Stats/Gambling question

[digital goldfish]

I'm trying to work out how often one would win in the following scenario:

A game requires you to bet on what number dice will fall on. There are 3 dice, and the pay out is as follows:

1 of a kind pays 2x
2 of a kind pays 3x
3 of a kind pays 10x

By placing a single bet on the same number every time, how often should one win? (i've been betting on 4, and won quite a lot)

[Prester John]

I reckon the payback is about 45% of the stake based on some very rough calculations

2/6 + 3/36 + 10/216
= 0.46

Its rough because i haven't taken into consideration that that the 3 of a kind win reduces the 1 of a kind winnings, so i think the actual return will be slightly less.

Now someone destroy my math credibility........

[digital goldfish]

Originally posted by Prester John
I reckon the payback is about 45% of the stake based on some very rough calculations

2/6 + 3/36 + 10/216
= 0.46

Its rough because i haven't taken into consideration that that the 3 of a kin win reduces the 1 of a kind winnings, so i think the actual return will be slightly less.

Now someone destroy my math credibility........

Ye see, the thing is, i put £60 in to an account earlier, and kept betting £5 on a 4 coming up, and within about 5 minutes, i had £150.. They seem very good odds to me..

[The Don]

I'd say

either you're playing the real game and you've been very lucky OR
you've been playing the "demo" game and they're trying to suck you in (only the live game has to reflect real world odds)

[digital goldfish]

Originally posted by The Don
I'd say

either you're playing the real game and you've been very lucky OR
you've been playing the "demo" game and they're trying to suck you in (only the live game has to reflect real world odds)

I played the demo for ages to make sure i wasn't going mad, and then i switched to the real game. It appears to be completely legitimate, and although i noted the company is based in the dutch antilles, i suspect that's more for tax reasons. The people themselves are fully tied in with the London Evening Standard, who i would regard as reputable

[drkitten]

Originally posted by digital goldfish
I'm trying to work out how often one would win in the following scenario:

A game requires you to bet on what number dice will fall on. There are 3 dice, and the pay out is as follows:

1 of a kind pays 2x
2 of a kind pays 3x
3 of a kind pays 10x

By placing a single bet on the same number every time, how often should one win? (i've been betting on 4, and won quite a lot)

I assume normal, cubical, 6-sided dice here and not some topological crawling horror from the depths of Dungeons and Dragons.

There's one chance in six (1/6) of rolling your chosen number, 5/6 of not.

So the chance of rolling your number on the FIRST die and not on the second and third is 1/6 * 5/6 * 5/6 or 25/216. There are three different orders these dice can come in, so you have 75/216 chances of winning 2x.

Similarly, you have 15/216 chances of winning 3x, and 1/216 chances of winning 10x.

Your expected winnings are thus 150/216 + 45/216 + 10/216, or 205/216, a little less than 95%. In other words, the carnie will on average keep a 5 cents on the dollar, or 5p on the pound, or five ore on the crown, or whatever your local currency is. It's a mug's game, but still better odds than American rules roulette.

(This good enough, PJ?)

[Prester John]

If a casino is using it then the odds favour the house.

[digital goldfish]

Originally posted by Prester John
If a casino is using it then the odds favour the house.

It's an on-line game, and yes, they are 6 sided die.

[Prester John]

Goddamint i h8 math, its soooo obvious when ur mistakes are pointed out.

(searches pubmed for cherry picked study to prove he was right all along)

[The Don]

Never mind.....

[digital goldfish]

Originally posted by The Don
Well t'would appear that you've been very lucky then because, as PJ pointed out, on average you'll get 45% of your stake back.

After 1000 £5 plays not playing back any winnings, i.e. your original stake was £5000, you should expect to have £2250ish left

If you had an initial stake of £500 and played it though 10 times, you'd most likely have nothing left

(assume 50% return for eay maths (slightly higher than this game)

Iteration 1: start with £500 finish with £250 (play 100 games)
Iteration 2: start with £250 finish with £125 (play 50 games)
Iteration 3: start with £125 finish with £62.50 (play 25 games)
Iteration 4: start with £62.50 finish with £32.50 (play 12 games)
Iteration 5: start with £32.50 finish with £17.50 (play 6 games)
Iteration 6: start with £17.50 finish with £10 (play 3 games)
Iteration 7: start with £10 finish with £5 (play 2 games)
Iteration 8: start with £5 finish with £2.50 (play 1 game)

and you can't afford to play any more. You won't achieve such "nice" splits and of course as the number of plays per iteration reduces the impact of caruability in the split will increase

Ye see, of course i agree with you, but there is no such thing as luck (apart from in a richard wiseman, if you believe you are lucky, you'll take advantage of more opportunities etc etc)

I played maybe 5/600 iterations before playing with my own money, and i just couldn't lose... I'm not saying the maths is wrong, but it seems too good to be true.. (gambler's fallacy?)

[drkitten]

Originally posted by digital goldfish


Ye see, of course i agree with you, but there is no such thing as luck (apart from in a richard wiseman, if you believe you are lucky, you'll take advantage of more opportunities etc etc)

Well, no, perhaps not, but there is such a thing as improbable but favorable events that happen despite not being likely.

I think you just saw one :



I played maybe 5/600 iterations before playing with my own money, and i just couldn't lose... I'm not saying the maths is wrong, but it seems too good to be true.. (gambler's fallacy?)

or maybe (this is my natural suspicion talking) they aren't using "fair" dice in the random number generator, in an effort to persuade you to bet larger and larger sums. You won, what, ninety quid? If you decide (wrongly) that the odds are in your favor, you might come back tomorrow with a thousand in your pocket and play at the real odds. It's even better, of course, if you can be persuaded to tell all of your friends at the JREF board about this wonderful game you found at an on-line casino and we spend al our money, too. (By the way, you forgot to give us the web page, so it didn't work out quite how they had hoped.)

[digital goldfish]

Originally posted by drkitten


Well, no, perhaps not, but there is such a thing as improbable but favorable events that happen despite not being likely.

I think you just saw one :



or maybe (this is my natural suspicion talking) they aren't using "fair" dice in the random number generator, in an effort to persuade you to bet larger and larger sums. You won, what, ninety quid? If you decide (wrongly) that the odds are in your favor, you might come back tomorrow with a thousand in your pocket and play at the real odds. It's even better, of course, if you can be persuaded to tell all of your friends at the JREF board about this wonderful game you found at an on-line casino and we spend al our money, too. (By the way, you forgot to give us the web page, so it didn't work out quite how they had hoped.)

Indeed lol - Well they have two dozen other kinds of games, and this is the one with which i generated the most demo points, so that's the one i put money on. I very quickly withdrew it all though; i ain't stupid..

btw, go to http://www.thisislondon.com and i'm sure you'll see a link (suspect it's UK only tho)

[Prester John]

Apologies to the Don :D

There of course could be someone on another forum wondering why he has lost all his money so quickly when he should get a 95% return.

Do not question why you won, just take the money and run :)