Hi-Low

Torn City has introduced a new casino game: High-Low. How does it compare to slots and roulette?

• First off, play smart: If the dealer card is below 7, you bet higher. Dealer above 7, you bet lower.

• The probability of a correct guess depends on the dealer's card. If the dealer turns a 7, you are stuck with a 50% chance. If the dealer turns an ace or king, you can not lose. If we average each case's odds together, we get the total probability you will be correct: 76.923%

• The probability of winning round R is thus 0.76923^R, since all previous rounds must also have been won.

• The pot after round 1 is half your bet. The pot then increases each round by 50%.

• Unlike slots, you must actually pay each time you play high-low.  Therefore, the expected return = (odds to win) x (prize) - 1.

The chart to the left shows your odds of getting to and winning each round, the amount you win at that round, and the long term returns if you play to that round each time, meaning you ALWAYS take the pot if you win that round.

The prize money and odds of losing both increase exponentially, but the prize exponent is more powerful.  Thus, the expected return increases with each round and gets massive quickly.

As demonstrated previously, the expected returns for slots and roulette are around +40%.  Looking at the chart, you can do better than this in high-low by playing to the 11th round or greater.

The round you should play to depends on your financial goals.  If you are in a war and need income for supplies, then playing to round 14 might be best, since you will almost certainly walk away with winnings.  On the other hand, if you and thinking more long term (i.e. to buy a mansion), then a higher round would be better.

Obviously, you can not pick a target round too high or the odds of winning will be too low to be of practical use, despite the ginormous prize money.  Playing to round 25 will let you win once every 700 times or so, about every 9 days if you exhaust your casino tickets daily.   Playing to round 35, you will win every 14,000 tries, or every 6 months.....but your prize is almost 500,000 x your bet!!

Clearly, high-low offers the best returns in the casino.  It can generates the greatest immediate income as well as astronomically large winnings for the patient, math-savvy gambler.

However, high-low takes significantly more real time than the other games.  This is relevant to players who only log on to TC during lunch breaks or the like.  Whether or not the time expenditure is worth the better income is a decision I must leave to each individual player.