Can You Disguise Your Insurance Bet?
by Jake Smallwood
[From Blackjack Forum Vol. VIII #2, June 1988]
© 1988 Blackjack Forum
After a recent blackjack trip I was chastised by my teammates. They objected to the fact that, as a part of my card counting camouflage, I was taking insurance on everything but my minimum bet. The consensus was that I had fallen into “idiot” camouflage. I decided to get an idea of what my insurance yield should be and just how much I was giving up with my insurance camouflage plays. Most of my card-counting play (that particular trip) was on double deck blackjack games using the Hi-Lo count with a 1 to 20 spread ($10 to two hands of $100 actually). My betting scale is proportional only in the sense that my top bet is about half Kelly in size after accounting for two-hand covariance.
In order to simplify, I decided to set up three schedules of count per deck (true count) with the assumption that one deck of the two had been played. One schedule was developed with the quantity of each card type (plus, minus, zero valued cards) held constant for each table.
Of course, the sample would have been much more representative if I had prepared tables that took each group of cards with normal density, half normal density, and one-and-a-half normal. But that would be a lot of work and would require weighting by the probability of occurrence of each of the nine subsets. After all, I only wanted an indication, not a high-precision answer.
For all tables I assumed that 20% of the minus-valued cards (tens and aces) were aces. The result was a “profile” of a 52-card remainder for the counts between plus and minus six. I had some old frequency distribution approximations around which I used to weight for the occurrence of each count in the table. The insurance result was tabulated for each of the 52 cards in the remainder to estimate the edge at that count for that type of remainder subset.
The traditional blackjack player who insures at +3 or more count per deck would make about a 2.5% profit on insurance action. With a 20 to 1 spread the “insure all” approach would about break even.
The way I have been playing costs me about 15% of my potential insurance edge.
Actually, the cost is less since at +2 I am betting at two greens but only taking two reds of insurance. The pit knows I can’t be bothered taking more insurance with only two green out. I assume also that there is some element of risk aversion in the sense of fluctuation leveling with taking some negative expectation insurance. Any such effect is ignored.
Now, with my dumb style of play, I often get the pit personnel urging me to bet at 40 to 1 ratios and more. Well, what do you think? Based on the evidence, should I give up my idiot insurance camouflage?
[Snyder comments: It’s easy to see what Jake has done here and why his idiot camouflage works so well. Since he never insures his minimum bets, he doesn’t take insurance at those times when the house has its largest insurance advantage-at low counts. Since he always insures all bets above minimum, he always takes insurance when he has the advantage on these hands (high counts). The hands on which he took the insurance bet when the count was too low for this to be the proper play would for the most part be close to the “borderline” for taking insurance. Very little is actually given up on these incorrect insurance bets.
As a card counting camouflage strategy, Jake’s psychology is sound. Many gamblers and high rollers ignore insurance on insignificant bets. They seem to consider it a waste of time to insure piddling amounts of money.]
Insurance Return for Three Styles
Insure All Approach
| Cards Constant | Action | Return | % |
|---|---|---|---|
| 7,8,9 | 496.0 | -6.37 | -1.28 |
| 2, 3, 4, 5, 6 | 496.0 | 45.58 | 9.18 |
| 10, Ace | 496.0 | -38.19 | -7.29 |
| 14488.0 | 1.02 | .21 |
Insure +3 or More (Traditional)
| Cards Constant | Action (a) | Return (b) | % |
|---|---|---|---|
| 7, 8, 9 | 380.0 | 2.86 | -.75 |
| 2, 3, 4, 5, 6 | 380.0 | 56.18 | 14.78 |
| 10, Ace | 380.0 | -29.26 | -7.71 |
| 380.0 | 29.78 | 2.61 |
Insure All Except Minimum (My Style)
| Cards Constant | Action (c) | Return (d) | % |
|---|---|---|---|
| 7, 8, 9 | 427.5 | .86 | .20 |
| 2, 3, 4, 5, 6 | 427.5 | 56.89 | 13.31 |
| 10, Ace | 427.5 | -32.92 | -7.70 |
| 1282.5 | 24.83 | 1.94 |
Notes
- Sum count per deck of 3 to 6+.
- Cumulative win for count per deck of 3 or more.
- Sum count per deck 2 or more.
- Cumulative win for count per deck of 2 or more. ♠