The Gamblers Fallacy

The gambler’s fallacy is the belief that the chances of something happening with a fixed probability become higher or lower as the process is repeated. People who commit the gambler’s fallacy believe that past events affect the probability of something happening in the future. -Investopedia

I was playing golf with a friend of mine who brought along one of his co-workers. He was a nice guy, and we got to talking during the round. I found out that he enjoyed going to Atlantic City and playing craps. At the bar, after the round, we got into some strategies that he had at the craps table. I enjoy playing craps recreationally, as I know it is an impossible game to beat over time. But there is no more enjoyable game in the casino when you are on a lively table. I’m always curious to hear people’s strategies when it comes to table games. There are people out there who think they have a strategy that can beat these games when statistically, it is impossible. This guy proceeded to tell me his strategy where he would be betting more after a certain amount of sevens came out. His theory was that only so many sevens could come out in a given number of rolls. This thinking is the gambler’s fallacy.

If you have the time write down what you would imagine 100 random coin tosses will look like. Now flip a coin 100 times, writing down the result of each coin flip. The chances are both of these lists look dramatically different. When doing this exercise, most people will never account for the actual number of heads or tails that will show up in succession. We are biased in our thinking that a 50/50 proposition means that there are only so many heads or tails that can come in a row before flipping to the other side. If you look at your results from the actual coin tosses, you will notice you probably had five, six, maybe even seven straight flips of one or the other in a row.

For those who did not want to take the time to flip a coin 100 times, I did it for you in Excel by using a random number generator.

 

Flip # H/T
1 T
2 H
3 H
4 T
5 H
6 T
7 H
8 H
9 H
10 T
11 T
12 T
13 H
14 H
15 T
16 H
17 T
18 T
19 H
20 T
21 H
22 T
23 T
24 H
25 H
26 T
27 T
28 T
29 H
30 T
31 T
32 H
33 T
34 H
35 H
36 H
37 T
38 H
39 H
40 H
41 H
42 H
43 T
44 T
45 T
46 T
47 T
48 H
49 H
50 T
51 T
52 T
53 T
54 H
55 H
56 H
57 T
58 T
59 T
60 H
61 T
62 T
63 T
64 H
65 H
66 T
67 H
68 H
69 T
70 H
71 H
72 H
73 H
74 H
75 H
76 H
77 T
78 H
79 H
80 H
81 T
82 H
83 H
84 H
85 H
86 T
87 T
88 H
89 H
90 T
91 H
92 H
93 T
94 H
95 T
96 T
97 T
98 H
99 T
100 T

As you can see, there were several occasions where we went on a run of heads or tails with the longest being seven heads in a row from flip 70-76. It is unlikely that if you did this exercise without actually flipping a coin, you would come up with seven straight heads or tails. This mentality leads gamblers down a dangerous path. When betting on sports against the spread, we have approximately a 50% chance of winning and a 50% chance of losing that bet. If that is the case, the actual results of our bedding are going to look very similar to the chart above for random coin flips.

As a sports bettor, I view everything through a statistical lens. When I am watching a game, I am just watching numbers. Thinking about a game the way you think about the probability of picking a white or red marble out of a bag, or the simple toss of a coin takes a bit of the fun away. But in actuality, that is all sports betting is. We figure out the probability of an outcome and then look for offers from sportsbooks that give us a profitable return if our prediction on the result is correct. In simple terms, if someone was willing to pay you $0.55 every time you flipped heads and you owe them $0.45 every time you flip tails, you would take that back all day long.
Some of you may be thinking well it’s different in sports because I’m studying the games I know all the statistics I know the trends, so I have a bit more of a say in the outcome of my bet. That can be true, but the best professionals out there pick between 55% to 60% against the spread, with 60% being extremely high. Let’s assume that you predict sporting events against the spread at a 55% rate. That is still very close to a coin flip on every game. Your distribution is always going to look very similar to that of the coin flip example above. You should have a few more runs of seven straight wins than you will seven straight losses but not by a significant amount.

Now that we understand that our perception is not the reality when it comes to coin flips, how can we use this to help us in sports betting? This won’t make you a better handicapper, but it should help you steer clear of one of the more dangerous betting strategies I often encounter. First, let’s go back and look at the chart on coin flips above. Let’s assume that tails are wins and heads are losses on your NBA picks against the spread. On your first ten picks, you went 4 – 6. That is not unusual. I’m sure every one of us has had similar results over a random ten-game sample. Over the next ten games, you win six and lose 4, bringing you right up to our predicted 50% win rate.
We look at the next ten, and we stay hot, winning six out of four yet again. In fact, over the first 69 games, we went 35 of them, so we are one game over .500. During the 69 games, we saw some cold streaks and some hot streaks. Games 38-42 were extremely cold, but we followed it up from games 43-47 with a series of wins to make up for it. We now get to play 70. It is a loss. Game 71 is also a loss; in fact, we continue to lose games 72 and 73. You have seen these kinds of losing streaks before, and you know they will turn around. You want to get ahead of this and start increasing your bets. Game 74, you double up, but you lose. Game 75, you double up your game 74 bets and lose. Games 76, you double up again, now risking eight times what you usually risk and lose. You have now had what a very predictable losing streak is, and instead of losing seven units, you are down 18 units.
If you indeed doubled up again, risking 16 units, you would have won the next bet, but how many of us are going to continue risking that amount? What streaks like this typically do is either destroy our bankroll or destroy our psychological makeup. And in most cases, it does both. If we look at all 100 tosses, we would have lost 53 times while winning 47 times. This kind of outcome over 100 games for someone who picks about 50% is not unlikely. After those 100 games, a gambler who was not fooled by the gambler’s fallacy would be down but certainly not out. Perhaps the next 100 games, the bettor would win 53 times.

Start viewing your sports betting is nothing more than numbers, and statistics take the emotion out of it. In doing so, you will be more profitable over the long haul.