Lotteries and casino games have a very bad expected value, they are always negative (otherwise nobody would offer them).

Payouts, on the other hand, can be huge.

Is there a investment in the financial markets that can offer a better expected value than most lotteries, which is low threshold, high payout?

I am sure there is an error in thinking here somewhere. I assure you, it's a sincere question.

  • Is there a investment in the financial markets that can offer a better expected value than most lotteries - how about a savings account?
    – dwizum
    Commented Feb 6, 2020 at 18:57
  • @dwizum I think they are asking for something like the lottery... low chance of a very high payout, except with a positive expected value.
    – user12515
    Commented Feb 7, 2020 at 16:55

5 Answers 5


In the UK, there is a government-backed scheme called Premium Bonds

The general rule is that your investment in cash terms is guaranteed, and every month each "£1 bond" is entered into a prize draw where you can win up to £1 million.

Effectively you are gambling with the potential interest, but in absolute terms you can't lose and the expected return is (as of Feb 2020) +1.40% per year.

  • Love it. It's a bit of a hassle to apply from outside the UK. but I might give it a go. Commented Feb 12, 2020 at 10:23
  • 1
    The savings account version of Premium Bonds is often called a prize-linked savings account. Be aware that such schemes are often classified as gambling by governments. Such systems are generally considered a public good, since they cause people to save or invest money rather than buying lottery tickets. However, governments reliant on lottery revenue often disallow operating or participating in such schemes, despite the public benefit.
    – Brian
    Commented Feb 12, 2020 at 14:47

Randomly investing in equity of publicly traded stocks without researching about them is high-risk, low threshold and is non-negative in the long run. Make sure the fees don't eat up too much of the investment though.


Deep out-of-the-money options offer low premiums and high potential payouts. Whether the expected payout is positive or not is difficult to determine, since you don't know the odds of the stock crossing the strike, but if your broker publishes the implied volatility of an option, look for deep OTM options with a low IV (compared to other OTM options) since the higher the volatility, the higher the price.

  • The Probability of Touch of an option (the odds of the stock's price crossing the strike) is about twice the IV. One could make the argument that despite their higher cost, OTM options on higher average IV stocks are more likely to bring in that big payday. For example, consider a utility like Con ED with a historical IV of 0.12 and a $10 price range over the past year versus Tesla with an IV of 0.56 yet it moved up $400 over the past week. Also, OTM options tend to have a higher IV than ATM (volatility smile). Commented Feb 6, 2020 at 13:38
  • @BobBaerker Thanks for the insight. My thought was to find options that are underpriced to make the expected payout positive which is why I suggested looking at "low" IV. Since that's contextual (low compared to what?) I mentioned comparing to other OTM options. Certainly finding OTM options that have lower IV that ATM options would be very rare.
    – D Stanley
    Commented Feb 6, 2020 at 13:41
  • I think this is a good candidate, as historical studies have suggested that while buying options is normally a losing proposition, black swans actually give it a long term positive expected value.
    – user12515
    Commented Feb 7, 2020 at 16:57

Black Swan Options are the best answer for a low percentage of a large return on a small amount of investment. The option contracts can be priced for having a strike-price drastically offset, and out-of-the-money, from the spot price. And the option contracts can be priced for being close to expiration. Obviously, the options positions have to be replaced often. For instance with an options price of $0.50 then a single contract costs $50. In fact in the world of lotteries, $100 dollar lotto tickets are popular when there are big jackpots.

Futures, or leveraged forex, are opened close to the spot price and so there's not much choice of contract pricing. Well, futures do have some choice of contract pricing due to expiration dates. Now with futures or leveraged forex there is actually only a margin deposit and not a purchase price.

Consider a leveraged forex currency position opened with a stop-loss of 1/8 of one-percent and with a limit order of 1/8 of one-percent. That's like playing a daily lottery with a 50% chance of winning and a small payout. And since there will be a lot of tripped stops and limits, then there can be a lot of trades. Or trade with futures.

In fact I develop a forex software that offers a choice of five different levels of stops with limits. The idea is to help the trader be at least break-even. Then the trader can improve by reading the news and by reading economic reports.

Personally, I trade leveraged forex with a 1% stop-loss and no limit order. And I often receive roll-over interest for several days in a row. With a futures position that has the purpose of hedging, I often have a stop-loss at the maximum allowed by the unused amount of margin deposit.


I read about a shop selling lottery tickets many years ago that actually didn’t report sales to the lottery organization, but just paid out all the prices himself. Largest payout he had to pay was 100,000. Still made lots of money.

I also read of companies selling “guaranteed win” strategies with money back guarantee. You pay me $100 and give me your ten lucky numbers. I calculate a set of numbers to choose that are guaranteed to win. If you play for a year at $50 per week and don’t at least win 52 times $50, you get your $100 back. Of course that means you have to bet $2,600 to get your $100 back and few people will do that.

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