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Lucky Ladies
Introduction
Lucky Ladies is one of the most popular blackjack side bets ever. It started in Washington state and now can be found in casinos all over the place. The idea is that any player 20-point hand wins something. Certain twenties, especially those involving two queens pay more. I've seen various versions through the years, which I label as A, B, C, D, and E. There is also a progressive version called Bonus Lucky Ladies.
A word about terminology. A "matched pair" means the same card in both rank and suit.
Lucky Ladies — Pay Tables A and B
| Hand | Table A | Table B |
|---|---|---|
| Q of hearts pair & dealer has BJ | 1000 to 1 | 1000 to 1 |
| Q of hearts pair | 125 to 1 | 200 to 1 |
| Matched 20 | 19 to 1 | 25 to 1 |
| Suited 20 | 9 to 1 | 10 to 1 |
| Unsuited 20 | 4 to 1 | 4 to 1 |
Lucky Ladies — Pay Table C
| Hand | Table C |
|---|---|
| Pair of queens with dealer BJ | 250 to 1 |
| Pair of queens | 25 to 1 |
| Ranked 20 | 9 to 1 |
| Suited 20 | 6 to 1 |
| Any 20 | 3 to 1 |
Lucky Ladies — Pay Table D
| Hand | Pays |
|---|---|
| Queen of hearts pair | 100 to 1 |
| Matched 20 | 30 to 1 |
| Suited 20 | 10 to 1 |
| Any 20 | 3 to 1 |
| One queen | 1 to 1 |
Lucky Ladies — Pay Table E
| Hand | Pays |
|---|---|
| Queen of hearts pair | 100 |
| Matched 20 | 25 |
| Suited 20 | 10 |
| Any 20 | 3 |
| Queen of hearts | 2 |
| Any other queen | 1 |
Following is the pay table for the progressive Pay Table F.
Lucky Ladies — Pay Table F
| Hand | Pays |
|---|---|
| Queen of hearts pair + dealer BJ | Jackpot |
| Queen of hearts pair | 25 |
| Suited 20 | 10 |
| Unsuited 20 | 2 |
Analysis of Pay Table A
The next table is an analysis of pay table A with six decks. The lower right cell shows a return of 75.29%, or a house edge of 24.71%.
Lucky Ladies Pay Table A — 6 decks
| Hand | Permutations | Probability | Pays | Return |
|---|---|---|---|---|
| Q of hearts pair & dealer has BJ | 135360 | 0.000015 | 1000 to 1 | 0.014563 |
| Q of hearts pair | 2738340 | 0.000295 | 125 to 1 | 0.036827 |
| Matched 20 (same rank and suit) | 43105500 | 0.004638 | 19 to 1 | 0.088115 |
| Suited 20 | 193112640 | 0.020777 | 9 to 1 | 0.186990 |
| Unsuited 20 | 744863040 | 0.080139 | 4 to 1 | 0.320554 |
| Non-20 | 8310740400 | 0.894138 | Loss | -0.894138 |
| Total | 9294695280 | 1.000000 | -0.247089 |
Analysis of Pay Table B
The next table is an analysis of pay table B with six decks. The lower right cell shows a house edge of 17.64%.
Lucky Ladies Pay Table B — 6 decks
| Hand | Permutations | Probability | Pays | Return |
|---|---|---|---|---|
| Q of hearts pair & dealer has BJ | 1,000 | 135,360 | 0.000015 | 0.014563 |
| Q of hearts pair | 200 | 2,738,340 | 0.000295 | 0.058923 |
| Matched 20 (same rank and suit) | 25 | 43,105,500 | 0.004638 | 0.115941 |
| Suited 20 | 10 | 193,112,640 | 0.020777 | 0.207767 |
| Unsuited 20 | 4 | 744,863,040 | 0.080139 | 0.320554 |
| Non-20 | -1 | 8,310,740,400 | 0.894138 | -0.894138 |
| Total | 9,294,695,280 | 1.000000 | -0.176391 |
Analysis of Pay Table C
The next table is an analysis of pay table C with one deck, which is what pay table C was designed for. The lower right cell shows a house edge of 29.89% (ouch!).
Lucky Ladies Pay Table C — 1 deck
| Hand | Permutations | Probability | Pays | Return |
|---|---|---|---|---|
| Pair of queens with dealer BJ | 1344 | 0.000207 | 250 to 1 | 0.051713 |
| Pair of queens | 28056 | 0.004318 | 25 to 1 | 0.107951 |
| Ranked 20 | 88200 | 0.013575 | 9 to 1 | 0.122172 |
| Suited 20 | 137200 | 0.021116 | 6 to 1 | 0.126697 |
| Any 20 | 411600 | 0.063348 | 3 to 1 | 0.190045 |
| Non-20 | 5831000 | 0.897436 | Loss | -0.897436 |
| Total | 6497400 | 1 | -0.298858 |
Analysis of Pay Table D
The next table is an analysis of pay table D with six decks. The lower right cell shows a house edge of 13.34%.
Lucky Ladies Pay Table D — 6 decks
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Queen of hearts pair | 100 | 15 | 0.000309 | 0.030918 |
| Matched 20 | 30 | 225 | 0.004638 | 0.139129 |
| Suited 20 | 10 | 1,008 | 0.020777 | 0.207767 |
| Any 20 | 3 | 3,888 | 0.080139 | 0.240416 |
| One queen | 1 | 5,184 | 0.106851 | 0.106851 |
| Loser | -1 | 38,196 | 0.787287 | -0.787287 |
| Total | 48,516 | 1.000000 | -0.062206 |
Analysis of Pay Table E
Following is my analysis of pay table E, based on six decks.
Lucky Ladies Pay Table E — 6 decks
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Queen of hearts pair | 100 | 15 | 0.000309 | 0.030918 |
| Matched 20 | 25 | 225 | 0.004638 | 0.115941 |
| Suited 20 | 10 | 1,008 | 0.020777 | 0.207767 |
| Any 20 | 3 | 3,888 | 0.080139 | 0.240416 |
| Queen of hearts | 2 | 1,296 | 0.026713 | 0.053426 |
| Any other queen | 1 | 3,888 | 0.080139 | 0.080139 |
| Loser | -1 | 38,196 | 0.787287 | -0.787287 |
| Total | 48,516 | 1.000000 | -0.058682 |
House Edge Summary
The next table summarizes the house edge for versions A through D for one to eight decks.
Lucky Ladies — Summary
| Decks | Pay Table A | Pay Table B | Pay Table C | Pay Table D | Pay Table E |
|---|---|---|---|---|---|
| 1 | 29.89% | ||||
| 2 | 30.05% | 24.94% | 25.51% | 12.66% | 11.37% |
| 4 | 26.04% | 19.46% | 23.35% | 7.82% | 7.24% |
| 5 | 25.24% | 18.37% | 22.92% | 6.86% | 6.42% |
| 6 | 24.71% | 17.64% | 22.64% | 6.22% | 5.87% |
| 8 | 24.05% | 16.73% | 22.28% | 5.42% | 5.19% |
Bonus Lucky Ladies
Bonus Lucky Ladies is a $1 progressive side bet. I first noticed it on June 5, 2015 at the Palace Casino in La Center, Washington. Following is the pay table table. All wins are on a "for one" basis, meaning the player does not get his original wager returned on a win.
Bonus Lucky Ladies — Pay Table
| Player | Dealer | Pays |
|---|---|---|
| Queen of hearts pair | Dealer BJ in hearts | 100% of Jackpot |
| Queen of hearts pair | Dealer suited BJ (not hearts) | 25% of Jackpot |
| Queen of hearts pair | Dealer BJ (not suited) | 5% of Jackpot |
| Queen of hearts pair | Anything else | $125 |
| Matched 20 | Anything | $19 |
| Suited 20 | Anything | $9 |
The next table shows the probability and return of each event, based on six decks. A question mark means a variable win, depending on the jackpot size.
The table above shows the fixed wins return 31.19%. Each $10,000 in the meter will add 2.13% to the return. To reach break-even the jackpot would need to reach $328,372.59.
Analysis of Pay Table F
Following is my analysis of the progressive pay table F, based on six decks. Wins are on a "for one" basis.
Pay Table F Analysis ‐ Six Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Queen of hearts pair + dealer BJ | Jackpot | 33,840 | 0.000015 | ? |
| Queen of hearts pair | 25 | 684,585 | 0.000295 | 0.007365 |
| Suited 20 | 10 | 59,054,535 | 0.025414 | 0.254143 |
| Unsuited 20 | 2 | 186,215,760 | 0.080139 | 0.160277 |
| Loser | 0 | 2,077,685,100 | 0.894138 | 0.000000 |
| Total | 2,323,673,820 | 1.000000 | 0.421785 + ? |
The following table shows a return to player of 42.18%, not including the value of the jackpot. For every 10,000 bets units in the jackpot, the return increases by 14.56%.
I saw this as a "red light" $1 bet at the Rampart on January 29, 2021. At the time, the jackpot was $17,347.43. That would make the return at that time and place 42.18% + 14.56% × $17347/$10000 = 67.44%.