Difference between indices of 0 and -1 when flooring

[Tarantula]

I was having a discussion elsewhere about Don Schlesinger's new complete guide to index play, and we started talking about indices of 0 and -1, such as for 12v4 and 13v2 respectively. Specifically, how are those indices treated differently?

I'm used to truncating my TCs, so in that context it makes sense for 0 and -1 to be distinct. But for flooring, I would assume that any TC >=-1 and <0 should floor to -1. And as far as I conceive, that would eliminate any distinction between 0 and -1 indices.

I am not super well-read and haven't seen Don's other work, so I haven't been able to square this. Can anyone set me straight?

[Gronbog]

I was having a discussion elsewhere about Don Schlesinger's new complete guide to index play, and we started talking about indices of 0 and -1, such as for 12v4 and 13v2 respectively. Specifically, how are those indices treated differently?

I'm used to truncating my TCs, so in that context it makes sense for 0 and -1 to be distinct. But for flooring, I would assume that any TC >=-1 and <0 should floor to -1.

Yes.

And as far as I conceive, that would eliminate any distinction between 0 and -1 indices

Well no, because any TC >= 0 and < 1 floors to zero.

As an additional aid, when flooring, indices of zero can be employed based on the running count alone. If RC >= 0, the index applies.

[Tarantula]

Well no, because any TC >= 0 and < 1 floors to zero.

As an additional aid, when flooring, indices of zero can be employed based on the running count alone. If RC >= 0, the index applies.

That makes sense for mathematical flooring, but why wouldn't something at a 0 index just be basic strategy in that case?

[Gronbog]

It is a common misconception that TC=0 strategy is the same as basic strategy. 16 vs T is the most obvious difference but there are others depending on the rule set. To understand why, remember that basic strategy is for playing your first two cards, head to head vs the dealer off the top of the shoe. Then relate that to what I said about indices of zero and the running count (i.e. what is the running count when you are looking a two card 16 vs T?)

[Tarantula]

That's a good point, and it makes perfect sense for 16vT since it always creates an RC of -1. And at RC 0 it's extremely close to equal EV for standing/hitting, tilting one way or the other in 6D based on exact deck composition.

But I'm still a bit confused on 12v4. All the basic strategy I've seen is to stand, and that makes sense since the average RC would be ~1.6 (based on the average RC from the 8 two-card combinations to make a player 12). So why would we deviate at a floored index of 0? Is the deal just that Don's BS is to hit 12v4?

[Gronbog]

No. There is no discrepancy for 12 vs 4. The index to stand is zero. The RC is always positive for a two card 12 vs 4, so we stand which once again agrees with basic strategy.

[Freightman]

In simplest terms
In positive situations, the value floored or truncated is the same value.
In negative counts, flooring reduces to the lowest value, therefore -1.5 is floored to -2.
Truncation always heads in the direction closest to zero, therefore, +1.5 truncates to 1 and -1.5 truncates to -1.

[BJGenius007]

I was having a discussion elsewhere about Don Schlesinger's new complete guide to index play, and we started talking about indices of 0 and -1, such as for 12v4 and 13v2 respectively. Specifically, how are those indices treated differently?

I'm used to truncating my TCs, so in that context it makes sense for 0 and -1 to be distinct. But for flooring, I would assume that any TC >=-1 and <0 should floor to -1. And as far as I conceive, that would eliminate any distinction between 0 and -1 indices.

I am not super well-read and haven't seen Don's other work, so I haven't been able to square this. Can anyone set me straight?

My simulator program said at TC 0.1, players should stand regarding 12 v 4. At TC -0.1, player should hit. At TC 0.0, you flip a coin. So for every book, no matter they choose stand or hit on 12 v 4, they are all half right and half wrong. Note my simulator can exclude samples too rich or too poor on Ace or mid-cards (8 and 9) if I want to. If I conduct the simulations to include all samples, or simulation with only neutral ace shoes, or simulation with only neutral mid-card shoes, all reach the same conclusion. IMO when Basic Strategy was formulated, there was 50% of the chance that the book said players should hit on 12 v 2, 12 v 3, 12 v 4.

[Cacarulo]

Many years ago, many of us were taught that "truncating" was the correct method for rounding a TC. As time passed, it became evident that "flooring"
was a more accurate approach, given that all TC bins were of equal size. The issue with "truncating" always revolved around bin "0" because it was twice the size of the other bins.

The problem lay in the fact that no simulator made the effort to divide bin "0" into two equal parts, namely "0+" and "0-", mirroring the size of the other bins.
This means that if we were to segregate the indices that equate to "0" into "0+" and "0-", we could continue to employ the "truncating" method without encountering any complications.

For instance, in Hi-Lo, 16vT and 12v4 would fall into the "0+" category, while 12v6, 13v2, and 9v3 would belong to the "0-" category.

Sincerely,
Cac

[Tarantula]

Thanks all for the replies. I appreciate the details here, and it has helped me with the 0 index. Your explanations make perfect sense especially in the context of 16vT, where basic strategy differs from RC = 0 strategy.

I think in terms of actual playing decisions & EV, I was and am fine, which is most important and good to know. But on an intellectual level, I'm still a bit thrown by 12v4, which does not have the same misalignment between basic strategy and RC = 0 strategy that we see in 16vT. Basic strategy says to stand, and RC = 0 strategy says to stand. So why wouldn't the index to hit be -1?

BJGenius007 nailed how this is basically an academic distinction. I just want to understand what drove the decision for it to be 0, rather than -1. Is it because this decision point is so centered on RC = 0 that Don wants to highlight that fact? Is it an unknowable mystery? Something else? All these are fine, I just want to know.

[Gronbog]

You're making the mistake of thinking of indices as counts where we deviate from basic strategy above the index. This is not the case. They are simply the counts at which the decision changes from one play to another. In the case of 12 vs 4, the index to stand instead of hit is zero and I did show that it is in agreement with basic strategy. The actual deviation is to hit below the index.

[Tarantula]

You're making the mistake of thinking of indices as counts where we deviate from basic strategy. This is not the case. They are simply the counts at which the decision changes from one play to another. In the case of 12 vs 4, the index to stand instead of hit is zero and I did show that it is in agreement with basic strategy

Ooooooooohhhhhhh, well that solves it, yes. I was looking at indices as deviations (a la the BJA charts).

There we go, all set. Thank you! (:

[aceside]

There is confusion here. By basic strategy, you mean the pre-deal TC=0 situations; by card-counting TC=0, you mean the post-deal TC=0. They are quite different for single and double deck games.

Regarding the truncating or flooring argument, I used to believe that truncating is the more scientific rounding function; however, recently I started to think that flooring should produce more EV because the EV versus TC function is a lot more nonlinear at negative TCs, so it makes more sense to analyze these situations with more discrete negative TC numbers. Need your confirmation on this part.