Gizmodo Monday Puzzle: What’s the Best Way to Cheat at Poker?

Online poker faces a cheating crisis. The AI revolution has imperiled the multi-billion dollar industry as computers continue to outshine humans at their own games. Poker-playing bots can now routinely thrash human experts, and it can be difficult to detect when anonymous online players are using real-time assistance engines to inform their decisions. Cheaters no longer have to brave a tableful of greedy eyes, desperate to avoid detection as they palm a card or deal from the bottom of the deck. Online poker servers have had to beef up their anti-fraud efforts in response, causing an algorithmic arms race as cheaters try to outwit the anti-fraud teams and vice versa. This is the new reality of living among machines that can literally do our bidding for us.

In this week’s puzzle, you’ll go all-in on cheating as Lady Luck herself feeds you cards.

Did you miss last week’s puzzle? Check it out here, and find its solution at the bottom of today’s article. Be careful not to read too far ahead if you haven’t solved last week’s yet!

Puzzle #9: The Best Full House

You are playing a simple poker game with one deck of cards. Everyone is dealt five cards, and whoever is dealt the best five-card poker hand wins. Lady Luck has promised to deal you a full house of your choice. Which full house should you choose to maximize your chances of winning? Standard rules apply: there are no wild cards, aces can be high or low for straights (10, J, Q, K, A and A, 2, 3, 4, 5 are both valid), but straights cannot “wrap around” (Q, K, A, 2, 3 is not valid). Check here if you need a refresher on poker hand rankings.

I suspect most readers will have a knee-jerk answer for the best full house. Determining why the obvious solution fails will be a key step in solving the puzzle. Or am I just bluffing?

I’ll be back next Monday with the solution and a new puzzle. Do you know a cool puzzle that I should cover here? Send it to me at gizmodopuzzle@gmail.com

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Solution to Puzzle #8: The Cognitive Reflection Test

Last week’s puzzle came from a real psychological test. In his famous book Thinking, Fast and Slow, psychologist Daniel Kahneman discussed two modes of thinking, with the admittedly unilluminating names ‘System 1’ and ‘System 2.’ System 1 is automatic and relies on intuition and quick heuristics. System 2 is slower, more deliberate, and more calculating. You might rely more on System 1 when eyeballing how many scoops of grounds to put in the coffee maker. Sure, the tin recommends a specific amount per cup of coffee, but for most of us, close enough is good enough. On the other hand, System 2 comes in handy when adding the tip to the meal cost at a restaurant, because faulty math could unintentionally stiff the waiter. Both types of cognition are useful and important.

System 1 serves, in some sense, as a default. You mosey through life figuring that your body will fit through that doorway or an extra snooze won’t make you late for work (a perennial pitfall of System 1 thinking) without needing to stop and calculate. Kahneman argues that many of our cognitive biases stem from relying too heavily on System 1 and not recognizing when it’s appropriate to switch into the more effortful System 2. The Cognitive Reflection Test was designed to measure the degree to which people make this switch. The idea is to give people three questions, each with obvious answers that happen to be dead wrong. Those who score well must override their gut instincts in favor of more strenuous contemplation. To the several of you who submitted three correct answers, congratulations on breaking into the 17%. Shout-out to reader DH84 for resisting System 1. Let’s take them in turn:

• A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?

The natural answer is that the ball costs 10 cents. In fact, the ball costs 5 cents (and the bat costs $1.05). For many people, System 1 erroneously simplifies the phrase, “The bat costs $1.00 more than the ball” to “The bat costs $1.00.” Upon deeper reflection, it becomes clear that $1.05 is one dollar more than $0.05 and that these prices sum to $1.10.

• If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

It would not take 100 minutes, but rather 5 minutes. If 5 machines make 5 widgets in 5 minutes, this means that, on average, each machine takes 5 minutes to make 1 widget. So after 5 minutes, you’ll have as many widgets as you have machines. Meaning 100 machines will produce 100 widgets in 5 minutes.

• In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

24 days is the tempting answer. Engaging System 2 might lead you to 47 days, the correct answer. The patch of lily pads doubles in size every day. So on day 1 it is half the size it will be on day 2. On day 13 it is half the size it will be on day 14. On day 47 it is half the size it will be on day 48. On day 48, the entire lake is covered. So on day 47, half of the lake is covered.

In an analysis of multiple studies in which over 3,400 people were given The Cognitive Reflection Test, only about 17% of them got every question correct. Some respondents answered other types of questions as well, such as

A banana and a bagel cost 37 cents. The banana costs 13 cents more than the bagel. How much does the bagel cost?

Even though this is a harder math problem than the bat and ball puzzle, more people answer this correctly! That’s because there is no bait answer to lure System 1. It’s simply an algebra problem, and people have no choice but to engage System 2 to solve it.

So, are you in the majority that follows their gut when faced with these questions? Or did you suppress heuristic thinking and puzzle through to the correct conclusions?