expected Value
$10,452,254 0.00000004 $0.418
$2,000 0.00001115 $0.022
$50 0.00065512 $0.033
$3 0.01339365 $0.040
$0 0.98594004 $0.000


$0.51

Source: Wizard of Odds

So let's see how our aspiring analyst "Bob" goes wrong about this.  The $10,452,254 listed in the table is the average winning jackpot.  Bob reasons that if the jackpot were to go above a certain amount, then Lotto Texas would become a positive-expectation game.  That is, for a $1 bet, the expected value would be more than a dollar.  That much is true.  And here's how that would work.


  Expected Value of Lotto TX w/big jackpot 
Prize Odds Expected Value
$22,900,000 0.00000004 $0.916
$2,000 0.00001115 $0.022
$50 0.00065512 $0.033
$3 0.01339365 $0.040
$0 0.98594004 $0.000


$1.01

So, Bob calculates that when the Lotto Texas jackpot grows to $22,900,000, Lotto Texas becomes a positive expectation game and it's worth playing!  Right?  Wrong!  For so many reasons.

The reason that expected value works for casino games is that it doesn't take long for your actual losses to approach the expected losses.  You'll probably be within 5 percentage points of the house edge after just 100 rounds on a table game.  By contrast, with the lottery you likely won't be anywhere near the house edge even after a million plays.

Let's use my House Edge Simulator to see how expected value is useful for a casino game.  It plays roulette a bunch of times and you can see the results.

House Edge Simulator
Bet $5 on red...
Total Amount Bet
Amount Won
or Lost
Percentage Loss
1 time
$5
10 times
$50
100 times
$500
1000 times
$5000
100,000 times
$500,000
1,000,000 times
$5,000,000

What you saw is that you're gonna be a long-term loser, and anything can happen in the short term, but even after just 100 rounds your actual losses were likely in the ballpark of expected losses.  The house edge and expected value are useful here because this is a game where you'll likely play a bunch of rounds, and the chances of winning any individual round is almost 50-50.  Wins are frequent in this game.

And now let's see it for the Lotto Texas:

Lotto Texas Simulator
Buy $1 ticket...
Total Amount Bet
Simulated Result
w/$10M jackpot
Simulated Result
w/$22,9M jackpot
1 time
$1


10 times
$10


100 times
$100


1000 times
$1000


100,000 times
$100,000


1,000,000 times
$1,000,000



What you saw is that even with a million freaking lottery tickets, your results were pretty much the same for both the smaller and larger jackpots.  The jackpot size doesn't matter.

The thing is, the odds of hitting the top jackpot in Lotto Texas are incredibly long:  a whopping 1 in 25 million.  Even if you bought a million tickets you're very unlikely to hit the top prize.  That being the case, the size of the jackpot means exactly squat.

And remember, the odds are 1 in 25M no matter how high the jackpot grows.  A "positive" jackpot is exactly as hard to hit as a negative one.

When you buy a ticket, one of two things is gonna happen:  you're either gonna win or you're not.  If you win, then all that matters is that you're suddenly multiple millions of dollars richer.  If the game had been negative-expectation when you played, so freaking what?  Your actual return was way better than your expected return, which is all that will matter to you.

If you lose, then again, the size of the jackpot was completely irrelevant.

The only thing that really matters when buying a lottery ticket is this:  Is the chance of winning $X jackpot worth a dollar to you, if the odds are Y to 1 against your winning?  If yes, then buy one.  If not, then don't.  But don't even consider the expected value, because it has no usefulness when applied to the lottery.

Looking at expected value has a lot of benefit in casino games where your actual loss will likely approach the expected loss fairly quickly, but it shouldn't become a religion that's applied uselessly to long-odd games like the lottery.

There's another reason Bob erred when he thought he should buy lottery tickets when the jackpot reaches a certain amount:  When the jackpot grows, more people buy lottery tickets.  Not because those buyers are calculating the expected value (most people have no idea what that is), but because they're more excited about winning a bigger pile of money.  The more people play, the more likely it will be that more than one person picks the winning numbers, so the prize will be split among all the winners.  If two people win a $20 million jackpot, they each get $10 million—the same as if one person won a $10 million jackpot.  Therefore, you can't assume that the expected value goes up in relation to the amount that the jackpot goes up, because if you do win, you're less likely to have won the whole thing yourself.

Don't mistake all this to mean that the lottery is a good deal.   It's not.  The odds are bad no matter how you cut it.  The point is just this: when the jackpot gets big, you aren't any more likely to win.  And for that reason there's no point in waiting for a bigger jackpot.  If you want to play the lottery, play it whenever you like, it won't affect your odds.  Those odds will be terrible no matter when you play.

If you do want to get the best odds when going for a big jackpot (and why wouldn't you?), then you can get a better return on a progressive slot machine or at a table game using my jackpot betting system.


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