The conjunction fallacy occurs when a lotto player believes that two events happening together are more likely than one occurring alone. For example, someone might think picking “lucky numbers” on a “lucky day” increases their likelihood of winning. The truth is that combining events doesn’t make winning more likely.
A lottery wheel user sent me an email I want to share with you today. I hope you’ll find some helpful insights from our conversation. If you’re interested, let’s dive in!
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A Letter from a 6/48 Lotto Player
Hi Edvin
I got the 6/48, and I’m using the 12 number covering.
Now, what I did was to create four csv templates for different numbers. Now each csv has 12 numbers covering, so I created four of those csv files, essentially trying to cover a total of 48 numbers.
I chose this method instead of 24 numbers, because 24 is expensive, and using 12 numbers per csv, creating four of them covering 48 numbers in total is a lot cheaper.
Do you perhaps have any suggestions. Please let me know what you think.
Multiple CSV Files Don’t Work
Playing the 6/48 game with four separate lottery wheels is even more expensive. In fact, playing them together is not strategic because that’s not how a lottery wheel works.
Let me explain.
Supposed you divide 48 numbers into four groups of 12 numbers:
Group A = 12 numbers covering 924 tickets.
Group B = 12 numbers covering 924 tickets.
Group C = 12 numbers covering 924 tickets.
Group D = 12 numbers covering 924 tickets.
We can calculate the probability of each group as follows:
P(All 6 numbers in one group) = 924/12,271,512
And since there are 4 groups, we can multiply this by four.
P(6 winning numbers from all groups) = 4 × 924/12,271,512 = 3,696/12,271,512
Thus, there are 3,696 ways to match 6 winning numbers, and the probability is 1 in 3,320 instead of 1 in 12 million.
Understanding the lottery’s random behavior
Of course, winning is every lottery player’s objective. Unfortunately, a lottery game is truly random and matching the jackpot is truly hard.
Since these four groups are isolated lottery wheels and do not collectively cover the entire range of combinations, the only valid scenario in which a player can match six winning numbers is if all six numbers belong to the same group.
Always remember that a genuine random game will not favor certain groups. Expect the probability to be fairly distributed across the number field.
Therefore, the most likely scenario is that the winning combination may match two numbers from Group A, one from Group B, and three from Group C.
So, thinking that playing all groups A, B, C, and D together will provide you with a strategic approach is an example of a conjunction fallacy.
What is the Conjunction Fallacy?
In gambling, the conjunction fallacy occurs when people overestimate the intersection of different events. We express this fallacy when people believe that the probability of two events happening together, P(A ∩ B), is greater than P(A).
In reality, the probability of Event A and B happening together cannot be greater than Event A occurring alone. In short, the correct probability is the product of the individual probabilities. The result is always less than or equal to the smallest probability.1
P(A ∩ B) ≤ P(A)
For example, let’s consider these two events:
- Event A: At least several tickets from each group (A, B, C, and D) will win a small prize.
- Event B: At least several tickets from each group (A, B, C, and D) will win a small prize, and one jackpot ticket will come from one of these groups.
Probabilistically speaking, seeing Events A and B happening together is less likely because the product of two probabilities is always less than or equal to the smallest probability.
The intersection of two events, A and B, is given by:
P(A ∩ B) = P(A) × P(B∣A)
Given the calculations:
P(A) ≈ 0.99999988
P(B) ≈ 0.000301
We found:
P(A ∩ B) = 0.99999988 × 0.000301 ≈ 0.000301
Since: 0.000301 ≤ 0.999999880. This confirms that having four CSV files is expensive and ineffective.
The conjunction fallacy demonstrates how gut feeling can lead to poor decision-making.
Stick With Just One CSV File
I can confirm that buying more tickets will increase your chances of winning. However, if you aim to trap the 6 winning numbers, wheeling 12 numbers in a single CSV file is better strategically than having four separate CSV files combined.
If you want to trap more winning numbers, increase your covering size and subject all the numbers collectively into one lottery wheel. The caveat is that you must buy more tickets. The number of possible combinations increases quickly as you increase your covering. Covering strategy is expensive. The truth may hurt, but that’s the truth.
Recommended Strategy Against Conjunction Fallacy
- Make it simple. Use the Lotterycodex Calculator as your lottery wheel and make informed choices when buying tickets.
- Play the same list of combinations each time.
- Always save some entertainment money when playing the lottery.
- Spend the money you can afford to lose.
- Consider playing as a syndicate to cover more combinations, especially if you’re using a lottery wheel. If you’re a solo player, buy only one ticket.
- And more importantly, play for fun.
I hope that helps.
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