Player Loss

How to deal with Actual Loss in the casino industry.
By Andrew MacDonald
Gaming Manager, Casino Operations, Adelaide Casino, 1993
Casino Analyser
Reference

Rebate on Loss

Introduction | What is the cost of rebating? | How large a value? | Unit Normal Linear Loss Integral | Baccarat (Player/ Bank 50% Equivalent) | Roulette (single number play on single zero Roulette) | Conclusion |


To more accurately calculate the percentage to be rebated it is merely necessary to utilise smaller sections when integrating and refer to normal distribution tables for the probabilities or to utilise a lesser known statistical function referred to as the “UNLLI” or Unit Normal Linear Loss Integral. This is basically analogous to the sum of all possible values of a standard normal variables positive distances above the number “a”, multiplied by their corresponding probabilities of occurrence.

To put this into practice the following steps may be followed:-

1. Find expected loss for the player.

2. Find standard deviation of player result.

3. Calculate z = expected loss / standard deviation.

4. Look up UNLLI table corresponding to z (see table below).

5. Multiply UNLLI value by standard deviation.

6. Add number calculated from point 5 to number calculated from point 1.

7. Take whatever percentage of point 1 is to be returned and divide by the result of point 6.

Example:-

Hands = 750
Edge = 1.25%
Payouts = even money
Theoretical loss equivalency = 50%

1. 750 x 1.25% = 9.375
2. square root (N) 750 = 27.386
3. 9.375 / 27.386 = 0.342
4. UNLLI = 0.2508
5. 27. 386 x 0.2508 =
6.868 6. 9.375 + 6.868 = 16.243
7. 9.375 x 50% / 16.243 = 28.859%

Unit Normal Linear Loss Integral (table)

 

Z .00 .02 .04 .06 .08
0.00 .3989 .3890 .3793 .3697 .3602
0.10 .3509 .3418 .3329 .3240 .3154
0.20 .3069 .2986 .2904 .2824 .2745
0.30 .2668 .2592 .2518 .2445 .2374
0.40 .2304 .2236 .2170 .2104 .2040
0.50 .1978 .1917 .1857 .1799 .1742
0.60 .1687 .1633 .1580 .1528 .1478
0.70 .1429 .1381 .1335 .1289 .1245
0.80 .1202 .1160 .1120 .1080 .1042
0.90 .1004 .0968 .0933 .0899 .0866
1.00 .0833 .0802 .0772 .0742 .0714
1.10 .0686 .0660 .0634 .0609 .0585
1.20 .0561 .0539 .0517 .0496 .0475
1.30 .0456 .0437 .0418 .0401 .0383
1.40 .0367 .0351 .0336 .0321 .0307
1.50 .0293 .0280 .0268 .0256 .0244
1.60 .0233 .0222 .0212 .0202 .0192
1.70 .0183 .0174 .0166 .0158 .0150
1.80 .0143 0..0136 .0129 .0122 .0116
1.90 .0110 .0104 .0099 .0094 .0089
2.00 .0084 .0080 .0075 .0071 .0067
2.10 .0063 .0060 .0056 .0053 .0050
2.20 .0047 .0044 .0042 .0039 .0037
2.30 .0036 .0034 .0032 .0030 .0028
2.40 .0027 .0026 .0024 .0023 .0022
2.50 .0021 .0018 .0017 .0016 .0016

For the game of Baccarat it is then possible to calculate the following table:-

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2018-09-12T05:01:44+00:00