Poll

3 votes (16.66%)
2 votes (11.11%)
11 votes (61.11%)
2 votes (11.11%)
2 votes (11.11%)
4 votes (22.22%)
1 vote (5.55%)
1 vote (5.55%)
4 votes (22.22%)
2 votes (11.11%)

18 members have voted

Wizard
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August 2nd, 2016 at 4:56:57 PM permalink
You've probably heard of the Millionaire Maker side bet on a host of poker-based games at the Caesars casinos. Well, now they have it in blackjack too. At least at the Cromwell and O'Shae's. Here are the rules:

Wins are based on the dealer hand. Eight decks are used and the dealer hits a soft 17. The bust card, if there is one, counts. Dealer does not draw out if all players bust. $5 minimum bet.

Six-card straight flush: $1,000,000*
Full house: 100 to 1
Three of a kind: 15 to 1
Pair: 2 to 1

* Pays only $100,000 at the Cromwell (quite the misnomer).

This may the the hardest blackjack side bet I've ever analyzed -- but I'm up to the challenge! Meanwhile, if anybody else cares to tackle this, have at it!

It would be easy to say that it would favor a low count.

I'll get back to you with an analysis. The question for the poll is would you play this side bet blind?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
speedycrap
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August 2nd, 2016 at 6:33:44 PM permalink
Please explain how to play?
ThatDonGuy
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August 2nd, 2016 at 7:05:13 PM permalink
The problem with the analysis is, it depends on how many players there are, and what strategy they are using. The probability of all players busting (and, if any players split, all of the split hands busting), and thus the dealer being limited to two cards, needs to be taken into account.

Question: does, for example, a dealer hand of 7,7,6 count as a pair, or does it have to be exactly two cards?
Ibeatyouraces
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August 2nd, 2016 at 7:49:23 PM permalink
When we had blackjack at our charity poker room I dealt at, I dealt out A-6 of diamonds as my hand. This was from a 6 deck shoe as well.
DUHHIIIIIIIII HEARD THAT!
beachbumbabs
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August 2nd, 2016 at 8:24:17 PM permalink
Quote: Ibeatyouraces

When we had blackjack at our charity poker room I dealt at, I dealt out A-6 of diamonds as my hand. This was from a 6 deck shoe as well.



Yeah, and if you start with the 6-5-4, you're never going to see the 3-2-A. As to the pair, if it's within the hand, it should count, as their other MM bets work that way.

Funny they don't pay quads or 5oak, when they're paying trips. I guess a paytable is what somebody says it is.

I don't like the bet. Won't be playing it.
If the House lost every hand, they wouldn't deal the game.
Wizard
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August 2nd, 2016 at 10:15:09 PM permalink
Quote: ThatDonGuy

The problem with the analysis is, it depends on how many players there are, and what strategy they are using. The probability of all players busting (and, if any players split, all of the split hands busting), and thus the dealer being limited to two cards, needs to be taken into account.



My analysis will just assume at least one player didn't bust and I'll footnote that assumption.

Quote:

Question: does, for example, a dealer hand of 7,7,6 count as a pair, or does it have to be exactly two cards?



That counts as a pair. As long as there is a pair in there somewhere.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
tringlomane
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August 3rd, 2016 at 5:17:57 AM permalink
Is that really the full paytable? What about 5 card straights and flushes? What about four of a kind? 5 of a kind? 5-card straight flush?

Is a five card straight flush actually a losing hand???
ThatDonGuy
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August 3rd, 2016 at 7:54:16 AM permalink
A quick simulation of about 110 million hands, using the 1,000,000 payout for the suited A-6, shows a house edge of...

Turns out it was a little too quick - I subtracted 1 from each payout. See below for the corrected value.
Last edited by: ThatDonGuy on Aug 3, 2016
Wizard
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August 3rd, 2016 at 9:32:07 AM permalink
Quote: tringlomane

Is that really the full paytable? What about 5 card straights and flushes? What about four of a kind? 5 of a kind? 5-card straight flush?



Yes. I saw it with my own eyes on Monday.

Quote:

Is a five card straight flush actually a losing hand???



Yes.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
ThatDonGuy
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August 3rd, 2016 at 10:23:06 AM permalink
Quote: ThatDonGuy

A quick simulation of about 110 million hands, using the 1,000,000 payout for the suited A-6, shows a house edge of...

Turns out it was a little too quick - I subtracted 1 from each payout. See below for the corrected value.


The correct value, after 320 million hands, is about 15%.

Here's what I get for the calculated values:
Jackpot Probability = 2.21653016730404E-08 (1 in 45,115,560)
Full House Probability = 0.000883390523457394 (1 in 1132)
Trips Probability = 0.00891848362078757 (1 in 112)
Pair Probability = 0.197838006742154
Loss Probability = 0.792360096948299
House Edge = 15.2402475133398%

If I am calculating the variance correctly, it is about 22,179, just about all of which is caused by the jackpot
Last edited by: ThatDonGuy on Aug 3, 2016
Wizard
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August 3rd, 2016 at 5:35:18 PM permalink
Quote: ThatDonGuy

The correct value, after 320 million hands, is about 15%.

Here's what I get for the calculated values:
Jackpot Probability = 2.21653016730404E-08 (1 in 45,115,560)
Full House Probability = 0.000883390523457394 (1 in 1132)
Trips Probability = 0.00891848362078757 (1 in 112)
Pair Probability = 0.197838006742154
Loss Probability = 0.792360096948299
House Edge = 15.2402475133398%



I agree with the probabilities to within a very small margin. Here is my return table based on a $1,000,000 at a $5 bet.

Event Pays Probability Return
Straight flush 200000 0.00000002216530 0.00443306
Full house 100 0.00088339052300 0.088339052
Three of a kind 15 0.00891848362100 0.133777254
Pair 2 0.19783800674281 0.395676013
Loser -1 0.79236009694789 -0.792360097
Total 1.00000000000000 -0.170134716


Can I trouble you to double check the house edge, assuming your probabilities are correct? Perhaps you didn't adjust that a $1,000,000 net win on a $5 bet is equivalent to a pay of 200,000 to 1?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
ThatDonGuy
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August 3rd, 2016 at 6:08:33 PM permalink
Quote: Wizard

Can I trouble you to double check the house edge, assuming your probabilities are correct? Perhaps you didn't adjust that a $1,000,000 net win on a $5 bet is equivalent to a pay of 200,000 to 1?


I didn't realize the $1 million was only for a $5 bet - I assumed all bets were $1. That would increase the house edge by 800,000 / 45,115,560, which makes it pretty much match your number.
Wizard
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August 3rd, 2016 at 6:12:25 PM permalink
Quote: ThatDonGuy

I didn't realize the $1 million was only for a $5 bet - I assumed all bets were $1. That would increase the house edge by 800,000 / 45,115,560, which makes it pretty much match your number.



Thank you for your confirmation on this! I owe you another beer. I believe that makes it three?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
tringlomane
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August 3rd, 2016 at 8:48:14 PM permalink
Quote: Wizard

Yes. I saw it with my own eyes on Monday.



I feel like someone really messed up the paytable stricture then. People will complain quick when dealers get 5 card poker hands that lose.
Deucekies
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August 3rd, 2016 at 10:26:52 PM permalink
Yeah, Count me as someone who will never play this in a million years.
Casinos are not your friends, they want your money. But so does Disneyland. And there is no chance in hell that you will go to Disneyland and come back with more money than you went with. - AxelWolf and Mickeycrimm
Wizard
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August 4th, 2016 at 3:42:12 AM permalink
Quote: tringlomane

I feel like someone really messed up the paytable stricture then. People will complain quick when dealers get 5 card poker hands that lose.



I think the casinos would argue that Caesars properties already has Millionaire Maker side bets on other poker-based games and the straight flush pay was in keeping with that theme.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Joeman
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August 4th, 2016 at 6:24:09 AM permalink
Quote: Wizard

I think the casinos would argue that Caesars properties already has Millionaire Maker side bets on other poker-based games and the straight flush pay was in keeping with that theme.

I've only played MM on the 6-card bet in 3CP. IIRC, it pays lesser amounts for all pat poker hands. Do the MM side bets for their other games pay for pat hands? If so, I'm with Tring on this one.

Quote: tringlomane

I feel like someone really messed up the paytable stricture then. People will complain quick when dealers get 5 card poker hands that lose.

If the dealer deals himself 2-6 or a 5-card flush, the side-betting folks are going to get upset.
"Dealer has 'rock'... Pay 'paper!'"
Wizard
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August 4th, 2016 at 11:27:30 AM permalink
Quote: Joeman

If the dealer deals himself 2-6 or a 5-card flush, the side-betting folks are going to get upset.



Don't tell me -- I didn't have anything to do with it.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Wizard
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August 4th, 2016 at 4:52:08 PM permalink
Here is my new page on Millionaire Maker. As always, I welcome all comments, questions, and especially corrections.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
tringlomane
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August 4th, 2016 at 5:10:53 PM permalink
Quote: Joeman

I've only played MM on the 6-card bet in 3CP. IIRC, it pays lesser amounts for all pat poker hands. Do the MM side bets for their other games pay for pat hands? If so, I'm with Tring on this one.



As far as I know they all had the same paytable (except some evil properties only paid 100k on the super royal in diamonds) until now because they always made enough cards for a 6 card hand.

Now obviously I don't expect straights, flushes, four of a kinds, or straight flushes to pay the same as the other games where 6 cards are always given, but not including them at all is really shortsighted imo. Rarer poker combinations should have been included.
TheoHuxtable
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August 10th, 2016 at 9:22:06 AM permalink
A $10 wager allows the player the to substitute one of the cards in their hand with one card in the dealer's hand in effort to achieve the 6 card straight flush. A $15 wager allows a player to substitute two cards in their hand with two of the dealer's hand in similar fashion.
Views are my own...
GWAE
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August 10th, 2016 at 3:11:25 PM permalink
I played a game thus weekend that was similar to this. Well it was a side game and I didn't play but it was at the table. It is called something like axe. It works ike millionaire where you make hands out of the dealers cards only but the K diamonds is wild and if you get a K diamonds in one of your first 2 cards then the paytable is doubled, if you have 2 king of diamonds then the paytable is 5x. I can't remember the pay table but I think the 5 card straight flush only paid 500 to 1 plus a possible 5x multiplier. I didn't see the game listed on wizards listing.
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MB
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August 10th, 2016 at 4:16:26 PM permalink
Any idea what the edge would be if the true count is very negative? Of course, we shouldn't even be at the table in that case...
Wizard
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August 10th, 2016 at 4:51:55 PM permalink
Quote: MB

Any idea what the edge would be if the true count is very negative? Of course, we shouldn't even be at the table in that case...



I haven't looked at that. Clever, or accidental, of them to create a side bet that does better in negative counts.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
ThatDonGuy
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August 10th, 2016 at 7:49:02 PM permalink
Some quick (and unverified) simulating shows that there is an AP if the TC is -7 or lower; -6 is pretty much a wash.
MB
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August 11th, 2016 at 8:51:17 AM permalink
Quote: Wizard

I haven't looked at that. Clever, or accidental, of them to create a side bet that does better in negative counts.



If you had to bet, would you pick "clever" or "accidental"?
ThatDonGuy
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August 11th, 2016 at 10:27:53 AM permalink
Quote: ThatDonGuy

Some quick (and unverified) simulating shows that there is an AP if the TC is -7 or lower; -6 is pretty much a wash.


-7 is for eight decks. With six decks, -8 appears to be the magic number.
onenickelmiracle
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August 11th, 2016 at 11:45:21 AM permalink
Quote: Wizard

Here is my new page on Millionaire Maker. As always, I welcome all comments, questions, and especially corrections.



1. For purposes...the player('s bet) is...

Is the original $5 bet kept if the bet is won?
I am a robot.
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