ksdjdj
• Posts: 1707
Joined: Oct 20, 2013
July 9th, 2014 at 4:42:04 PM permalink
Hi,

I would like to know what the net gain in value would be for hitting, instead of doubling or standing on:

(a) a hand consisting of 2 'red' 5's (even when basic strategy says to double, eg player 10 vs dealer 2 - 9 up card)

(b) a hand consisting of 3 'red' 5's (even when basic strategy says to stand, eg player 15 vs dealer 2 - 6 up card)

----------------

Game Info:
" ALL RED 5-5-5-5 BlackJack 6 Deck, Multiple Hand
After each hand played, a new 6 deck shoe is shuffled and dealt. Blackjack pays 3/2. Dealer hits on soft 17. Double down on all 2-card combinations, even after splits. Split pairs up to 4 times. May split aces once. Late surrender available, even after splits. Insurance pays 11/5."

---------------

Assumptions:

1. Assume that correct basic strategy is used for all hands, besides for the above scenarios, a and b

2. The basic strategy for this game is about - 0.528% EV, if the game did not have the "All red 5-5-5-5 bonus"

3. The gross value of the "ALL RED 5-5-5-5" bonus is about: + 0.639% when playing at the table minimum, (this bonus pays \$5000 when playing at the \$1 table minimum)
AxiomOfChoice
• Posts: 5761
Joined: Sep 12, 2012
July 9th, 2014 at 4:57:10 PM permalink
There is definitely a large gain. Eg, hitting red 5, red 5 (with the plan to hit again if you catch a red 5) is worth almost \$5 from the bonus, which completely dominates any loss in EV on the \$1 hand. Hitting red 5, red 5, red 5 is worth almost \$150.

Rather than enumerate the size of the gain, don't you want to know the amount of the loss on the main game of hitting? You already know the value of the bonus (does it not require a side bet?)
ksdjdj
• Posts: 1707
Joined: Oct 20, 2013
July 9th, 2014 at 6:26:19 PM permalink
yes i probably didn't word the question right, but what you said here is what i wanted to know, '... the amount of the loss on the main game of hitting?'

it does not require a side bet,

AxiomOfChoice
• Posts: 5761
Joined: Sep 12, 2012
July 9th, 2014 at 6:29:26 PM permalink
I don't know exactly, but, to figure it out:

1. Look at the Wizard's BJ appendix 9 to find the cost each suboptimal play vs each dealer upcard.
2. Use simple combinatorics to figure out what percentage of the hands this occurs on
3. Multiply for each situation.
ksdjdj
• Posts: 1707
Joined: Oct 20, 2013
July 9th, 2014 at 7:16:07 PM permalink
thank you
98Clubs
• Posts: 1728
Joined: Jun 3, 2010
July 9th, 2014 at 7:18:06 PM permalink
Quote: ksdjdj

Hi,

I would like to know what the net gain in value would be for hitting, instead of doubling or standing on:

(a) a hand consisting of 2 'red' 5's (even when basic strategy says to double, eg player 10 vs dealer 2 - 9 up card)

(b) a hand consisting of 3 'red' 5's (even when basic strategy says to stand, eg player 15 vs dealer 2 - 6 up card)

----------------

Game Info:
" ALL RED 5-5-5-5 BlackJack 6 Deck, Multiple Hand
After each hand played, a new 6 deck shoe is shuffled and dealt. Blackjack pays 3/2. Dealer hits on soft 17. Double down on all 2-card combinations, even after splits. Split pairs up to 4 times. May split aces once. Late surrender available, even after splits. Insurance pays 11/5."

---------------

Assumptions:

1. Assume that correct basic strategy is used for all hands, besides for the above scenarios, a and b

2. The basic strategy for this game is about - 0.528% EV, if the game did not have the "All red 5-5-5-5 bonus"

3. The gross value of the "ALL RED 5-5-5-5" bonus is about: + 0.639% when playing at the table minimum, (this bonus pays \$5000 when playing at the \$1 table minimum)

Since Basic Strategy dictates that 5-5 doubles against 2-9 up, the initial hand stands a much higher advantage by doubling over hitting. If you have two red 5's the chances are 1 in 31 you will draw another red-5. Having anything else drawn would favor doubling. Say you draw a third red-5. The chances are now 3 in 103 to draw the fourth red-5. So the total chance of drawing 2 more red-5's are 1/31 * 3/103 = 1/1064.333 for a payoff of 5000 + bet.

Finally the chance of being dealt 2 red-5's as the initial hand are 1 in 176. In short, if one plays \$1 on every hand dealt, it would take about 176 * 1064.333 or \$187,000+ to win the \$5000.
Some people need to reimagine their thinking.
AxiomOfChoice
• Posts: 5761
Joined: Sep 12, 2012
July 9th, 2014 at 7:25:55 PM permalink
Quote: 98Clubs

Since Basic Strategy dictates that 5-5 doubles against 2-9 up, the initial hand stands a much higher advantage by doubling over hitting

.

What? No! You hit!

Quote:

If you have two red 5's the chances are 1 in 31 you will draw another red-5. Having anything else drawn would favor doubling. Say you draw a third red-5. The chances are now 3 in 103 to draw the fourth red-5. So the total chance of drawing 2 more red-5's are 1/31 * 3/103 = 1/1064.333 for a payoff of 5000 + bet.

Right, so hitting (with the intention of hitting again if you catch a red 5) has an EV of almost \$5. You are giving up a few cents by hitting instead of doubling (remember that the initial bet is only \$1). Giving up a few cents for \$5 in EV is obviously a good play.

Quote:

Finally the chance of being dealt 2 red-5's as the initial hand are 1 in 176. In short, if one plays \$1 on every hand dealt, it would take about 176 * 1064.333 or \$187,000+ to win the \$5000.

He said that there was no side bet required. In other words, you are just betting \$1 per hand on the main game and getting the bonus for free. This is obviously a +EV play (although, for such low limits, it would only be worth your time if you had very little money)
RS
• Posts: 8626
Joined: Feb 11, 2014
July 9th, 2014 at 7:43:53 PM permalink
What about insurance? 11:5 really? :)
AxiomOfChoice
• Posts: 5761
Joined: Sep 12, 2012
July 9th, 2014 at 7:44:26 PM permalink
Quote: RS

What about insurance? 11:5 really? :)

Isn't that common for online casinos?
ksdjdj
• Posts: 1707
Joined: Oct 20, 2013
July 9th, 2014 at 8:27:51 PM permalink
thanks for the info, Axiom

from the information here i think that the loss in value of hitting rather than doubling on those two red 5 hands is roughly 0.015%, (see link below, for table)

https://wizardofodds.com/games/blackjack/appendix/9/6dh17r4/

i didn't bother looking for the loss in value for always hitting a red 5-5-5 (15) since i assume the loss in value would be a lot less than that of the 2 card red 5's

so the net value of this game is slightly less than about 0.096% in the players favour

------

nb there is also a \$10 minimum table game that pays \$50,000 bonus for the same rules, but at my maximum rate of play it is only worth about \$8.60 per hour (at 900 hands per hour) which is about the fastest rate of play for me with minimal mistakes, (so not worth playing for normal game play, but may be worth playing for grinding out a bonus or something)
ksdjdj
• Posts: 1707
Joined: Oct 20, 2013
July 9th, 2014 at 8:32:40 PM permalink
Quote: RS

What about insurance? 11:5 really? :)

Insurance seems to be a minimum of 11:5 at this casino, see link below for list of all games as proof

http://www.5dimes.eu/BonusCasinoCharts/chartblackjack.html
98Clubs
• Posts: 1728
Joined: Jun 3, 2010
July 9th, 2014 at 9:37:00 PM permalink
Quote: AxiomOfChoice

.

What? No! You hit!

Right, so hitting (with the intention of hitting again if you catch a red 5) has an EV of almost \$5. You are giving up a few cents by hitting instead of doubling (remember that the initial bet is only \$1). Giving up a few cents for \$5 in EV is obviously a good play.

He said that there was no side bet required. In other words, you are just betting \$1 per hand on the main game and getting the bonus for free. This is obviously a +EV play (although, for such low limits, it would only be worth your time if you had very little money)

Sorry about that, I thought it was a side-bet. You are correct, as is the OP. Its a small +EV at \$1 (or \$10 if one has the bankroll).

EDIT after FREE PLAY:

Holy Crap, the free game is very good. It asks me if I want to surrender on any A,K,Q,J,10 BEFORE revealing/testing BJ. To test this I surrendered "early" on hard 14 v. Ace. I only lost the 50c for Surr. You will see a black box Play/Surrender upon initial deal. After this box dissapears, the Ace (in my case) was tested and revealed a 10. 50c went back to bank. Must be early Surr., if it were a late surrender, the full \$1 would be lost as late surrender occurs after the test.
Some people need to reimagine their thinking.
ksdjdj
• Posts: 1707
Joined: Oct 20, 2013
July 9th, 2014 at 11:06:42 PM permalink
Quote: 98Clubs

Sorry about that, I thought it was a side-bet. You are correct, as is the OP. Its a small +EV at \$1 (or \$10 if one has the bankroll).

EDIT after FREE PLAY:

Holy Crap, the free game is very good. It asks me if I want to surrender on any A,K,Q,J,10 BEFORE revealing/testing BJ. To test this I surrendered "early" on hard 14 v. Ace. I only lost the 50c for Surr. You will see a black box Play/Surrender upon initial deal. After this box dissapears, the Ace (in my case) was tested and revealed a 10. 50c went back to bank. Must be early Surr., if it were a late surrender, the full \$1 would be lost as late surrender occurs after the test.

yeah your right about the Early surrender, the rules that are different from the stated rules are listed below:

Actual rules: Early Surrender, stand on all 17, and can split and re-split A's

Stated rules: Late surrender, hit on soft 17, and no re-splits of A's

the games Actual Rules are worth upto roughly + 0.92% EV, when playing the table minimum and at the moment i can play to 900 hands per hour, so it is worth up-to about \$82.8 per hour EV, and even with out Red 5's bonus it is still worth about \$26.5 per hour

ps i was going to let the cat out of the bag on this one, eventually, in about 6 months time or when i had won the \$50 grand once, but i now hope everyone gets a good play at this before the casino realizes their mistake
ksdjdj
• Posts: 1707
Joined: Oct 20, 2013
August 17th, 2014 at 12:50:55 AM permalink
Just thought i would put up when the player should go from aiming for the '4 red 5's bonus' to 'playing correct basic strategy (b.s.)'***, this is only applicable when the player's FIRST TWO CARDS ARE Red 5's .

b.s.***: use these parameters to work out correct b.s., 6 Deck, Early Surrender, stand on all 17, can split and re-split A's, split to 4 hands, Double any two cards, and DAS

All figures expressed in UNITS and 1 Unit is the table minimum, so 1 unit at the \$5 to \$500 table would be \$5.00 (obviously).

Dealer's Up Card ------ Units^^^ (when to disregard '4 red 5's bonus' and play to 'correct b.s.', instead)

2------------------------- 25.53+
3--------------------------22.19+
4------------------------- 19.52+
5------------------------- 17.38+
6------------------------- 15.68+
7------------------------- 32.54+
8------------------------- 50.24+
9------------------------- 144.39+

units^^^: figures are correct to 2 decimals places (rounded down)

-------------------------

Edit from previous post,

"the games Actual Rules are worth upto roughly + 0.92% EV, when playing the table minimum and at the moment i can play to 900 hands per hour, so it is worth up-to about \$82.8 per hour EV..."

The EV per hour for me is about \$73 not the \$82.80 stated (betting \$10 at the \$10 minimum table) because i forgot to take into account 'the final bet to initial bet ratio', so i can play about 800 hands per hour, not the 900 stated
(but \$73 per hour EV is still good for a \$10 bet per 'round')