Ten years ago I was introduced to the game of Texas Hold ‘em. I spent some time reading and studying the game and in most situations can hold my own. A big reason for this is because I understand “pot odds.” It’s a must learn concept for poker players, and it helps explain why insurance is a bad deal.
Some Basic Math
For you poker nuts and statisticians out there, I completely acknowledge the math you’re about to see is an over simplification. But it conveys the point. With that disclaimer out of the way, let’s continue.
Assume you’re sitting at a poker table with four hearts in your hand and one card left to deal. You’re certain that if you get a 5th heart you’ll win the hand. If you don’t get the heart, you’re certain you’ll lose. There’s $100 in the pot and the current bet is $10. Should you stay in the game or get out?
Here’s the math: You have a 25% chance of winning (1 chance in 4 you’ll get a heart) and all you have to do is pay in 10% of the pot. You should make that bet because you’re expected return ($25) is greater than your investment ($10).
Think about it this way, let’s say you had that exact situation 1000 times. 25% of those times you would win and the total of those winnings would be $25,000 (250 * $100). 75% of the time you’ll lose but that will only cost you $7,500 (750 * $10). Profit of $17,500 if you play a 1000 times.
Now change things up. There’s $100 in the pot and you still have those 4 cards for a flush. This time the bet is $50. In other words, you have to put up 50% of the pot with only a 25% chance of winning. In 1000 hands, you’d win that same $25,000 but this time you’re loses would total $37,500 for a net loss of $12,500.
When the pot odds are in your favor, place the bet. If not, fold.
Law of Large Numbers
You can’t say with certainty which hands you’ll win, but you can be confident that if you encounter the above situation 1000 times you’ll come out ahead if you do what the pot odds tell you to. Do it 100,000 times and you’ll be even more confident in the outcome.
This is referred to as the law of large numbers. It doesn’t state that you’ll win or lose any specific hand but, rather, if you play that exact hand a bunch of times you can be extremely accurate in predicting the overall outcome. The more times you play it, the more confident you can be.
It is this mathematical theory that insurance companies use to make money (as well as casinos). They don’t know for sure if they’ll make money on you or not, but they know that if they can find a million people just like you and price things properly, they will win.
Cell Phone Insurance is a Bad Deal
Let’s get out of the world of Texas Hold ‘em and talk about cell phone insurance. We’re going to use Apple’s new iPhone 5S as the example. The 16GB version retails for $649. You might get it for $199 when you sign a two-year contract but if you break it, it will cost you $649 to replace.
This is where the insurance pitch comes in: “Would you like the insurance? It means if you lose or break this phone you won’t have to spend $649 to get it replaced. It’s only $7/mo.”
You think that sounds like a pretty good deal, right? $7/mo and they replace a $650 device if you lose it. Sign me up!
Then you find out there’s also a $199 deductible if you need to file a claim. Well, still, $199 plus $7/mo sounds like a decent offer.
Let’s check the math…
According to Squaretrade, about 13% of iPhone owners will break their iPhone in the first 12 months of ownership. This means your expected cost if you don’t buy the insurance is $649 * 13% = $84. Your required payout to the insurance company is $7 * 12 months = $84. Looks like a wash.
But we haven’t figured in that deductible yet. If there’s a 13% chance you’re going to break your phone, then you can assume 13% of that deductible must also be paid. This brings your total expected cost of using the insurance to $84 + (13% * $199) = $110. In other words, not getting the insurance leaves you with an expected cost of $84 and getting it leaves you an expected cost of $110.
The insurance is a bad deal.
Here’s what you might be thinking. “Well, if I need the deductible then this is a good deal, right? Otherwise I’d be shelling out the entire $649.”
On the surface that seems like a good argument, and that’s probably what the AT&T guy trying to sell you the insurance will say. So let’s think about this another way. Assume you own a company with 1000 employees and you’re going to buy everyone an iPhone 5S. Should you buy the insurance?
Using the law of large numbers we can be fairly certain that about 130 people will break their phone. So the cost of having the insurance is 1000 people * $84/year in insurance + (130 * $199 deductible) = $109,870. That’s what it will cost if you buy the insurance.
What if you don’t buy the insurance? Then you’ll be replacing 130 phones at a retail cost of $649. That comes to a total of $84,370.
If you’re the CTO of your company and you buy the insurance, you should be fired.
If you’re an individual buying cell phone insurance, the odds are you’re wasting money.
What about AppleCare+?
The above numbers come from the insurance offered by Asurion. That’s the plan most cell phone carriers offer. The above math makes it pretty clear it’s not a good deal.
But that’s not the only insurance plan out there. What about Apple’s very own AppleCare+. This costs $99, is good for 2 years, and charges you $79 if you need to use it (it does not cover lost or stolen phones like the Asurion plan does). Let’s do the math again on a 1000 phones. The plan is good for two years so we’ll need to change our possible breakage rate to 26% (bad assumption but it’s a worst case scenario).
With Insurance: (1000 * $99) + ($79 * 1000 * 26%) = $119,540
Without Insurance: 1000 * 26% * $649 = $168,740
Hmmm… In this case it looks like the insurance is a good deal. But there’s a catch.
By far the most common cell phone damage is a cracked screen. There are a lot of third party companies out there that will fix a cracked iPhone screen. Let’s assume that 80% of all smartphone damage is a cracked screen and the rest is something catastrophic – like water damage – that requires a new phone. Let’s also assume the 3rd party cost for an iPhone 5S screen repair is $199.
With Insurance: Still $119,540
Without Insurance: (260 * 80% screen repair * $199) + (260 * 20% total loss * $649) = $75,140
Once again, the insurance turns out to be a bad deal. I’ll go so far as to guarantee that if you do the math, you’ll discover insurance is always a bad deal.
Then why would I ever buy insurance?
There is a simple rule to buying insurance: You should buy it if the cost of the catastrophic event is so great that there’s no way you could cover it but the recurring fees are feasible for you to pay (or if it’s required by law).
Car insurance is something you should always buy. Let’s say you have a $30,000 car and your insurance comes to $100/mo. Many people can afford $100/mo for car insurance if they paid $30,000 for their car. Very few of those people could shell out $30,000 if they totaled the car – or a couple hundred thousand dollars if they totaled the car, someone else’s car, and ended up in the hospital for a week.
The same holds for health insurance, home owner’s insurance, business insurance, and more.
The odds are, you will pay more for that insurance than you’ll get back. That’s why State Farm and Geico are in business. But the fact is, if you smash up your car, your house burns down, or you’re diagnosed with cancer, you will NEED that insurance because you won’t be able to pay for it out of your own pocket.
I would argue that you can afford $649 for a new smartphone. You might not want to, but you could. After all, you can presumably afford the $120+ per month cell phone plan, right? You do not NEED the insurance if your iPhone falls on the ground and the glass cracks or even if it falls in the bathtub and you have to replace the entire thing.
Do the smart thing and say, “No,” the next time that salesperson tries to convince you to buy the insurance plan.
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