PART #1

The Only Way to Win and the Unclimbable Mountain


If I offered you 98 cents in exchange for a dollar you would likely refuse the wager, yet this is exactly the type of exchange that most casino patrons accept every day. There is no functional difference between handing the casino a dollar and getting back 95 cents and a dollar wager made on roulette, yet one is accepted and the other is rejected. Why is this? It's because one situation contains a random element and the other does not, making the two nearly identical situations seem very different in our minds. We humans simply aren't very good at quantifying randomness. Here are the three main issues that address this particular human failing.

1.There are many cognitive biases which make the accurate in-head evaluation of random events impossible for anyone. It is not a mental deviation to which some rare gifted individuals are immune. It is a ubiquitous human trait we all share. People who follow the math appear to have limited immunity; they do not. What they have is a workaround (more on this later).

2.If people apply different logic to identical situations they will often come to different conclusions, as happens in gambling situations. The only way to resolve something like this is to move back from your original conclusions and evaluate the decision making process itself. Where randomness is involved this is difficult because the human mind is not wired to identify, understand or comprehend randomness. Evolutionarily we have developed nothing but pattern recognition infrastructure. All learning and thought (patterns of neurons) is by definition pattern driven; what goes with this, what goes with that, what has to do with something else, etc... Our brains are pattern using, pattern driven, pattern creating, pattern recognition engines that without patterns would be lumps of fat.

3.Therefore, by using different logic for identical situations we get different results. No one should accept less than a dollar for a dollar in a fair exchange, yet they do because their minds lead them astray.

A Shortcut to Heuristics
Let's talk for a moment about heuristics and cognitive biases. Cognitive biases are not insanities, nor are they unusual, aberrant, or in any way exceptional. They are simply a description of how all minds work. The human mind (the animal mind as well) cannot always (or ever) make decisions with perfect and complete information. Conventional thought therefore uses heuristics (short cuts) to reach decisions when perfect information is not available (sadly, that's most of the time). Total reliance on heuristics, which are inherently biased for decision making even when more complete information is available, can lead to cognitive distortion (very common). Only when an individual is completely unaware and unwilling to accept that they have made a snap decision based on imperfect information when better and more complete information is readily available does the field of psychology step in and say, “Hey, you might have a problem”. Taking a shortcut when another way is quicker and safer is imprudent.

If you wished to buy a car in under a lifetime, you would not look at (and test drive) every car available. You would look in the paper, pick out a few that fit your criteria, and make your purchase, knowing full well that you were using a time saving shortcut (heuristic). Only if you insisted that buying a car after looking at only four of them was as accurate as looking at thousands of them and then buying (assuming doing so was equally easy) would your biased application of a common useful heuristic be upgraded to a mental problem. The two methods of car acquisition are not equal in time expenditure, so the see-four-and-buy method is probably preferable, even if it is obviously inferior in result. To think that your chances of getting the best deal looking at four cars or a thousand would be equal in result is insane. As long as you know you are taking a shortcut that is likely to have an inferior result, but is far superior in time usage, you are fine.

The Road Not Taken
Perhaps the most problematic bias that effects casino patrons' perceptions is the attentional bias. If left unchecked it will ride roughshod through what's left of our rational thought, leaving confirmation bias and the illusion of control in its wake. The classic textbook example of attentional bias is when one states emphatically that God answered their prayers, without considering all the times in their life they prayed and didn't get what they asked for, all the times they got something they wanted and hadn't prayed, and the even more common, not asking and not getting.

There are four (+1: the base rate occurrence of whatever was asked for) avenues of information that are imperative to make a rational and accurate assessment of whether or not God was really the source of one's wish fulfillment. If we assign “P” for praying and “G” for getting what you asked for , and use plus and minus symbols to signify their presence or absence we get:

1.+P +G = Praying and getting
2.+P -G = Praying, but not getting
3.-P +G = Not praying, but getting anyway
4.-P -G = Not praying, and not getting (most common)

In the biased (normal) mind only option #1 is given attention with options 2-4 being completely overlooked, or intentionally ignored. What we are left with is unfounded confirmation in the prayer's mind. The only way to confirm this scientifically would be to go back in time, do nothing different except for refraining from praying, and see if one then failed to get the what they had asked for in the other time-line. That's one way to say “It's not possible to be sure of anything.” The believer says, “I prayed, I got. End of story. Logic be damned.” 75% of the information needed to make an informed decision is not present and not available, yet people seem very happy to declare the puzzle completed with only 25% of the pieces present.

Where this bias rears its ugly head in video poker is when people make a certain play and get a hand they wanted, and then attribute their hold to achieving the end result. The road not taken is neither considered nor available, and so we are left only with their destination, and their own biased belief that is was their choice of path that got them their. Whenever one reaches a fork in the road and turns left or right, the only way to be sure they have taken the best path is to take both and compare results. As this is impossible outside of laboratory triple blind studies we will never know what vistas the road not taken would have lead us to.

Climbing Mount Everest Naked in the Snow
How does all this apply to quantifying, understanding and correctly evaluating randomness? Hmm... Good question. In order to accurately assess in your head an event involving randomness like video poker, one would need to accurately remember all the hands they had ever been dealt, all the cards they had ever held, and all the results they had ever gotten...but wait that's not all. One would also have to remember each and every combination with equal weight. This means that regardless of whether or not they had been dealt a pat Royal Flush in hearts, or the 2s 4c 6h 8s Td, neither could stand out more in their minds than the other, because they have equal frequency. How much the hands pay is irrelevant to the calculation. Unfortunately, for the cause of clear thought, how much these equally probably hands pay is not so irrelevant to the human mind. You'll remember a dealt Royal in Hearts. Good freaking luck remembering when you got dealt a 2s4c6h8sTd off suit.

Herein lies the problem: We lack the mental capability to identify or quantify randomness in our heads. We are always forced to use a heuristic in lieu of perfect information. Here, though, shortcuts cannot be used with even a modicum of accuracy. In some really interesting studies I read, researchers showed participants truly random number sequences and simulated random number sequences (sequences made by people) and discovered a 28% bias towards people thinking the truly random numbers were fake, and the fake ones were truly random. That means that left to their own devices 78% of the time the subjects could not spot true randomness at all, and instead favored the non-random number sequences over the real ones. The conclusion is clear: truly random events seem biased and non-random to our pattern seeking minds and vice versa. We can't see the forest for the trees, because we have no idea what a twree even looks like, or how to spell it.

You were wondering where the subheading title came from? As it turns out, climbing Mount Everest naked in the snow and accurately quantifying random events in your head are about on par in impossibility. Their difficulty level diverges only in how it's perceived. People don't oft try to climb the highest mountain in the buff, but they try to make in-head judgments about random events all the time, sadly with equal chances of success.