Lucky Ladies

I recently moved to an area of the country where they offer a side bet on BJ that I had not seen previously. It is called "Lucky Ladies" and pays 4 to 1 if your first two cards total 20 (any total of 20 including A,9). There are also other higher payouts if the first two cards are Queens (with progressively higher payouts if they are suited Queens, etc). I also believe that it is possible to make a side bet that is more than your BJ bet.

For the sake of simplicity, I will ignore the payouts other than the basic 4 to 1 for a initial 2 card total of 20, unless someone is more familiar with this side bet and wants to fill in the missing info. For obvious reasons, it appears to me that this side bet would be very susceptible to counting (especially a ten count). Does anyone know what the Hi-Lo and Ten count indexes would be for this side bet. Also, does anyone know the initial house advantage for this bet (I am assuming that it is a sucker bet ignoring the count).

I have read Professional Blackjack and seen other discussions of various side bets, but have not seen mention of this one. Thanks for your help.

Thanks. Given that huge house edge, I am assuming that the count would have to extreme in order for this play to make any sense. It may be good cover though since most people make a minimal bet ($1).

I am not extremely strong in math (at least not in comparison to some of the people on this board), but it seems like this play may make sense at a TC of 5 since the likelihood of getting two 10 value cards would then be 4/8 X 4/8 or 25%. This would also be somewhat convenient since my max bet is at a TC of 5, so it would be easy to remember.

Yes I know that the Hi-Lo count would mean that you actually would have a 5/8 chance of getting EITHER a ten value card or an ace at a TC of 5, which is why I said approximately. Also, there is also the A,9 combination that I have not factored in.

Any thoughts?

Looking only at the possibilities of a T-T in a single-deck game:

With more than 35 cards remaining to be played, the wager is unprofitable. Seeking a result of .200 or higher for a 4:1 wager:

36 cards remaining.............240/1260 = .190
35 cards remaining.............240/1190 = .202
34 cards remaining.............240/1122 = .214

Note that the above figures assume that NONE of the 16 tens available in a fresh deck have already been played. They must all still be available even after 17 "non-tens" have been played from a single deck!

Here are the number of tens which must still be present in the unplayed deck at various points of penetration:

30 cards remaining.............182/870 = .209 (14 tens remaining)
26 cards remaining.............132/650 = .203 (12 tens remaining)
20 cards remaining..............90/380 = .237 (10 tens remaining)
15 cards remaining..............56/210 = .267 (8 tens remaining)*
10 cards remaining...............20/90 = .222 (5 tens remaining)
5 cards remaining.................6/20 = .300 (3 tens remaining)

*With 15 cards left in the deck, this wager breaks even when 7 tens remain to be played. (7*6)/(15*14) = .200

So, you can see that you would need a situation in which roughly half of the cards remaining to be played are tens. If you ever find yourself in such a situation (and you probably never will), you'd be better off raising your regular BJ bet through the roof, but only if a proportionate number of aces remain to be played as well.

Remember that I didn't account for the A-9 portion of this wager. In addition, the other "exotic" wagers will increase your chances slightly, but I'm willing to bet that the payoffs are equally as bad for those wagers, too.

For a six-deck shoe, you wouldn't find a favorable situation for the T-T portion of the wager until 98 cards have been dealt and none of them were tens! (96*95)/(214*213) = .20007

For all practical purposes, the rule that roughly half of the remaining cards must be tens still holds. But don't worry about remembering it; you'll never have the chance to use it!

Thanks for the info. It sounds like this is a bet that is best avoided.

I heard somebody on the Green pages analyzed this and indicated the true count had to be over +11 for the side bet to start to be good -- I can't vouch for the analysis though.

I too live in an area where this bet is common (Wa, as must you being a Cougar fan), and I avoid the bet. The wife likes it, and one night got the 125 to 1 two queen of hearts with the bet out. Two hands later I also got the two queen of hearts but avoid the bet. Her win salvaged an otherwise loosing session for both of us. At extreme positive counts I sometimes do it "just for the heck", especially if I haven't seen any queen of hearts out. I call it "20 push" insurance, and I suspect it offers a bit of cover. But I am really being stupid to bet it ever.

I use KO count, and have simulated the Lucky Ladies with a version of the simpsim.bas program. It looks like at something around 20 over the pivot point it MAY start to be a good bet :-) Of course the situation happens so infrequently the simulation rarely encounters these very high counts so I haven't yet been able to run enough rounds to get a more statistically valid index. I would need to modify the program a bit as it runs into some integer overflow problems trying to run enough sims to get a more precise answer.

I've also tried a few count modifications, including tracking the Queen of hearts, using the insurance count (which would seem to be a bit better at helping for this side bet), with little improvement.

My conclusion, the bet is a waste of my money, and me spending any more effort at simulating the situation is a waste of my time :-)