Based in LOs angeles, ca, bet, build, go is a blog by derek kwan. his posts explore building products at startups, and sometimes poker.

Probabilistic Thinking Section from Bet, Build, Go

A section from chapter 3 of the book, Bet, Build, Go

 

The 50-50-90 rule: anytime you have a 50-50 chance of getting something right, there’s a 90% probability you’ll get it wrong.
— Andy Rooney

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Probabilistic Thinking

Some poker players seem to have this magical ability to read their opponents’ hands with frightening accuracy. Except it’s not magic. It’s a mix of critical thinking, observation, pattern recognition, and a little math. And the end result is being able to narrow hands down to a range, and then play against that range accordingly.

This is “probabilistic thinking” in a nutshell. You will rarely have all the information when making decisions, and you can’t drag on decisions waiting for all the data. You will need to use whatever tools you have at your disposal to make a call, and sometimes you will be wrong. In reference to the section above, applying some statistical thinking, intuition, and heuristics can help you narrow down both the problem and solution spaces. The output of this analysis will be a decision that carries a certain probability that you will achieve the outcome that you want. This isn’t a guarantee, it’s just a likelihood that some event will happen. This explicitly means there is always a non-zero chance that your choice will lead to a bad outcome, but this does not mean your decision was incorrect. This topic will be covered thoroughly in a later chapter.

Just about every poker hand ever played applies this concept, because you cannot see your opponent’s cards, and are therefore always making a judgement on your probability of winning a hand. But we can pick one fun hand to use as an example, from a poker show called “High Stakes Poker” back in 2010, where two legendary players, Phil Ivey and Tom Dwan battled one another in a pot worth almost $1 million dollars. Both players are extremely aggressive and quite adept at applying mixed strategies, which means they can play similar situations very differently, making them very hard to play against. We will discuss mixed strategies in a later chapter. 

Tom Dwan had re-raised several players to $28,900 before the flop with a hand we’ll keep hidden for now, chasing away all the other players except for Phil Ivey, who calls with the A♦6♦. On a flop of K♦Q♣T♦, Dwan bets $45,000, representing a very strong hand that connects with all those high cards, which is believable because of his big raise before the flop. Phil Ivey knows this, but also knows Dwan can be bluffing a lot here, so he calls, thinking his high card (Ace) may still be currently the best hand. Ivey can also make the best flush with one more diamond, and a straight with a Jack. The pot is now $162,300. The turn brings the 3♠, which doesn’t help Ivey at all. Dwan bets again for $123,200, signifying extreme strength. Phil Ivey thinks for a little while, and makes a pretty tough call here with just Ace high and a few draws, making the pot $408,700. The river comes the 6♣, for a final board of K♦Q♣T♦3♠6♣, which now makes Ivey a pair of sixes, which is not a very strong hand here based on how aggressive Dwan has played thus far. As we mentioned earlier, you can never really know what your opponent has. Dwan goes all-in on the river (which means he bets all his remaining chips) for $268,200, making the pot $676,900. What would you do? Could you call another $268,200, making the pot almost $1 million, with just a pair of sixes?

Most players would be correct to just fold here. There is really a high number of hands that beat a pair of sixes, especially with the aggressive way Dwan played the hand. However, Dwan is also such an aggressive player that he could be completely bluffing here with absolutely nothing. The monetary pressure of such a huge pot also plays another uncomfortable factor. Ivey thought for a very long time, while Dwan sat stone faced, not moving for several long minutes, before eventually and reluctantly folding. 

Phil Ivey was working out the probability that his pair of sixes would be the best hand, likely by assigning probabilities to the various hands that Dwan could have. In the end, he felt that there was a higher probability that Dwan held a hand that was better than his. There are some more advanced poker concepts at play here, such as assigning ranges of hands to your opponent, calculating how your hand does against that range, and calculating your “pot odds” (how much money do you have to call compared to how much total money you would win), as well as some psychological analysis based on a number of different factors. A deep dive into these concepts are out of scope for this book, but in summary, Ivey was applying all this analysis to determine the probability his hand was the best. It was impossible to know for sure, and ultimately, he determined it was not, but it was clearly a very close decision. 

So what did Dwan have? Incredibly, he only had the 9♠8♠, which was a complete bluff, meaning Phil Ivey had folded the best hand with a pair of sixes. However, this does not mean that Phil Ivey’s fold was a bad decision. And as a matter of fact, Ivey being so close to a call with such a marginal hand in an absurdly large pot shows how talented these top pros really are.

You can apply this model of probabilistic thinking to many startup decisions. Oftentimes, decisions will be straightforward with fairly known risks and outcomes. As we mentioned earlier, some rapid application of logic and statistics are appropriate in these situations. Your probability of achieving a specific outcome should be quite high, if done correctly. But there are many decisions where you can’t ever know exactly what will happen. You can, however, find ways to assign a probability to an outcome, or better yet, to several outcomes.

Let’s take one of our questions from a previous exercise: Who would be the early adopters of a flying car? You can’t know for sure, but we can apply several of the discussed concepts to arrive at some potential outcomes and assign them probabilities. There is some research that shows the wealthy tend to be early product adopters. 

A simple way to forecast the future is to look at what rich people have today; middle-income people will have something equivalent in 10 years, and poor people will have it in an additional decade. Think of VCRs, flat-screen TVs, mobile phones, and the like. Today, rich people have chauffeurs. In 10 years or less, middle-income drivers will be able to afford robotic cars that drive themselves, at least in some circumstances.

So looks like there is some indication that the wealthy might be a good place to start. What would your early adopters be using flying cars for? A flying car can certainly be viewed as a novelty item at first launch, as there should be low inventory and a product that no one has ever seen before. This also fits into the above study–new products tend to be novel, and adopted by the wealthy more frequently. Who would definitely not be an early adopter? Technophobes and risk-averse people would be unlikely. While these traits can exist in people of any income demographic, we can definitely see this more often in older individuals. Seems like our answer is skewing greatly towards “wealthy and young”. Also, the cost of goods sold for developing a flying car will be quite high in the beginning, and may get cheaper over time if you can achieve economies of scale, so it would generally make sense strategically to price your product high in the beginning. Furthermore, Tesla strategically targeted the wealthy with the Model S with great success, with base models starting at $80,000, going up to $150,000 fully loaded, and may be a good case study to model your flying car after. So now we can assign some rough probabilities to our answer:

  1. Wealthy and young: 70%

  2. Wealthy and old: 25%

  3. Low income and young: 4%

  4. Low income and old: 1%

The probability of our early adopters being wealthy and young appear quite high. What about government obstruction? It appears that a flying car would be quite risky, and would need to clear a lot of regulatory hurdles to get off the ground. Do wealthy people vote? What about young people? Young people have for a very long time been the lowest turnout for voting, with 18-29 was 19.9% in 2018, while 65+ was 59.4%. In 2018, the youth turnout improved dramatically, but still only at 35.6%, while 65+ rose to 66.1%. So it looks like young people won’t help us with moving the government much. But if we peg wealth to education level, people without a high school diploma voted at 22.2% in 2014, 27.2% in 2018, while those with advanced degrees turned out 62% and 74% respectively. So looks like our demographic may or may not help with pushing for changes at the government level, looks like a coin flip at 50%. So the chances of getting through government regulations quickly seems quite low.

And we can continue with more estimation questions to target a good demographic for launch, to understand the risks, and also to formulate our messaging and positioning, as well as our sales strategy. When thinking about features, we can also cater to that specific demographic more, hoping they will be market makers. There will be no guarantees, but these types of exercises can give you good estimates to understand what might be ahead of you.

If you can keep making decisions on the correct side of probabilities, driven by your own critical thinking, observation, and measurements, the results will come, as will long term success.

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