Statistics

[Cunchy]

Gentlemen, Ladies, members of the gaming industry that keep an eye on this board (we know who you are), I have noticed various threads on this and the roulette forum discussing statistics and whether on-line RPGs (roulette etc.) and slot machines are rigged, heavily biased, kick-in losing streaks when you win etc., choose numbers for you on bonus games that may appear to the user to be random etc.

A certain large and arguably reputable site has recently added a version of Deal or No Deal to its online gaming, with a demo mode. Because of the way the game works it is quite simple to calculate the percent payout of the game.

There are 26 boxes. Using a £100 stake the lowest box is worth £2 and the highest worth £1000. The sum of the 26 boxes (lowest value £2, highest value £1000) adds up to £2482. Therefore the 'average' box is work £95.46.

The payout is therefore 95.46% (compare that to an allowable minimum of 70% for a mechanical slot!!) and the house advantage is therefore 4.54%. For comparison, the house advantage for an unbiased European roulette wheel (single zero) is 2.7% and for an American wheel (two zeros) is 5.3%.

This continues throughout the game. If, after you have picked the first 6 boxes, there is a total of £1556 left in the remaining 20 boxes then the 'banker' will offer you £77.80 for your box, i.e. £1556/20 (which you paid £100 for), thus still keeping the 4.54% advantage.

This continues up to the final two boxes (if you haven't already accepted the banker's offer), when the game becomes 50/50. If there is, say, the £2 box and the £1,000 box left then the banker will offer you exactly half, £501 (for the box that you paid £100 for). Similarly, if you've really blown it and the last 2 boxes are £2 and £4 then the banker will offer you £3 (for the box you paid £100 for).

Bizarrely then, and if my basic grasp of statistics is correct, if you play the game a statistically large number of times and always accept a banker's offer before the final round then you will ultimately lose, at a rate of 4.54%. If, however, you always see the game through to the final two boxes and accept either the banker's offer or the box you initiallly chose then you will utlimately end up breaking exactly even.

So, if you want to gamble but don't like the idea of winning or losing then play this game a million times to the last two boxes!

I have not tried this in 'real money' mode but it would be very simple to check the maths, and given this and the credibility of the site I doubt that they would risk a a 'real money' game that didn't play exactly the same as the demo mode.

I'm not aware of any other on-line number game that allows such an easy calculation of house advantage, but perhaps there are some. I don't play a great deal.

This doesn't, of course, answer the question as to whether some on-line number/fruit games are biased/rigged etc. (roulette/slots/dice etc.) but it does clearlly indicate that this particular site is happy to provide a game with only a 4.54% house advantage.

Trust that this is useful.

Cath

[Cunchy]

Folks etc.

Having had a strong coffee I realise now that my grasp of statistics is basically correct but that the game always shows house advantage of 4.5%, even if you play to the last 2 boxes...d'oh.



Cath

[SteveDude2]

Yep, no different to covering every number on roulette with the same amount every time - you'll just lose 1/37 of your overall bet every time because of the edge...

I can see that Deal or no Deal game being quite flat if the number of boxes higher than £100 is the same as the number that are lower. The offer will stay roughly the same all the way through. I haven't seen the game so I don't know...

Nice post though!