MauiSunset’s True Roulette Odds

Copyright June 20, 2012 by – all rights reserved.  You may NOT use the True Roulette Odds Tables without this copyright notice.

The 200+ year old Roulette Odds Table is wrong – it’s built on the “Gambler’s Fallacy”, the Roulette House Advantage (HA) is 16% and not 5.26% as has been reported for 200+ years.

I noticed that what Nevada casinos report a Roulette House Advantage (HA) of 16% and not the 5.26% which has been used for 200+ years. What could account for this impossibility and what does it mean to the gambler?  The numbers that started me down this path are from the Nevada Gaming Commission – here is a sample report.

The posted HA for Roulette is 5.26% for any and all bets and combination of bets, with any kind of money management possible – with the exception of the First 5 bet, applicable to American tables, which has a HA of 7.89%.  99% of all bets I see are NOT the 1st 5 so the HA the casinos report must be close to 5.26% -right?  But the casinos report a HA of 16% – what can account for this difference of 3 times as much HA?

I found the answer and it has to do with the quirk of random numbers – that 1/3 of the numbers on the Roulette wheel will not show up in the next spin – the proof is at the end of this article.  I built new Roulette Odds Tables reflecting this difference and this accounts for the 16% HA the casinos report in real gambling and not theoretical odds calculation.

Basically the game of Roulette turns out to be a very good game for the casinos and a horrible game for the gambler.  If you want to play Roulette, I recommend ONLY outside, Equal Chance bets and under NO circumstances bet Straight Up single number bets – you don’t stand a chance.

Here are the MauiSunset True Odds Table for American Wheels:

Here is the MauiSunset True Odds Table for European Wheels:

Since the Single Number, “Straight Up” bet is the most common Roulette bet you would expect the HA the Casinos report to be more than 14.86% and 16% makes a lot of sense.

The existing odds table demand that each of the 38 slots on the Roulette wheel has an equal chance of being spun – this is false, about 1/3 of the 38 numbers will not show up on the next spin – therefore the odds table that currently exists showing a HA of 5.26% is based on the Gambler’s Fallacy which demands that the next spin be 100% reflective of the 38 numbers showing up – which is false.

The MauiSunset True Roulette Odds tables above remove the Gamblers’ Fallacy from the calculations.

Basically you stand a horrible chance of having any winnings if you bet Straight Up – betting Equal Chance is much better at a HA of 7.14% but even that is above the stated HA of 5.26%

The “Law of the Third of Random Numbers”

If the chance of spinning a single number is 1/38 then the chance of NOT seeing the number is 37/38 and for 38 spins is (37/38)^38 = 36.3%, that means for a Roulette wheel 38 * .363 = 13.8 or 14 numbers will not show up in 38 spins.


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