The lottery offers

Scenario 1:

Intend a lottery offers one-off as a $1 Choose 3 variant video game as well as just pays prizes for exact suits or having a solitary digit off by one. Let the exact match prize be $284 and let the single-digit one-off reward be $36. After that the anticipated return is

( 0.001 x $284) + (0.006 x $36) = $0.50.

This is the same return for a common $1 straight bet that pays $500, so it is no better or even worse than a straight bet.

Circumstance 2:

Expect a lottery supplies one-off as a $1 Choose 3 alternative video game and pays prizes for one, two, or 3 off digits, but does not payout for the specific match. Allow the prize framework to be

  • 0 one-off digits (exact suit): $0.
  • 1 one-off figure: $40.
  • 2 one-off figures: $10.
  • 3 one-off digits: $18.

The expected return is.

( 0.006 x $40) + (0.012 x $10) + (0.008 x $18) = $0.504.

This is a slightly much better-anticipated return than a typical straight bet, so your finest action is to pick one-off as your play type, rather than straight.

Situation 3:

Mean a lottery supplies one-off as an add-on game for an extra $1 (making your complete cost $2). Allow the payout table for a $2 wager is.

  • 0 one-off figures (specific suit): $500.
  • 1 one-off number: $35.
  • 2 one-off numbers: $15.
  • 3 one-off figures: $10.

The expected return for a $2 wager is.

( 0.001 x $500) + (0.006 x $35) + (0.012 x $15) + (0.008 x $10) = $0.97.

This is equivalent to a return of $0.485 per $1 invested, making it an even worse wager than a common straight bet.

Scenario 4:

Suppose a lottery’s Pick 3 straight video game pays $600 instead of the extra normal $500. That is, the anticipated return on the base game is $0.60 as opposed to $0.50. (As of this writing, Missouri Kentucky has such payments.) Expect also that the lottery offers one-off as a $1 Pick 3 alternative video game with the following prize structure for a $1 wager.

  • 0 one-off digits (precise match): $300.
  • 1 one-off figure: $29.
  • 2 one-off numbers: $4.
  • 3 one-off figures: $9.

The expected return on a $1 bet is.

( 0.001 x $300) + (0.006 x $29) + (0.012 x $4) + (0.008 x $9) = $0.594.

Considering that this is a little less than the expected return of $0.60 on a straight wager, the clever choice is to skip one-off.

As you can see from the 4 circumstances, whether to play one-off depends upon the reward structure. In some locations, it’s a great bet, while in others it’s much better to stick with the classic straight bet.