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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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?
It's not whether you win or lose; it's whether or not you had a good bet.
speedycrap
speedycrap
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August 2nd, 2016 at 6:33:44 PM permalink
Please explain how to play?
ThatDonGuy
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
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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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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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.
It's not whether you win or lose; it's whether or not you had a good bet.
tringlomane
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
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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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.
It's not whether you win or lose; it's whether or not you had a good bet.
ThatDonGuy
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

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