Insurance for Games without 10's

I got a request to help calculate the insurance index for the game without 10's (you know which one!) so I figure I would post the results here. If the requester wishes to be known, he/she can speak up here!

Okay, here it goes. All my methodology is based on http://www.blackjackforumonline.com/content/AlgebraicIndices.htm

Firstly, the insurance EV off the top is:
EV_Top = 12/48 * 2 + 36/48 * -1 = -1/4

Then, we want the EOR for a given card. So let's remove a non-ten.
EV = 12/47 * 2 + 35/47 * -1 = -11/47
EOR_NonTen = -11/47 - (-1/4) = 3/188

The EOR of a ten is:
EV = 11/47 * 2 + 36/47 * -1 = -14/47
EOR_Ten = -14/47 - (-1/4) = -9/188

As a proof of concept, let's make sure the EOR = 0 for a full 48-card deck:
36 * 3/188 + 12 * -9/188 = 0

Next, we will use a simple ace-neutral count with 2,7,8,A as 0, 3-6 as +1, and 9-X as -1 in an 8-deck shoe (384 cards).

Since the Aces aren't counted, we don't need to rebalance the tags after we remove an Ace (read the website above). For Ace-reckoned counts, it becomes a bit more complicated, but easily do-able.

The equation from the website requires the sum of squared tags (y) for the entire shoe, which yields y = 127 * 0 + 128 * (1)^2 + 128 * (-1)^2 = 256. So we have TC * (+/- 1) * 383/256 for each card. This would be different if the tags had to be rebalanced.

We can then combine all the EV's to determine the overall insurance EV at a given count:
EV =
-1/4 + <-- Off the top
3/188 * 47/383 + <-- Dealer's Ace upcard
127 * TC * 0 + <-- 2,7,8,A are 0 since they aren't rebalanced
128 * TC * 383/256 * 3/188 * 47/383 + <-- 3 through 6
32 * TC * -383/256 * 3/188 * 47/383 + <-- 9
96 * TC * -383/256 * -9/188 * 47/383 <-- Faces

Simplifying:
EV = 9/8 * TC - 95/383

Setting EV to 0, we get:
9/8 * TC = 95/383
TC = 760 / 3447

Then, we use the equation in the website above to get the index:
Index = (760 / 3447 - 1/383) * 48 = 12061/1149 = 10.46

So when the TC > +11, take insurance.

In the first place; that's a pretty backwards method for counting that game. The best way to count a SP21 game is to simply start counting the 8-deck shoe with an off-the-top RC of -32. That way, EVERYTHING - including insurance; correctly falls into place.

Counting systems are "linear approximations" of deck variation play, they are by no means exact. They apply best if the counting system is designed for the average deck.
Although you make most money when far off the average deck, this is the regime where counting systems are less effective. That is not a problem of counting systems - it is the nature of linear approximations.

In the above game, you may technically use a BJ system with RC=-32. But the counting system far off the average 0 has less efficiency. But since this is the true average deck, it's much better to design the counting system from that position, and use linear approximation there.

This is the way everyone I know has been doing it since the game was introduced more than a decade ago. It makes it very simple to switch back to standard BJ games as the AP sees fit.

In order to use a count that starts with 0 you would have to assign different values to the cards in order to balance the count. I have never read KW's book (supposedly the best book on the game), but I'm told that SHE advises the reader to start with a negative count. Obviously; the TC conversion will be slightly different because of the fact that the deck only has 48 cards, and the playing indices will also be much different because of the rules; but this will be true no matter HOW you count the game.

Indeed, your recommendation is a fine way to count this game (and one I advocate to others!). However, I personally use a different counting system tailored to this specific game which includes side counts. That's why I had to help develop a method for figuring out the insurance index for different counts.

Assume_r's method offers a significantly higher SCORE for this game.

Unlike blackjack where the level 2 counts and side counts aren't worth as much.

Wouldn't This Work

If you apply a regular count, just adjust for the missing 10s and take insurance at normal index.

You'd have to start at a non-zero IRC, and then all your TC's won't center around 0. For example, using HiLo with this game, the IRC is -32 for 8-decks, and it centers around -4. So you'd have to recompute the index regardless, and it wouldn't necessarily be the same as in regular blackjack.

The other reason, besides that, is that the Insurance Effect of Removal is significantly different in this game. For HiLo, for example, the Aces contribute 1/4 of all the -1's (high cards), while in regular blackjack, the Aces contribute 1/5 of all the -1's (high cards) and hence the index must be adjusted accordingly, as I did in the original post.

Brute Force

centers around -4? I guess you mean per deck? I agree.
The index would be the same if insurance pays the same. Its the same as if the first 32 cards dealt were all 10s in an 8 deck shoe, you agree? The insurance bet is a ratio bet.

The effect of removal is different if you don't adjust for the missed 10s, we agree?

I did not check your math so am not commenting on the correctness of your post.

I see two options:
Learn a new game with no 10s
Adjust one's play for the loss of 10s

I believe so, but it would be slightly off. In your example you're pretending that you only have 7.5 decks remaining, which becomes your maximum TC divisor.

However, in actuality, you should be dividing by groups of 48 cards remaining. Just pretending the first 32 cards were 10's, and using the traditional HiLo index of +4 (or 8 above your neutral count of -4) might be close.

Agree, I Think

There should be no change. The first 32 cards out of the pack are indeed 10s. They were just removed pre shuffle, so the remaining pack is deficient that many cards. So when you consider your divisor you are just looking at the remaining cards in the shoe. So with the first hand it is approx 7.5 decks remaining as you state.

Right, but that's not how you should calculate the TC for this game, especially when you sim it. So if you indeed used 7.5 as your initial divisor, and -32 as your IRC, then you could probably just use the regular blackjack index. But people who play this game use 8 as the initial divisor. And that changes the frequencies of getting each TC and the actual proportion of remaining 10's for each TC.

depends on how one plays?

One can create & learn a whole new system or apply existing techniques. Would imagine existing methods would be easier to use but less profitable. For this game applying old BS would probably be costly, so wonging would be needed

In this game if one were to use regular B.S. they'd be playing at a 3% disadvantage, and hence learning a whole new system is required, not optional

not quite

A lot of employed neg. indices would work or don't play when negative. Yes. Off the top normal BS would be poor

With all the different bonus payouts and doubling and surrender rules it is a totally different game than blackjack. Don't fool yourself into thinking the strategy is similar. It was purposely designed to be as different a game strategy wise as possible. That is where the money for the casinos lie. People playing horrible strategy because they assume it is similar to blackjack.