Jackpot EV question

I work at a casino that offers the following jackpot for blackjack (6 deck shoe, double after split, split to 4 hands)

Player gets 8, 8, 8 and Dealer gets 7, 7, 7 then $100,000 jackpot

So my question is this...Say you are dealt 8, 8 and the dealer has 7 as their up card...What is the EV of hitting the 16 hoping for the jackpot as opposed to the EV of splitting the 16 following basic strategy.

If the original bet size matters then use a minimum $5 bet or whatever works best for the hypothetical situation (min $5, max $600)

Quick back of the envelope calc using infinite deck probabilities found on woo site says to split and not go for jackpot.

Odds of getting your third 8H and the dealer getting the two 7S required = 4/309 * 5/308 * 4/307 = 1 in 365,222.55

So value of jackpot is $100,000/365,222.55 = 0.27$

EV for splitting 8s: 0.3254*$5
EV for hitting 8s: -0.4148*$5
Giving a cost of : $3.70 on a $5 bet.

Not worth it to go for jackpot!

I sure don't follow the math but I would agree with the result since I would tend to expect all such jackpots offered to be virtually illusory. Oh, I'm sure they eventually hit and some lucky slob get the jackpot and the WG2 form. Its just that all along the house has been getting those unlucky slobs to violate the "Always split 8s" rule by making an illusory promise.

Quote: AndrewPao32

I work at a casino that offers the following jackpot for blackjack (6 deck shoe, double after split, split to 4 hands)

Player gets 8, 8, 8 and Dealer gets 7, 7, 7 then $100,000 jackpot

So my question is this...Say you are dealt 8, 8 and the dealer has 7 as their up card...What is the EV of hitting the 16 hoping for the jackpot as opposed to the EV of splitting the 16 following basic strategy.

If the original bet size matters then use a minimum $5 bet or whatever works best for the hypothetical situation (min $5, max $600)

The odds of getting the third 8 of hearts is the number of 8 of hearts left in the shoe divided by the number of cards left in the shoe. On average if you are not counting it will be 1/52.

If the dealer has a 7 of spades left, the odds of him pulling two seven of spades is the number of 7 of spades left in the shoe divided by the cards left in the shoe, multiplied by 1 less than the number of 7 of spacdes left in the shoe divided by the cards left in the shoe less one.

Formulaic-ally, then, it is H*S(S-1) / n (n-1) (n-2). Where H is the number of 8 of hearts left in the show, S is the number of seven of spades left in the show, and n is the number of cards left in the shoe.

So, for example you're about one deck in the shoe and you see the combination occurring.

The expected value is 4 x 5 x 4 / (260 x 259 x 258) = .00000460466 for an expected value of $.46

If you get two 8s against a 7, the expected value of splitting is $1.55 on a $5 bet if you can double after a split (dealer hits soft 17) while the value of hitting is -$2.40 on a $5 bet. Add in the $.46 EV for the situation above to get the EV of hitting two 8s to be -$1.94. So, on every $5 bet, the decision to hit for a 217,180:1 shot at $100,000 instead of splitting would be $3.49.

That said, most people will still take a shot at the $100,000 grand as the odds of you getting into the situation where you can even take the shot at the opportunity is about 100,000:1.

Quote: AndrewPao32

I work at a casino that offers the following jackpot for blackjack (6 deck shoe, double after split, split to 4 hands)

Player gets 8, 8, 8 and Dealer gets 7, 7, 7 then $100,000 jackpot

So my question is this...Say you are dealt 8, 8 and the dealer has 7 as their up card...What is the EV of hitting the 16 hoping for the jackpot as opposed to the EV of splitting the 16 following basic strategy.

If the original bet size matters then use a minimum $5 bet or whatever works best for the hypothetical situation (min $5, max $600)

Andrew, this is a lame jackpot, IMHO. The idea is that players can hope for the big payout, but you almost certainly will never pay it. In fact, the probability of winning it is:

(6/312)*(5/311)*(4/310)*(6/309)*(5/308)*(4/307) = 0.000000000016385

Or roughly, 1-in-61,032,583,812, that's 1-in-61 BILLION!

Given that it pays $100,000, it adds $0.00016385 to the value of each hand for the player.

Why not pay for any triple-8 against any triple-7? This has probability of winning: 0.000000167802825, or 1-in-5959375, making it at least *possible*. Pay the player $100,000 for this, and it adds $0.168 cents (about 1/6 of a penny) in return to the value of each hand for the player. That is real value.

Players will know that your casino's promotion is bogus and it will not do anything to increase blackjack play. They must create a promotion that actually has a chance in hell of hitting if they want it to drive player response and increase incremental blackjack revenue. If you have any connection with management, I would make sure they know this.

--Dorothy

Dorothy,

Your math is a tiny bit off. Roughly, at the start of the shoe, assuming one player, the odds of you hitting 3 eights against 3 sevens is about 5,732,011:1. At $100,000 payoff, it adds $.01745 to your expected value or about 0.348% on a $5 table. This is actually quite significant as it lowers the HA from about .66% (for hitting a soft 17) to .31%.

Will the jackpot bring in more players? Absolutely. The enticement of getting $100,000 without the player really thinking about the odds will get more people playing. If it were me, I would offer the same promotion with a $1,000,000 payoff. That would get alot more people playing.

Quote: boymimbo

Dorothy,
Your math is a tiny bit off. Roughly, at the start of the shoe, assuming one player, the odds of you hitting 3 eights against 3 sevens is about 5,732,011:1.

p = (24/312)*(23/311)*(22/310)*(24/309)*(23/308)*(22/307) = 0.0000001678.

This is 1-in-5959375.

Quote:

At $100,000 payoff, it adds $.01745 to your expected value or about 0.348% on a $5 table. This is actually quite significant as it lowers the HA from about .66% (for hitting a soft 17) to .31%.

I don't think people are playing perfect basic strategy. I don't think that at a $5 table, people are all playing the table min just to maximize their return against this promo. Saying this is "quite significant" is overstating the case by an order of magnitude, IMHO. Given the typical 1.25% house edge against an average player, and an average bet of $15, this reduces the income per player per hand from 18.75 cents to 17.07 cents (wait, is that right?). Yes, that's a hit, but that's what a promo is all about.

Quote:

Will the jackpot bring in more players? Absolutely.

Odds of over 50 billion to 1 are transparently awful.

Quote:

I would offer the same promotion with a $1,000,000 payoff. That would get alot more people playing.

Agree. And have an insurance company underwrite it for 14 cents.

--Dorothy

I remember from one of those Travel Channel shows, casinos never offer a bet unless there was a profit in it for them. The more the profit, the smaller the minimum bet. Take a look at the craps table. All those stupid bets in the middle with little space for the chips. And those bets can be much less than the table minimum. What does that tell you?



Your $100,000 bonus? With NO required side bet? Do you really think that the casino set that up just to give away money?

Hell no! The 'cost' is sacrificing your great advantage of splitting eights!

Quote: DorothyGale

The idea is that players can hope for the big payout, but you almost certainly will never pay it. In fact, the probability of winning it is:

(6/312)*(5/311)*(4/310)*(6/309)*(5/308)*(4/307) = 0.000000000016385

Dorothy - your math is based upon a mistaken assumption. You've calculated the odds of this occuring. We don't care about that.

The decision to 'go for it' only comes up if you have two 8H and the dealer shows 7S. At that point, CardShark got the math right:

Quote: cardshark

Odds of getting your third 8H and the dealer getting the two 7S required = 4/309 * 5/308 * 4/307 = 1 in 365,222.55

So value of jackpot is $100,000/365,222.55 = 0.37$

Unfortunately, CardShart got that last calculation incorrect. 100,000 / 365,222 = .27 (maybe that was a typo).

Quote: FleaStiff

I sure don't follow the math but....

FYI: Both of the above calculations are based upon a fresh shoe. In short, the odds of getting one of the 4 remaining 8H out of 309 remaining cards, and the dealer getting one of the five remaining 7S out of the 308 remaining cards, plus one of the four remaining 7S out of the 307 remaining cards, is 1 in 365,222.


But lets have a little fun with this.

Let's say the shoe is very near the 2/3 penetration where they reshuffle, AND you were paying attention and you haven't seen ANY 8H or 7S played. Yep, we're at the height of our chances, when you get dealt two 8H and see a dealers 7S. There's 101 cards left. The chances of hitting are:

4/101 * 5/100 * 4/99 = 1 in 12,498.75

That makes the value:

100,000 / 12,498.75 = $8.00!

At that point, if you're betting $5, then, I guess it does get mathematically worth it. But remember, that's when you haven't seen ANY of the required cards, AND are at the end of the shoe!

Quote:

Dorothy - your math is based upon a mistaken assumption. You've calculated the odds of this occuring. We don't care about that.

I care about it. I assume I are "we" too. My point is that the promo is dumb. My math is right on to make that point. I think the OP needs to reconsider the whole idea from scratch and come up with something that achieves the goals of offering the promo to begin with.

--Dorothy

Andrew-

Since you work there, can you say how close anyone has come to the jackpot? I'm guessing no one has ever won, but did anyone hit and at least get the 3 Eight of Hearts against the 7? Did they have to stop the hand and wait for a boss to come and watch the rest of the deal?

Quote: DorothyGale

Or roughly, 1-in-61,032,583,812, that's 1-in-61 BILLION!

Is that 61 thousand million, or 61,000,000,000 x 60,999,999,999 x 60,999,999,998.... x 2 x 1? ;)

Pardon me while I take cover.

I think that the promotion is just "fun".

It's difficult to calculate the odds because if you do hit this situation, it will be mid shoe with a number of players and the odds will be based on the exact # of cards available to win.

Still, if you are the 1:100,000 of getting the situation, there is no way that I would ignore the possibility of winning double my bet by splitting vs the possibility of winning $100,000. Certainly the EV of splitting is way better than hitting for the third 8 of hearts, but $100,000 is $100,000!!!!

Quote: Nareed

Quote: DorothyGale

Or roughly, 1-in-61,032,583,812, that's 1-in-61 BILLION!

Is that 61 thousand million, or 61,000,000,000 x 60,999,999,999 x 60,999,999,998.... x 2 x 1? ;)

Pardon me while I take cover.

As Freud said, sometimes an exclamation is just an exclamation.

--Dorothy

Quote: DorothyGale

Quote: DJTeddyBearr

Dorothy - your math is based upon a mistaken assumption. You've calculated the odds of this occuring. We don't care about that.

I care about it. I assume I are "we" too. My point is that the promo is dumb. My math is right on to make that point. I think the OP needs to reconsider the whole idea from scratch and come up with something that achieves the goals of offering the promo to begin with.

You misunderstood my point. FYI: There was no insult intended. Sorry if you took it that way.

The point of this thread, and the original question, was the EV of this jackpot. Since there is no extra bet required, and the decision to 'go for it' doesn't even exist until you have two 8H and the dealer shows 7S, the EV needs to be calculated at that point.

Your calculation is for the TOTAL odds of getting it. My calculation is for the odds of getting it once you have a qualifying starting hand.

And, as I mentioned, your odds were based upon a new shoe. I at least took it a step further by showing the marginal odds using a very heavily stacked shoe.

Quote: boymimbo

Still, if you are the 1:100,000 of getting the situation, there is no way that I would ignore the possibility of winning double my bet by splitting vs the possibility of winning $100,000. Certainly the EV of splitting is way better than hitting for the third 8 of hearts, but $100,000 is $100,000!!!!

Ding, ding, ding! We have the typical gambler who is willing to buck the odds and house edge on a once is a lifetime shot.

Quote: DJTeddyBearr

You misunderstood my point. FYI: There was no insult intended. Sorry if you took it that way.

NP.

Quote: DJTeddyBearr

Ding, ding, ding! We have the typical gambler who is willing to buck the odds and house edge on a once is a lifetime shot.

This isn't true. If it were true then every game with a high payout would succeed. There is a real market out there, some things work and others don't. I don't think this particular promo is well designed to help the casino meet its marketing objectives. The casino that is hosting this promo is in good need of a highly talented (and good looking) specialist to help them. Wizard?

In trying to do it on their own, they've created a bozo of a promo.

--Dorothy

Quote: DJTeddyBear

Unfortunately, CardShart got that last calculation incorrect. 100,000 / 365,222 = .27 (maybe that was a typo).

Oops, yeah that was a typo, I changed my post to 0.27$. Thanks for letting me know!

I will admit that casinos are intended to be festive places, that patrons are often consuming alcohol which is generally provided to them free of charge and in liberal quantities by lovely young ladies. In such circumstances decisions will often be made that favor a massive payoff even though the odds of it taking place are quite low. A high but unlikely payout bears a certain lure which is why states find lotteries to be so profitable.

Therefore I would assume that a precise calculation of the odds for this jackpot is of great academic interest but subtle factors of sobriety, card counting skills, fatigue and shoe position would play a role that might defeat the precise calculations of the various posters.

The "center bets" at craps do often pay off. One stickgirl even called out "get your sucker bets" and still got action on them. I think its probably the same way with this blackjack jackpot. Even those who are armed with the various posters mathematical results may well opt to "go for broke" in the spirit of slightly-inebriated fun. I hope that if I am ever in the situation, I split the 8s without hesitation. If that situation does occur, I sure hope I do it without any later regrets!!

Quote: DorothyGale

Players will know that your casino's promotion is bogus and it will not do anything to increase blackjack play. They must create a promotion that actually has a chance in hell of hitting if they want it to drive player response and increase incremental blackjack revenue. If you have any connection with management, I would make sure they know this.

--Dorothy

Actually you're right it is bogus and it is meant to be so. Its is a casino where the house doesn't bank their own games. I actually work for the 3rd party that comes in to bank the games. To prevent bank chasers from coming in and stealing our action they require you to be able to cover the table and then have this jackpot that no one will want waste capital on covering in order to chase the bank. I should add that there is a $25k jackpot for any 3 suited 8s vs any 3 suited 7s. So there's 7 seats at the table...the max payout would be 2 people getting the $100,000 and 5 people getting the $25,000 for a total of $325,000 in order to cover the maximum payout on the table. Make sense?

Its one of those casinos where the house gets their money on pay per hand.

Anyway no one has hit the jackpot and not many people pay attention to the fact that it exists. Its more of a formality I suppose. I was just curious about the odds.