Five Card Frenzy promotional mailer - what are the odds?

Promotion is for each Thursday in January.

The mailer I received shows 2 five card poker hands that I believe are unique to my mailer.

Each Thursday a promotional dealer at the casino will reveal the five card poker hand for that promotional day.

I am to take my mailer to the casino...2 cards match win $50, 3 cards match win $500, 4 cards match win $10,000, 5 cards match win $150,000

Since I have two hands I assume I could actually win twice.

Is this a good promotion to participate in? I have a 2 hour drive to and like to plan trips around the better promotions.

Can a moderator please correct my spelling in the thread title? thanks!

1.) Please determine whether you are actually going to receive two hands, or whether you will only receive one hand, but can WIN by matching either hand from your mailer.

2.) If you are only going to receive one hand that can match either hand from your mailer, do you have any repeating cards?

Once you have answered these questions, you can actually use the following Keno calculator at the bottom of this page:

http://betstarter.com/lottery/KenoOdds.asp

Inputting n = 5 (You pick five numbers, they're cards, but they're actually numbers), N = 52 (There are 52 total cards), and D = 5 (They are drawing five numbers)...after you receive the probabilities, you shall multiply them by the pays.

For example, one hand to match one hand on your card is:

(1/16 * 50) + (1/240.4 * 500) + (1/11059.4 * 10000) + (1/2598960 * 150000) = 6.1667904672614721

If it were only one chance at one hand, the expected value will be $6.17, it will be just less than double that if you have one chance to match one of two hands if there are no repeating cards. The reason it is just under double is because, for every card you match on one hand, you cannot possibly match that card on the other hand. (i.e. matching one on one makes matching five on the other impossible)

But, it's not relevant because even $12.34 isn't worth the drive, absent any other offers, Free Play or an advantage play. Anyone you could car pool with?

I would think that the casino knows how many of each combinantion they mailed out will be a winning combination. Nothing random about the cards at all, there are pre-determined five card poker hands and the casino exposure is known. In fact, I would doubt that all the mailers are unique. Many will have a the same losing combination with a few having the correct combinations.

So the only want to calculate the EV is to know the number of mailers that were sent out and how many of each prize they will award at each level.

It's low anyway, even if you assume randomness. It does sound like there will be a dealer actually dealing a physical five-card hand, though.

The mailer says "Match the five-card poker hands below with the dealer's hand any Thursday and receive a cash prize for 2-5 cards matched". Yes a dealer dealing a real deck of cards is how it sounds to me as well.

OK, maybe I'm wrong. When you wrote "reveal" it didn't sound to me like they were actually going to deal a hand. If you go, can you update the thread about how the winning hand is generated?

Understood. The mailer is not clear, "reveal" was the word used in the mailer along with "promotional dealer". Right now I am not planning to go.

This sounds like one of those deals where a car dealership mails out [bogus]keys to a particular car and you have to show up to give your key a try, if the car starts it's yours. Yeah right.

Quote: Alan

This sounds like one of those deals where a car dealership mails out [bogus]keys to a particular car and you have to show up to give your key a try, if the car starts it's yours. Yeah right.

This is exactly what I was thinking of while reading this, along with scratch-offs; there are a pre-determined number of winners at each level in both. They WANT you to think it's random, but they know their exposure, and they're almost sure not to pay all prizes, because they're not going to get 100% of the people who received them in there. Hard to believe variance would be allowed to have its way, since it's a very small (5 draws on 5 Thursdays) sample.

Quote: beachbumbabs

This is exactly what I was thinking of while reading this, along with scratch-offs; there are a pre-determined number of winners at each level in both. They WANT you to think it's random, but they know their exposure, and they're almost sure not to pay all prizes, because they're not going to get 100% of the people who received them in there. Hard to believe variance would be allowed to have its way, since it's a very small (5 draws on 5 Thursdays) sample.

It's possible it's not random, but it's a damn casino though. If they can't afford a $150k payout or two, then they are running their business wrong. No way they have to pay out all 5. Hell, most likely they won't have to pay any 5 out of 5 winners. It really ticks me off when casinos are too scared to gamble.

Either way, random or not, it's not worth that much.

This is a pretty cool little thing to keep in mind, though, because I have both personally seen and heard of many promotions that take on a form very similar to this, the Keno Calculator can often be a very useful tool. Many things ARE just Keno, but expressed differently, most lotteries are just Keno.

When I get pull tabs I can't see through with a flashlight, I just tear them open and say to myself, "guess I'm not going. Darn didn't win $10000!" I don't know how they can say you could win when they already know you can't and didn't. Just hate how they never reveal odds, actual winners, nothing. Bob Dancer had the story once where million dollar winners were mailed to people who hadn't been to the casino in 5 years or something along those lines. Just complete trash normally. I've talked to the people running the end phase of these things and didn't get the impression anyone came through getting the ten thousand after the whole day.

Quote: beachbumbabs

This is exactly what I was thinking of while reading this, along with scratch-offs; there are a pre-determined number of winners at each level in both. They WANT you to think it's random, but they know their exposure, and they're almost sure not to pay all prizes, because they're not going to get 100% of the people who received them in there. Hard to believe variance would be allowed to have its way, since it's a very small (5 draws on 5 Thursdays) sample.

Actually, I'm going to do some work on this, but it will have to wait until later...

Quote: beachbumbabs

This is exactly what I was thinking of while reading this, along with scratch-offs; there are a pre-determined number of winners at each level in both. They WANT you to think it's random, but they know their exposure, and they're almost sure not to pay all prizes, because they're not going to get 100% of the people who received them in there. Hard to believe variance would be allowed to have its way, since it's a very small (5 draws on 5 Thursdays) sample.

Excellent, I have a few minutes now to do this.

1.) I think that it is random, from the player standpoint, but only semi-random, from the casino's standpoint. If the House really wanted to play it safe with advertising, then the result would have to be possible in order to put that in the mailer. Now, if you have a pre-determined outcome, that means one mailer has got it, but you don't want to actually do that in case they come in, much better off with a random outcome.

2.) They do know their exposure, and they are almost sure not to pay all prizes, but even if they had to, no big deal.

This Is What I Am Thinking

Let's think about that 2598960, what is it?

That number is a Royal Flush, but not just a Royal Flush, but a Royal Flush on the deal...in a specific suit.

The easiest way to assure that there is only one potential winner, but to keep it random to the player, is simply to have a computer select random five-card poker hands, throwing away any repeats, and putting those on the mailer. Again, provided the draw when one arrives is truly random, then the cards are truly random to the player, but only semi-random for the casino, because the casino can only pay the big one out once.

Now, the 2598960, but two hands per mailer, give the opportunity to send out 1,299,480 mailers, and only have one potential big winner, but there probably aren't even that many mailers.

Let's break this down a little further:

We don't want to think of cards, we want to think of Keno.

Cards will be Known as Numbers from this Point Forward

The first thing that I want to do, as the casino, is limit my exposure. The way I am going to do that is that I am going to make sure that no two cards are exactly alike, therefore, I could only have to pay out the 150,000 once per drawing.

I'm going to go back to cards, for just a second, and we're going to look at Texas Hold 'Em where every player starts with two hole cards, except, we're going to use, "Hole numbers."

There are 1,326 unique pairs of two numbers if you want to guarantee that every player starts out with two unique numbers. This would enable me to send mailers to my 663 best customers because there are two sets of numbers per mailer while absolutely GUARANTEEING I pay out the 150K, at most, once per drawing.

What about community cards, er, numbers?

You simply remove certain numbers from the possible choices of numbers. For example, let's say that I have a ticket out there that has two fixed numbers: 1,2...okay for every other ticket that, "Starts with," a 1, the number 2 cannot happen. For every ticket that starts with a 2, the number one cannot happen.

So, if our Keno drawing goes:

1, 2, 17, 31, 45

There are only a few ticket combinations that can even possibly win the jackpot, specifically, these are tickets in which the, "First two," numbers match out of the five on the ticket. This will describe:

(5/52 * 4/51) = 0.00754147812 * 1326 = 9.99999998712 or 10 such tickets, inclusive to:

1,2
1,17
1,31
1,45
2,17
2,31
2,45
17,31
17,45
31,45

Okay, so there are only two tickets that are even allowed to have these numbers to start with and any chance of matching the rest, and the beauty of all of this is that:

We are STILL playing Keno!

Okay, in order for any of these tickets to pay more than $50, what must happen is they have to match 1:3, 2:3, or 3:3 other numbers out of 50.

((1 - 1/6 - 1/139 - 1/19600) * 50) + (1/6 * 500) + (1/139 * 10000) + (1/19600 * 150000) = 204.233244017 which is the EV of each from the casino's standpoint which results in a total EV of:

204.233244017 * 10 = 2042.33244017

For these tickets.

Now, there will be tickets in which one number matches and one does not, specifically:

((47/52 * 5/51) + (5/52 * 47/51)) * 1326 = 235 of them.

The thing to keep in mind with these tickets is that NONE of them can possibly match all five numbers, therefore, each ticket has a Max win of $10,000 and the goal is to Match either 1:3, 2:3 or 3:3 or 50 remaining numbers.

(1/6 * 50 * 235) + (1/139 * 235 * 500) + (1/19600 * 235 * 10000) = 2923.55503352

Which is the expected value of those tickets.

This leaves a total of 1326-245 = 1081 tickets (47/52 * 46/51 * 1326) = 1081 tickets in which neither of the two starting numbers match. The best these tickets can do is hit either 2:3 or 3:3 out of 50.

(1/139 * 50 * 1081) + (1/19600 * 500 * 1081) = 416.425451476

Which is the total EV of those tickets.

2042.33244017 + 2923.55503352 + 416.425451476 = 5382.31292517

In my scenario, is the casino's expected loss on each drawing, even though the Odds to the player would imply:

(1/16 * 50) + (1/240.4 * 500) + (1/11059.4 * 10000) + (1/2598960 * 150000) = 6.1667904672614721 * 1326 = 8177.16415959

A better combined Expected Value.

The reason that the Expected Value is not as the player would believe is because there are actually two different Expected Values. The Expected Value to the player remains the same because he has five numbers, and he will either hit or not hit 2-5 out of 5 randomly drawn numbers.

The Expected Loss for the casino is different because they have created a situation in which only ONE TICKET can even possibly win the grand prize, only ten tickets can possibly start off with two numbers correct and only 235 tickets will have one out of two numbers correct. The casino knows that 1081/1326 81.52% of all of the starting tickets will automatically have two numbers wrong.

It also works the other way, too, in terms of weighing the results low. If the combinations of numbers on the mailers themselves were random, but 1,326 mailers were still sent, it is mathematically possible for every single combination of numbers to whiff. 663 players, 0 winners.

That's no fun. With my system, while it is true that only ONE player can even possibly win the top prize in a single drawing, and only ten combinations will even have a chance, those same ten combinations automatically include the ten worth a combined minimum of $500. 1,326 combos, at least ten winners, probably more, of course.

Conclusion

There's much more work that can be done on something like this, but the conclusion is that the casino can create a promotion that appears to have an expected value to the player in excess of the expected loss to the casino. In addition to that, the casino can hold a drawing in which the drawing itself is random, but the events leading up to the drawing (i.e. the mailers) are not. It doesn't affect an individual player's odds of winning, but it affects the casino's exposure and how many wins it could even potentially have to pay out.

This is also just an example I came up with of one way that the casino could orchestrate something like this, the casino could, and probably did, use a different method for doing that.

If you'll recall the Cash Windfall lottery game that three or four teams (including an MIT team) exploited in Massachusetts, that is basically what the casino is doing with something like this, just in reverse. MIT could have fixed a specific win (if they were the only ones buying tickets) by covering every individual number. Similarly, if the casino were to send out 1299480 mailers covering 2598960 all possible number combinations for a draw of five out of fifty-two, then if everyone showed up each week, it would be a fixed loss of:

(1/16*50) + (1/240.4*500) + (1/11059.4 * 10000) + (1/2598960 * 150000) = 6.16679046726 * 2598960 = 16,027,241.7528 per week

Since it is very unlikely that the casino sent out nearly 1.3 million mailers, or has any plans of enduring over 80M in losses over this promotion, I would imagine that the computer generated numbers, while systematically kicking out results that would result in a duplicate ticket...or quite possibly...any TWO tickets in which even four numbers out of five could happen more than once...and basically has a Maximum Possible Loss.

And THEN you have the winners who don't actually show up, although, they want everyone to show up...or they wouldn't send them.

I missed a detail of the promotion...it also has a progressive prize pool. "PROGRESSIVE PRIZE POOL, if there are no winners for the four or five card match, the prize pool will be rolled to the following week. FINAL FRENZY The final week top prize for a five card match will be raised to $1,000,000 if there are no prior winners."

Also, FWIW....the two hands I received shown in the mailer, none of the hand two cards I received match any of the cards of hand one.

"Must have mailer in hand to participate. No copies will be accepted. Not responsible for lost or stolen mailers"