Example of Luck Adjusted

Let's suppose you are the first player, and you are about to draw your last card. You are drawing to a flush and have 7 outs in 28 cards, so there is a 25% chance that you hit. Let's suppose that the net evaluates every flush as 10 (sweep + 4 royalty), and every miss as -6. The weighted average of these is -2. If you hit the flush, the net estimates that you are lucky by 12 points. If you miss, the net estimates that you are unlucky by 4 points. On average, your luck is 0. If you simulate this situation without luck adjustment, you sometimes get +10 and sometimes -6, and these might not balance out. With luck adjustment, you subtract the 12 points of estimated good luck from the +10 results to get -2, and you add +4 to the -6 results to get -2. In this example, the luck adjustment is perfect, and the simulation would converge instantly to the correct result of -2, while a simulation without luck adjustment would take hundreds of games to say the result should be -2 +- 0.5.

In general, the situations will be so complicated that the net's evaluations are not perfect. The luck adjustment will still help the results converge in fewer trials without adding any bias. For example, if the net is wrong and thinks hitting is worth +8 and missing is -4, then it will say hitting is lucky by 9 points and missing is unlucky by 3 points. The adjusted result when you hit will be 10-9 = +1, and the adjusted result when you miss will be -6+3 = -3. The weighted average of -3 when you miss and +1 when you hit is still -2. If you add up +1 when you hit and -3 when you miss, this will converge to -2 faster than if you add +10 and -6. The fluctuations around the correct long run result of -2 would be 4 times as small by using luck adjustment.