Blackjack Side Bet: Red Flex Bet house advantage

Sorry if this is in the wrong section, I am new to this forum. At my local casino there is a side bet you can make that has a payoff schedule as follows: if the dealer has 2 consecutive red card cards, you are paid 1:1. If he has 3 consecutive red cards, you are paid 5:1. four red cards is 10:1. five red is 50:1. six red is 100:1 and seven red is 200:1. The casino uses a 5 deck CSM and hits on soft 17. What would the house advantage be for such a side bet? even when all players bust the dealer will still deal out his hand until 17-21 or busting because this bet exists. Also if the dealers first 2 cards are red, the next one is black, then the next 4 are red you only get paid on the first 2 that are red. Conversely, if his first card is black and the next 6 are red, you dont get anything. its starts the count at his first two cards. Hopefully this explanation is as clear as possible. I tried figuring it out on my own with no luck, and even called the maker who couldn't tell me because of confidentiality purposes. google doesnt even know! Any math magicians out there who know this would be greatly appreciated! ALL HAIL THE WIZARD!!

Nothing like sugarcoating a welcome. LOL

Since you buttered me up so nicely, here you go.

Reds	Pays	Prob	Return
7+	200	0.00000230011	0.00046002216
6	100	0.00006438572	0.00643857156
5	50	0.00115421980	0.05771099013
4	10	0.01220995252	0.12209952522
3	5	0.06849517726	0.34247588632
2	1	0.16710871362	0.16710871362
1	-1	0.25096525097	-0.25096525097
0	-1	0.50000000000	-0.50000000000
Total	0	1.00000000000	-0.05467154196

Lower right cell shows a house edge of 5.47%.

Once again the man behind the curtain proves he truly is the WIZARD !

thanks wizard! I tip my hat to you good sir

we hear he is a whiz of odds if ever a wiz there was because because because becauuuuuse. because of the wonderful things he does. na na na na na na na na na. oh we're off to ask the wizard. the wonderful wizard of odds!!!

Quote: OzzyOsbourne

thanks wizard! I tip my hat to you good sir

You're welcome. May I ask where this bet may be found? I'd like to add it to my blackjack appendix 8. Now, go bring me the witch's broom.

it can be found at the elsinore casino in southern california.

http://www.lercasino.com/

20930 Malaga Road, Lake Elsinore, CA
(951) 674-5160

for the record i dont recommend ever going there for any reason

Quote: OzzyOsbourne

for the record i dont recommend ever going there for any reason

That's pretty funny.

Quote: OzzyOsbourne

even when all players bust the dealer will still deal out his hand until 17-21 or busting because this bet exists.

Ozzy -
Assuming all players busted, does he still continue to play his hand if he has any black cards?


APs -
Out of curiosity, does seeing extra cards for free help or hurt card counters? Would your answer change if it was a shoe game rather than a CSM?

Quote: DJTeddyBear

Ozzy -
Assuming all players busted, does he still continue to play his hand if he has any black cards?


APs -
Out of curiosity, does seeing extra cards for free help or hurt card counters? Would your answer change if it was a shoe game rather than a CSM?

See!

Everyone hated my, "Two Off the Top," side bet for the very reason that there could be extra cards getting pulled out at the end of the hand, and look, this side bet already (potentially) does the same thing.

I'm going to answer your question to the best of my ability DJTeddyBear, and I am nowhere near the BJ level of many of our posters. I would say that free cards almost always help very early on in the shoe because (absent an extreme count) you're not going to be playing at an advantage early on in the shoe anyway, at least, not in terms of HE. I would say that whether or not free cards help late in the shoe is situational. If the free cards are low, then they always help. If the count is advantageous, and the free cards happen to be Tens/Aces, then that's probably going to irritate an AP. If the count is disadvantageous, but the draw pulls out a few low cards, then that is helpful.

I will say that some people will always be upset over the concept of having cards burned unrelated to the base game.

Quote: Mission146

I will say that some people will always be upset over the concept of having cards burned unrelated to the base game.

That's a given, for sure. I was just too lazy to mention it.

Surely no one would get mad, except maybe me, when after all hands had busted, the dealer then proceeded to take an Ace or two
to complete the side bet. I mean what players want their first card to be an Ace anyway. LOL

I maintain it is bad game design if the dealer has to pull out extra cards to resolve the side bet. However, in this case it would rarely happen. Every player at the table would have to bust and at the least the dealer's first two cards would have to be red, with the need to draw more. Another weakness to this side bet is that it is so countable it pretty much requires a CSM. However, it has a nice simple concept and doesn't require any strategy changes on the part of the player. I might add they could just as easily make a "black" version of this bet too. All in all, I give this one a B.

Just because a side bet makes it into a rinky-dink casino doesn't mean it is the next bread slicing machine. I've seen much worse games and side bets to make the casino floor. In non-competitive environments, players will be on just about anything, and casinos will put in just about anything.

Quote: Wizard

Just because a side bet makes it into a rinky-dink casino doesn't mean it is the next bread slicing machine. I've seen much worse games and side bets to make the casino floor. In non-competitive environments, players will be on just about anything, and casinos will put in just about anything.

For the record this is a more competitive environment than you might think, the largest casino in the west is 20 minutes south of there. The one thing that reccomends Elsinore is that it is the rare California cardroom where you do not have to pay a 50 cent or $1 collection for each hand you play. While I will stop by for 3 or 4 hands of baccarat when I have to pay a commission, I don't get the Asian players that will play Pai Gow Poker of all games. You pay $1 a hand just to push half the hands? Come on!

Yeah this bet would be very countable if they didnt use a CSM for all of their games

and yes the dealer will still deal out his hand if he has all black cards, or everyone busts and there are no live hands, even if nobody has bet on the reds

keep in mind they also have a rule there that if the banker hand busts 8-8-8 then player busted hands do not lose.

Quote: bigfoot66

keep in mind they also have a rule there that if the banker hand busts 8-8-8 then player busted hands do not lose.

Is this a player-banked casino? Usually such places have such a rule, because "21" games are illegal.

Regardless of that, I just added to my blackjack side bet page a couple table on Red Flex. I welcome all comments.

deleted

There are two card rooms in the Sacramento area with this side bet as well. Both are hit on S17 and 6 deck shoes (not CSM). Here are their payouts

Capitol Casino (Sacramento, CA)
2 reds: 2
3 reds: 3
4 reds: 8
5 reds: 50
6 reds: 100
7 reds: 250

Phoenix Casino (Citrus Heights, CA)
2 reds: 2
3 reds: 3
4 reds: 8
5 reds: 50
6 reds: 100
7 reds: 200
8 reds: 299

Interesting side bet, I've never seen it.

Can anyone show how the payoff table is calculated? For zero or one reds it's easy to calculate the probability since you only have to consider the dealer's initial two cards. Then it gets more complex since you have to calculate the probability of the dealer having to take additional cards. I suppose the only practical way to do this is via simulation?

On another note, it was mentioned that this bet would be very countable. I haven't calculated it, but at first glance it seems it wouldn't be since the reds have to come consecutively for a win. So just knowing the remaining deck is rich in reds might not be good enough.

Thanks
Ace

Quote: Ace

Interesting side bet, I've never seen it.

Can anyone show how the payoff table is calculated? For zero or one reds it's easy to calculate the probability since you only have to consider the dealer's initial two cards. Then it gets more complex since you have to calculate the probability of the dealer having to take additional cards. I suppose the only practical way to do this is via simulation?

On another note, it was mentioned that this bet would be very countable. I haven't calculated it, but at first glance it seems it wouldn't be since the reds have to come consecutively for a win. So just knowing the remaining deck is rich in reds might not be good enough.

Thanks
Ace

Mr. Wizard shown the probability distribution in page one, and I'm sure it's done by simulation, because if without considering the need of hitting for another card, the chance of 3 red cards in a row in a single deck would simply be 26/52*25/51*24/50.

As for card counting the side bet, you don't have to worry about red come consecutively, just like card counters don't worry about 10s come at certain time for a 20. When there is a surplus of one type of card left in the shoe, the chance of them coming together increases, consecutively or not. As for the system goes, red card definitely would have a minus value and blacks have plus value, and lower reds should have higher minus value than higher reds.

^ Getting three Reds in a row also depend on needing a third card, so the figures are not as simple as that. I'm guessing with a surplus of low cards, there's more chances of larger hands, so the bet would become a better proposition.

btw it's fairly easy to work out all the permutations of hands that the dealer can have (I did it once to work out the Bust 22 bet, there are about 54k possible perms with s17). It goes from AAAAAAA, AAAAAA2 to 10+6+9, 10+6+10, 10+7, 10+8, 10+9, 10+10.

17 01 01 01 01 01 01 01 00 00 00 00 00 00
18 01 01 01 01 01 01 02 00 00 00 00 00 00
19 01 01 01 01 01 01 03 00 00 00 00 00 00
20 01 01 01 01 01 01 04 00 00 00 00 00 00
21 01 01 01 01 01 01 05 00 00 00 00 00 00
17 01 01 01 01 01 01 06 01 01 01 01 01 00
18 01 01 01 01 01 01 06 01 01 01 01 02 00
....
17 10 06 01 00 00 00 00 00 00 00 00 00 00
18 10 06 02 00 00 00 00 00 00 00 00 00 00
19 10 06 03 00 00 00 00 00 00 00 00 00 00
20 10 06 04 00 00 00 00 00 00 00 00 00 00
21 10 06 05 00 00 00 00 00 00 00 00 00 00
22 10 06 06 00 00 00 00 00 00 00 00 00 00
23 10 06 07 00 00 00 00 00 00 00 00 00 00
24 10 06 08 00 00 00 00 00 00 00 00 00 00
25 10 06 09 00 00 00 00 00 00 00 00 00 00
26 10 06 10 00 00 00 00 00 00 00 00 00 00
17 10 07 00 00 00 00 00 00 00 00 00 00 00
18 10 08 00 00 00 00 00 00 00 00 00 00 00
19 10 09 00 00 00 00 00 00 00 00 00 00 00
20 10 10 00 00 00 00 00 00 00 00 00 00 00

Quote: DJTeddyBear

APs -
Out of curiosity, does seeing extra cards for free help or hurt card counters? Would your answer change if it was a shoe game rather than a CSM?

Quote: Mission146

...I would say that free cards almost always help very early on in the shoe because (absent an extreme count) you're not going to be playing at an advantage early on in the shoe anyway, at least, not in terms of HE. I would say that whether or not free cards help late in the shoe is situation. If the free cards are low, then they always help. If the count is advantageous, and the free cards happen to be Tens/Aces, then that's probably going to irritate an AP. If the count is disadvantageous, but the draw pulls out a few low cards, then that is helpful.

I will say that some people will always be upset over the concept of having cards burned unrelated to the base game.

Semi-correct Mission. In terms of not betting early in a shoe, I must disagree. At a 6 deck game with "decent" rules (such as S17 and late surrender) the HE is .36%. I've seen many times the first hand come out +6 (not that it's an every time occurrence, but often enough to mention). In this scenario with TC +1, there's a player edge (albeit small) and could possibly bet more. Give 1 more round and you could most definitely be betting larger on the 3rd round of the shoe.

The part about seeing these extra cards being situational is correct. In generalities, because we don't know what cards are coming out next it's the same situation as players before/after you taking cards when they "shouldn't" (according to basic strategy). It's just as likely to 'help' as it is to 'hurt'. So DJT, in the long run of the game it simply doesn't matter. Thus, it doesn't affect card counting, in my opinion. Now this would definitely hurt Shuffle Trackers though ;).

Well put clarification & correction, Romes! Thanks!

After correcting many typos, brainos, and arrrrg I did something totally wrongos, I finally finished my spreadsheet.
http://miplet.net/blackjack/redflex.xlsb
Now to tackle some of the dealer bust type bets. I'll but them in the blackjack directory.

Quote: miplet

After correcting many typos, brainos, and arrrrg I did something totally wrongos, I finally finished my spreadsheet.
/blackjack/redflex.xlsb
Now to tackle some of the dealer bust type bets. I'll but them in the blackjack directory.

Excellent spreadsheet. In h17 column B, what was the algorithm you used to generate all 70,000 permutations the dealer can have?

Quote: Ace

Excellent spreadsheet. In h17 column B, what was the algorithm you used to generate all 70,000 permutations the dealer can have?

I wrote a program to create the h17 and s17 sheets. Its in PHP.
http://miplet.net/redflex/index.phps
There are better ways to do it, but it worked for me.

Thank you.

I finally got around to calculating this bet. I like to make the calculations as simple as possible and without programming or simulations.

I assumed infinite deck, which is not much different from 8 decks or CSM.

The only tricky part is calculating how many cards the dealer will take, but it’s not that hard. I used a Markov chain and only went 7 iterations. There’s only about a 1 in 42,000 chance that more than 7 cards will be taken so I’m satisfied stopping there. The probability of the dealer taking exactly x cards in a H17 game is:

Cards......Probability
2.................0.33731
3.................0.44101
4.................0.17931
5.................0.03723
6.................0.00472
7.................0.00040
more.........0.00002
Total...........1.00000

It’s simple to calculate the probability of the dealer getting x consecutive reds in a row given the number of cards dealt. This is shown below (cards dealt on left axis, consecutive reds on top axis):

............0..............2..............3.............4..............5............6............7
2........0.7500 0.2500 0.0000 0.0000 0.0000 0.0000 0.0000
3........0.7500 0.1250 0.1250 0.0000 0.0000 0.0000 0.0000
4........0.7500 0.1250 0.0625 0.0625 0.0000 0.0000 0.0000
5........0.7500 0.1250 0.0625 0.0313 0.0313 0.0000 0.0000
6........0.7500 0.1250 0.0625 0.0313 0.0156 0.0156 0.0000
7........0.7500 0.1250 0.0625 0.0313 0.0156 0.0078 0.0078


Multiplying the first table by the second and summing each column you get the following:

...............0..................2..................3..................4...................5.................6..................7
2..........0.252982 0.084327 0.000000 0.000000 0.000000 0.000000 0.000000
3..........0.330758 0.055126 0.055126 0.000000 0.000000 0.000000 0.000000
4..........0.134481 0.022413 0.011207 0.011207 0.000000 0.000000 0.000000
5..........0.027926 0.004654 0.002327 0.001164 0.001164 0.000000 0.000000
6..........0.003539 0.000590 0.000295 0.000147 0.000074 0.000074 0.000000
7..........0.000297 0.000050 0.000025 0.000012 0.000006 0.000003 0.000003
Total..0.749982 0.167161 0.068980 0.012530 0.001243 0.000077 0.000003
Payout.....-1................1................5................10.................50...............100...............200
Return...-0.750.....0.167.......0.345..........0.125..........0.062...........0.008............0.001.......-0.042


So the return is shown as -4.2% for infinite deck.