A couple of examples
<em>It doesn't buy you all that much, just on the average adds/subtracts a few cards from play. But if you were playing a shoe game where you knew a couple of 5's had been thrown in the trash can, pretty good deal no? Once you calculate those two points, it's basically a freebie.</em>
Nice post. As you say, it doesn't buy you much, but it is better than nothing for virtually no effort.
A couple of examples might give other readers some idea of the likely value of this approach.
The tables below use the following key:
d = shoe size (in decks)
p = penetration point (i.e., the amount of decks before the shuffle card)
k = the amount of cutoffs
a = the amount of cutoffs cut into play
Nm = the expected amount of cutoffs in play with no smart cutting
Dv = deviation from the normal amount of cutoffs in play with smart cutting
AvBig = average number of big cards cut into play when cutoffs rich
AvSmall = average number of small cards cut out of play when cutoffs poor
N = number of pseudo decks in the played shoe (only relevant if the NRS approach is used)
r = multiplier (only relevant if the NRS approach is used)
(NB. I have arbitrarily assumed that when the count of the cutoffs is zero, the player cuts to minimize the number of cutoffs in play.)
Code:
Table 1
d p k a Nm Dv AvBig AvSmall N r
8 6 2 2.00 1.50 0.50 2.17 7.71 -0.43
1.90 1.50 0.40 1.74 7.81 -0.35
1.80 1.50 0.30 1.30 7.89 -0.26
1.75 1.50 0.25 1.09 7.93 -0.22
1.70 1.50 0.20 0.87 7.95 -0.18
1.60 1.50 0.10 0.43 7.99 -0.09
1.50 1.50 0.00 0.00 8.00 0.00
1.40 1.50 -0.10 0.39 7.99 0.09
1.30 1.50 -0.20 0.78 7.95 0.18
1.25 1.50 -0.25 0.98 7.93 0.22
1.20 1.50 -0.30 1.18 7.89 0.26
1.10 1.50 -0.40 1.57 7.81 0.35
1.00 1.50 -0.50 1.96 7.71 0.43
0.90 1.50 -0.60 2.35 7.59 0.51
0.80 1.50 -0.70 2.74 7.46 0.58
0.75 1.50 -0.75 2.94 7.38 0.62
0.70 1.50 -0.80 3.14 7.31 0.65
0.60 1.50 -0.90 3.53 7.14 0.71
0.50 1.50 -1.00 3.92 6.97 0.77
0.40 1.50 -1.10 4.31 6.78 0.83
0.30 1.50 -1.20 4.70 6.59 0.88
0.25 1.50 -1.25 4.90 6.50 0.90
0.20 1.50 -1.30 5.10 6.40 0.92
0.10 1.50 -1.40 5.49 6.20 0.96
0.00 1.50 -1.50 5.88 6.00 1.00
Table 2
d p k a Nm Dv AvBig AvSmall N r
6 4 2 2.00 1.33 0.67 3.08 5.33 -0.67
1.90 1.33 0.57 2.62 5.50 -0.58
1.80 1.33 0.47 2.16 5.65 -0.49
1.75 1.33 0.42 1.93 5.72 -0.45
1.70 1.33 0.37 1.70 5.78 -0.40
1.60 1.33 0.27 1.23 5.88 -0.29
1.50 1.33 0.17 0.77 5.95 -0.19
1.40 1.33 0.07 0.28 5.99 -0.07
1.33 1.33 -0.00 0.00 6.00 0.00
1.30 1.33 -0.03 0.14 6.00 0.04
1.25 1.33 -0.08 0.35 5.99 0.09
1.20 1.33 -0.13 0.55 5.97 0.15
1.10 1.33 -0.23 0.97 5.91 0.26
1.00 1.33 -0.33 1.38 5.82 0.36
0.90 1.33 -0.43 1.80 5.70 0.46
0.80 1.33 -0.53 2.21 5.56 0.56
0.75 1.33 -0.58 2.42 5.48 0.60
0.70 1.33 -0.63 2.63 5.39 0.64
0.60 1.33 -0.73 3.04 5.21 0.72
0.50 1.33 -0.83 3.46 5.02 0.78
0.40 1.33 -0.93 3.87 4.82 0.84
0.30 1.33 -1.03 4.28 4.61 0.89
0.25 1.33 -1.08 4.49 4.51 0.92
0.20 1.33 -1.13 4.70 4.41 0.94
0.10 1.33 -1.23 5.11 4.20 0.97
0.00 1.33 -1.33 5.53 4.00 1.00
EXAMPLE from Table 2:
The second table says, for instance, that if you are playing a 6-deck game where 4 decks are dealt, and the maximum amount of cutoffs that can be cut into play is 1.8 decks (out of a possible 2 decks), then of the times in which the cutoffs are rich, on average you will cut in 2.16 extra big cards.
Of course, if the cutoffs are poor, you will want to minimize the number of cutoffs in play. Suppose the minimum amount of cutoffs that can be cut into play is 0.75 decks. Then of the times in which the cutoffs are poor, on average you will cut 2.42 extra small cards out of play.
Obviously the further you can get away from normal dispersion of the cutoffs the better. If the cutoffs were distributed perfectly evenly throughout the shoe, the deviation from normal dispersion would be zero, and the gains from this approach would also be zero.
The simplest way to approach the situation described in this example would be to treat the game in the normal fashion; i.e., as a 4/6 game and an IRC of zero. Your indices and betting will err on the side of caution, which is not a serious problem, given that the shift in true-count distribution will only be subtle in the average case.
Improvement can be obtained by using the NRS parameters. When the player can cut 1.8 decks of cutoffs into play, table 2 indicates that the appropriate choice of N is 5.65 and r is -0.49. So, for instance, if the running count of the cutoffs is -6, set your IRC to +3 and treat the game roughly as if it were a 4/5.65 deck game.
Similarly, when the player cuts a minimum of 0.75 decks of cutoffs into play, the appropriate parameters are N = 5.48 and r = 0.6. If the running count for the cutoffs is +7, set your IRC to +4 and treat the game roughly as if it were a 4/5.5 deck game.
NOTE: There is a subtle but important difference between a literal game with N decks and the pseudo (NRS) game we are playing here. Specifically, with the NRS pseudo game we need to be sure that we will complete the round without the shuffle card being reached. This is because the cutoffs supposedly excluded from play due to the player cut come back into play once the shuffle card has come out. In other words, only use the NRS running count if the entire round can be dealt before the appearance of the shuffle card. (Aside: It is possible to treat the round involving the shuffle card as a boundary and base the bet on this boundary information, which I have described elsewhere.)
Although on average the impact of this sort of cutting on the true-count distribution will be small, in individual cases the effects can be more worthwhile. Continue considering the 4/6 game. From time to time the 2 decks of cut offs will have more extreme running counts. A cutoff running count outside the range [-6,+6] will occur about 37% of the time. About 15% of the time the cutoffs will have a running count outside the range [-10,+10].
This means that some shoes will be much more appealing than the average. For instance, if the cutoffs have a running count of -10 and the maximum amount of cutoffs that can be cut into play is 1.8 decks, then you are entitled to set your IRC to +5, giving an initial true count of almost +1 for the 5.65 deck pseudo game. If the cutoffs have a running count of +/-15 (cases this extreme or more extreme occur about 4.7% of the time), then you can set your IRC to +7 or +8, depending on the precise case.
Needless to say, if the cutoffs are more evenly dispersed throughout the shoe, the gains from this approach are even more modest. If the maximum amount of cutoffs that can be cut into play is only 1.6 decks, then in cases where the cutoffs are rich, the player will only cut an average of 1.23 extra big cards into play. The gains from the NRS approach are also reduced, N rising to 5.88 and r shrinking to -0.29. Then even a running count of +/-10 for the cutoffs would only justify an IRC of about +3 and an initial true count of just over +0.5. Just as obviously, if the cutoffs are less evenly dispersed, the gains can be greater than in the examples discussed above.