Explanations

*What do you think about the discrepencies occurring between simulation results?With all due respect for Cacarulo, I don't think that the difference between index 0 and index -1 can be talked away with reference to truncating and flooring.*

But that's the way truncating and flooring treat indices. There's nothing wrong with it. Allow me to explain the difference between flooring and truncating in terms of buckets or bins:

__Truncating__

+----+---------+

| TC | Bucket |

+----+---------+

| +2 | [+2,+3) |

| +1 | [+1,+2) |

| 0 | (-1,+1) |

| -1 | (-2,-1] |

| -2 | (-3,-2] |

+----+---------+

__Flooring__

+----+---------+

| TC | Bucket |

+----+---------+

| +2 | [+2,+3) |

| +1 | [+1,+2) |

| 0 | [ 0,+1) |

| -1 | [-1, 0) |

| -2 | [-2,-1) |

+----+---------+

Note that all buckets have size 1 (one) except for the truncated "zero bucket" which is double. Here comes the difference and the reason of why flooring is better than truncating.

Now, let's say the exact index is -1.0. So you will hit TCs < -1.0 but stand on TCs >= -1.0. What happen at the -1 bucket in both methods?

If you're truncating then you should hit the buckets <= -1 but stand on buckets >= 0. That's why the index is zero.

On the other hand, if you decide to use floored buckets then you should hit the buckets <= -2 but stand on buckets >= -1. Thus, the index is -1. Do you see the difference?

*Anyway rounding would be more appropriate.*
That depends. Some times rounding is better and some times flooring is better. The important thing of both methods is that the buckets have the same size (=1).

__Rounding__

+----+-------------+

| TC | Bucket |

+----+-------------+

| +2 | [+1.5,+2.5) |

| +1 | [+0.5,+1.5) |

| 0 | (-0.5,+0.5) |

| -1 | [-0.5,-1.5) |

| -2 | [-1.5,-2.5) |

+----+-------------+

*I'm still waiting to see a simulation result that will yield decimals instead of integers.*
It can be done with SBA. There's a trick for doing it that works pretty well. Suppose you want an exact index with one decimal using Hi-Lo:

1) Multiply the Hi-Lo tags by 10 getting the following system:

(-10 10 10 10 10 10 0 0 0 -10)

2) Generate the index you want

3) Divide the index found by 10

4) voila! there's your index with one decimal

Believe me, this method works!

*My -1.3 was obtained by calculation on the basis of an infinite deck and should be valid for any shoe game S17.*
If instead of using an infinite deck approach you used a 6-deck approach you would obtain an index of -1.0.

Hope this helps.

Sincerely,

Cacarulo