kantarou: lucky ladies

[kantarou]

what is the house edge on "lucky ladies" bets? (house pays 4:1 on players 20, 10:1 on players suited 20, 25:1 on players matched 20, 200:1 on players queen of hearts pair, and 1000:1 on players queen of hearts pair with dealer black jack.) also, what is the players edge if he starts his hand with 10 value card?

thanks,

[OldCootFromVA]

> what is the house edge on "lucky ladies"

Check out thewizardofodds.com

[Dog Hand]

kantarou,

You failed to mention how many decks are used, so I asumed 6 decks. In this case, as the Wizard of Odds indicates for this paytable (which he calls Table B), the house edge is 17.64%... OUCH!

Now if your first card is an X, the advantage shifts dramatically in your favor. Here we have to consider three possible outcomes: (1) No Queen of Hearts pair for you, (2) Qh pair but no dealer BJ, and (3) Qh pair with dealer BJ.

(1) If your X is NOT a Queen of Hearts, then you have no chance for the two big payouts. However, you have 5 out of 311 cards that will give you a Matched 20, for a return of 25*5/311 = 0.4019; 18 cards that will give you a Suited 20, for a return of 10*18/311 = 0.5788; 72 cards that will give you an Unsuited 20, for a return of 4*72/311 = 0.9260; and 216 cards that will give you a Non-20, for a return of -1*216/311 = -0.6945. Add these four returns and you get 1.2122, or a hefty 21.22% player advantage.

(2) If your X IS a Queen of Hearts but the dealer does NOT get a BJ, then you have no chance for the top payout. However, you have 5 out of 311 cards that will give you a Qh pair, for a return of 200*5/311 = 3.2154. Of course, you cannot get a Matched 20, and all the other returns are the same as for Case (1). Sum the returns and you get 4.0257, or a lofty 302.26% player advantage.

(3) If your X IS a Queen of Hearts AND the dealer DOES get a BJ, then you have 5 out of 311 cards that will give you a Qh pair and the top payout, for a return of 1000*5/311 = 16.0772. Of course, you cannot get the second payout or a Matched 20, and all the other returns are the same as for Case (1). Sum the returns and you get 16.8875, or an incredible 1588.75% player advantage.

Now the probability of a dealer BJ (when your first card is an X) is 2*24*95/(311*310) = 0.047298. Also, the probability that your X will be a Qh is simply 1/16. Therefore, your overall edge is given by this:

(15/16)*1.2122 + (1/16)*[(1-0.047298)*4.0257 + (0.047298)*16.8875] = 1.4261, or a sweet 42.61% player advantage. I believe that calls for a max bet ;-)

Hope this helps!

Dog Hand

[kantarou]

dear dog hand,

thanks truly for the detailed reply.

kantarou

[kantarou]

[Panama Rick]

> what is the house edge on "lucky ladies"
> bets? (house pays 4:1 on players 20, 10:1 on players
> suited 20, 25:1 on players matched 20, 200:1 on
> players queen of hearts pair, and 1000:1 on players
> queen of hearts pair with dealer black jack.) also,
> what is the players edge if he starts his hand with 10
> value card?

> thanks,

Using HiLo, the advantage increases by about 4% per TC. Using the paytable where a suited 20 pays 9:1, the breakeven point for 6 deck is TC between 6 and 7.

[Dog Hand]

kantarou,

First, when I said "Max Bet", I failed to warn you to check the casino's maximum LL payout. For example, if the LL max bet is $25 (pretty typical), but the casino's maximum LL payout is $10000 (as I've seen a few places), then you're only getting 400:1 on the "big" payout. Although this'll lower the player advantage, you should still make the max bet.

Second, you have to realize that the LL side bet has an extremely high variance... after all, you're going to lose the bet 216 times out of 311 even when you know your first card is an X. Thus, pack a HUGE bankroll!

Dog Hand