Torn City Math

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Using mathematics to make optimal decisions on www.TornCity.com

12 November 2005

Luggnutt's Gambling Guide for New Citizens

New players, or anyone with less than $50 x level:  play slots!  Once you get above $50 x level, play roulette and bet the maximum.  You will probably lose a few times, dropping you back below 50x.  When this happens, go back to slots.  

Here's a typical example:  after a day of work you have $100.  You play roulette 10 times and never win, setting you down to $50.  So you spend the rest of your tickets at the slots and break about even.  The next day, you spend more money at roulette but lose some more and switch to slots.  You get lucky and win big in slots at the end of your streak.  Day 3 you have enough money to play roulette several times and hit big twice, starting you well on your way to casino domination.

Rationale:

As previously posted, the best bet you can make is the max bet in roulette.

However, new players in Torn City will not have enough money to make this bet repeatedly (unless they are lucky and win early.)  Thus, for poor players, timing and losses need to be considered.

In roulette, you can expect to win every 38 spins.  This means you will lose an average of 37 times between wins, costing you 37x your bet.

In slots, you can expect to win big every 81 spins (all 3 match, paying 50x).  But slots also has little wins when 2 numbers match, which occurs about 1/3 of your spins and pays +2x your bet.  2/3 of your spins are losses, paying -1x your bet....
(1/3)(+2) + (2/3)(-1) = 0!!  Thus, the little wins you get every third spin pay for the losses, making the game easy to play with a small bankroll.

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