Chapter 12. Side Bet Data

First a few general comments on side bets. Competition caused by growth in the casino industry has resulted in numerous new side bets including: 21+3, Big Slick, Bonanza BJ, Dare any Pair, Field of Gold, High Tie Bonus, Lucky Ladies, Lucky Lucky, Match the Dealer, Over/Under, Pair Square, Perfect Pairs, Royal Match, Super 7's, Sweet 16 and Streak. Most side bets have shockingly large house advantages and should be avoided at all costs. However, some can be beaten. In some cases the normal card counting strategies are used. You can increase the edge by using specialized side counts — but these greatly complicate the game. Some side bets, like Red/Black, require specialized counts. Newer side bets usually include multiple payoffs. For example, Lucky Ladies pays different amounts for Two Queen of Hearts and a dealer BJ, Two Queen of Hearts, a matched 20 (two identical cards adding to 20), a suited 20 and an unsuited 20. Also note that some side bets have a fixed or maximum bet amount, a capped payout or a bet size relative to the main bet. Also, different casinos may have different payout tables for the same side bet. The payouts for Lucky Ladies used on this page are 1000:1, 125:1, 19:1. 9:1 and 4:1.

"These foolish games are tearing me apart" — Jewel, 1999


How do we card count Lucky Ladies?

Let us look at the Lucky Ladies side bet using standard Hi-Lo as the card counting strategy. First the good news. Although LL has an outrageous 25% house edge at a true count of zero, the advantage changes dramatically as the count changes. This chart plots the advantage by true count. We can see that the advantage turns positive at true count +7 and continues to increase substantially above that. So, if we make the side bet only with a TC of +7 or higher, we gain a theoretical advantage and "beat" the side bet. So far, so good.

Where do I win?

Let's look a little more deeply. The next chart displays only true counts of +5 to +15. The red bars indicate the amounts bet on Lucky Ladies assuming that you always make the side bet. The other colors indicate the amounts won. You will note that the red bar is taller at true counts of +5 and +6 indicating these are bad bets, and shorter at higher counts indicating positive EV bets. But, the winning amounts have been broken down into the five different payouts.

What we see here is that half of the return comes from the winnings for unsuited 20s, represented by the green bar. This is good news as variance would be too high if a rare event was behind most of the overall payoff.

The cyan colored area at the top of the payoff bars represents the 1000:1 payoff for a pair of heart queens and dealer Blackjack. The payoff is 1000:1, but it only occurs about 1 in 70,000 hands in a six-deck game. The amount is relatively small, but our actual results will vary an appreciable amount depending on whether we receive 0, 1 or 2 of these hands after playing a huge number of hands. What this means is that although we have a theoretical edge, at counts of +7 and +8, a major part of our advantage depends on a rare event. This adds to our risk.


How often do I win?

This chart shows the frequency of wins for the five different payouts by true count. The y-axis uses a logarithmic scale because the differences in frequencies are so large. All payouts increase in frequency as the count increases. The red line indicates the frequency of the top payoff. We can see that at a true count of +7 it occurs about .003% of the time.


What are the overall results?

This chart is a quick look at overall results both in terms of EV (expected value or advantage) in green and SCORE in red. The first column provides EV and SCORE for Hi-Lo if we never take the Lucky Ladies bet. The EV scale can be found at the left and SCORE scale at the right. Now let us make a LL bet equal to our max bet with all counts of +7 and above. We see that the EV climbs from 1.35% to 2%. But, the SCORE drops. This is because SCORE is risk-based and includes the standard deviation of the Lucky Ladies side bet. The SD is much higher with LL. So, let's try increasing the point at which we make the bet. If we make the bet only with a true count of +9 or higher, the SCORE and EV are both higher than when making no bets at all. However, the count is rarely that high.

In conclusion, yes we can make money at this bet. But unless the penetration is very deep, the bet is not as good as it first looks.


Sim details

  • Six decks, S17, DAS, Heads-Up, Hi-Lo, truncate, Sweet 16 indexes, half-deck resolution, penetrations 5/6 penetration, Spread $10-$150
  • Five-ten billion rounds each


copyright © 2007, Norm Wattenberger, All rights reserved