Lucky Ladies side bet in 2D

I come up with a true count of +7 to make the bet profitable.

Do I have this right? From a pure probability viewpoint:

QhQh = 2/104 * 1/103
XXmatch = 16 * (2/104 * 1/103)
20suited = 4 * ((8/104 * 7/103) + (2/104 * 2/103))
any20 = (32/104 * 31/103) + (8/104 * 8/103)

to simplify, skipping the common denominator and eliminating dups

QhQh = 2
XXmatch = 30
20suited = 88
any20 = 936
----------------
total = 1056 / 10712

Payouts:

QhQh = 250
XXmatch = 750
20suited = 880
any20 = 3744
----------------
total = 5624 = 52.5%

Panama Rick did the sims on this using several different count systems for both double deck and six deck. He did an outstanding job.

Not everyone here has a GC membership. I am attempting to get some technical discussion going on the free pages, rather than relegating all of it to the subscriber-only pages.

for every true count to find the point where your true count predicts enough tens density for your payouts to have positive expectation.

Damn I wish I didn't have hacking ex-inlaws and ex-es to go ahead and get on Green...I would want to compare notes.

So there, even the most stuborn free pager (me) sees value in going on Green chip here.

Panama Rick posted this on the free (beginner) page on 5/14/02 in response to my question on the same subject:

"The expected values for the various payouts are (6 decks):

Any 20 = 0.4007
Suited 20 (same suit) = 0.2078
Matched 20 (e.g. 2 jacks of spades) = 0.0928
2 Queens of hearts = 0.0371
2 Queens of hearts with a dealer blackjack = 0.0146

Total = 0.7529
House Edge = 24.71%

Note that A-9 counts as a 20.

My quick calculation shows that the break even point for this is around TC=6.5 (hi-lo), with the house edge decreasing around 4% per TC."

The interesting thing is, of course, the rapid decrease in house edge, which would imply a player edge of 2% at TC=7, 6% at TC=8, etc. Still a rare occurrence, but interesting.

By the way, my original question used the 6 deck version. You can search for the entire string on the beginner page.

Coug Fan,

Thanks much!

Turns out that different casinos in my area use different payouts. WILDLY different payouts. Like, one pays 15-1, the other pays 10-1. Apparently the licensor allows casinos to pick what odds they want to offer on this side bet.

Good luck against the puppies this year.

(1)First you find the relative frequencies of each type of 20

(2)Then you find the payouts for each type and multiply by the relative frequencys.

(3)You arrive at the average payout for having a 20.

(4)You then determine the probability of having any 20 that gives you positive expected value.

(5)You then determine the density of tens that will give you this probability in step (5).

(6)You determine the most probable full pack composition for a true count of +1 as the basis for further calculations. The rest will initially assume balanced counts:

_(a) Take the size of the full pack, in decks and multiply by 1/2 the number of low card or high card points.

_(b) Divide by the number of high cards (counting each tens rank as a seperate card type) per suit. this is your number of high cards you add. Example for six decks you add .6 tens, jacks, queens, kings and aces if you are seeking a +1 TC, for 6 decks and hi-lo.
_(c) Divide by the number of low cards for the similar number of each low card to subtract.
_(d) A most probable TC=+1, hi-lo 6 deck pack is: 12.4 2s to 6s, 13, 7 to 9s, 98.4 tens, and 24.6 aces

(7) From the this pack you estimate how high a TC is needed to have a tens density that matches the result of step (5). A TC=+1 shifted the tens density from (4/13) to (98.4/312).

The alternative is to follow the same steps you might use to find an insurance index algebraicly, where you use a point version of the ten count and (tens-9 all others +4), and find the index that realtes to the result of step (5) and then use Snyder's Algebraic Approximation paper to find the hi-lo index.

No kidding that payout schedules varry greatly. I skipped where you already had an estimate going for how high a tens density would lead to positive ev also--got to save something for the Greenchippers, I would like to join, except for the ex-es, to do;-)! My Blackjack Therapy ms. can show you how to find the balanced equivalents of unbalanced counts too---shameless plug for something I gave out for free (I know dumb).

They are in Pullman this year. A little rain / wind / snow and they will go home crying for their mommies like always.

Regarding the subject of your post, the other thing to consider is that a different count (than hi-lo) would be far superior (and easier to do the numbers for). I would think that a ten count (with a side count of Q of H for a bonus) would be best. Also, DD might be best for this bet since the side count would just be noting whether you had seen any Q of H yet (if any are out, you can't win the top bet).

I have had dealers tell me towards the end of a DD that I should place this bet since there have been no Q of H yet. I will usually oblige and place a $1 tip for them on it (if appropriate). This gets HUGE mileage from the tip $.