Around the World

Last Update: Dec 07, 2005

Introduction

Around the World is a game found at Internet casinos using Playtech software. The game can be found under the Arcade Games menu. The game uses a wheel with 52 stops, numbers 1 to 49, plus three special stops. As the player spins he guess whether the next number will be higher or lower. The further the player gets and the fewer the incorrect guesses the more the player wins, up to 105 times his original bet. Following are the rules in more detail.

Rules

As in slots or video poker once a wager is made it is never returned. So all pays indicated are on a "for one" basis.

1. The game shall have four levels of seven steps each.
2. The player shall start any level at step one and end it at step seven, thus six steps forward are required on each level.
3. At the beginning of each level a random number shall be drawn from 1 to 49, which will be made known to the player.
4. The player must then guess at each step whether the next number drawn will be higher or lower than the last number drawn.
5. Another random number shall then be drawn with the additional possibility of three special outcomes explained in rules 10 to 13. The special outcomes never occur at the start of a level.
6. Except on step one of any level the same number may never be drawn twice in a row. Thus there is never the issue of a tie.
7. If the player guesses higher or lower correctly then he shall advance to the next step.
8. If the player guesses higher or lower incorrectly he shall still advance to the next step but shall get a strike.
9. If the player accumulates two strikes on any one level the game is immediately over and the player loses.
10. In lieu of a number the player may "advance one step." In this case the player will move for free to the next step. Unless he arrives at the seventh step the number previously drawn will remain for purposes of the next turn.
11. In lieu of a number the player may "advance to the end of the level." In this event the player will automatically go to step seven.
12. The player may have a "strike removed" if he already has one. Note that the player does not advance a step if this happens.
13. On the first turn of any level all numbers shall have a 1 in 49 probability. On all other turns all possible outcomes (remember a repeat number is impossible) shall have the same possibility except the "advance to end of level" and the "strike removed" shall have half the probability of any other outcome.
14. If the player reaches the end of level one with one strike he shall get his original wager back, effectively pushing.
15. If the player reaches the end of level one with zero strikes then he shall win 2.5 times his original wager.
16. As long as the player reaches the end of level 1 to 3, with one or zero strikes, he has the option to cash out or to bet his balance and go onto the next level. The player must make his decision before the first number is drawn on the next level.
17. At the end of all levels if the player has one strike he shall retain whatever his balance was at the beginning of the level.
18. If the player reaches the end of level two with zero strikes he shall win 3 times what he bet at the beginning of the level. As with all games in this report all wins are on a "for one" basis, in other words the original bet is never returned.
19. If the player reaches the end of level three with zero strikes he shall win 3.5 times what he bet at the beginning of the level.
20. If the player reaches the end of level four with zero strikes he shall win 4 times what he bet at the beginning of the level.

So, the maximum win for completing all levels with zero strikes would be 2.5*3*3.5*4 = 105.

In the screenshot above I completed each level. However levels 1, 2, and 4 I each earned one strike (as indicated in red) so I only retained my original bet. Level 3 I completed with no strikes so I won 3.5 times my wager. So my final win was $1*1*1*3.5*1 = $3.50.

Analysis

On any level the following are the probabilities of each outcome.

• No strikes 18.95%
• One strike 38.21%
• Two strikes 42.84%

Following is the expected return according to various stopping points:

• Play to end of level 1 only: 85.58%.
• Play to end of level 2 only: 81.35%.
• Play to end of level 3 only: 85.04%
• Play to end of level 4: 96.95%.

The above table shows the optimal strategy is to play to the end or lose trying. With this strategy the return is 96.95%. In other words the house edge is 3.05%.

Disclaimer

I was hired by Playtech to help design all of their Arcade Games, which explains how I know the game in such detail. I was given permission by Playtech to publish this analysis.