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:-
