Help With Probability

[ukanonymous]

Help with probability

Say you are playing a gambling game which is 0.5 To play

The prizes are as follows:
52% lose
1% chance to win 0.52
1% chance to win 0.7
1% chance to win 0.72
45% chance to win 1.0


After 1000 games How much will you have spent and how much are you likely to win and how do you predict/ calculate how much you will win?

[fiction-factory]

If I have understood your question:

Playing 1000 games @ £0.50 costs £500
Winnings:
(520 x 0 ) + (10 x£0.52) +(10 x £0.70) + (10 x £0.72) + (450 x £1)

[fiction-factory]

So winnings = £469.40 (calculated in my head so please check)
Which means in the long run you can expect to lose £30.60 if you play 1000 times.
You might win more or less - this is just an average

[ukanonymous]

yes so you could be up or down at any point right?

[ToraToraTora]

this is not a probability issue, merely arithmetic. Eg 52% lose means that there are 480 wins assuming statistically perfect distribution which with a sample of 1000 will be close. So then take the 480 wins and dived it up as 1,1,1,45 as specified above. So there will be 450 + 0.72 + 0.7 + .52 = 451.94 so you will have 1000 goes at 0.5 = 500 and win 451.94 so overall you will lose 8.06. Taken to infinity you will lose 4.03%

[ToraToraTora]

sorry I meant lose 48.06 and the precentage to infinity is 9.6%

[ukanonymous]

The problem I am having is this Say you are playing a gambling game which is 0.5 To play

The prizes are as follows:
52% lose
1% chance to win 0.52
3% chance to win 0.7
1% chance to win 0.72
45% chance to win 1.0

I am getting a game takings of 500 but winnings of 483.4 This is not correct right?

[ukanonymous]

Sorry:

The prizes are as follows:
50% lose
1% chance to win 0.52
3% chance to win 0.7
1% chance to win 0.72
45% chance to win 1.0

I am getting a game takings of 500 but winnings of 483.4 This is not correct right?

[fiction-factory]

Yes, you could be up or down at any point but in the long run a player will lose.
I came to the same conclusion as ToraToraTora but I think our figures are slightly different as I think the 480 should be split 10,10,10, 450

[fiction-factory]

Just work it out in the same way using your revised figures and my method

[fiction-factory]

50% lose = £0
1% chance to win 0.52 = 10 x£0.52= £5.20
3% chance to win 0.7 = 30 x £0.70= £21
1% chance to win 0.72 =£7.20
45% chance to win 1.0 = £450
£483.40 is correct

[fiction-factory]

I hadn't realised you were the organiser not the player. So you will WIN in the long run, but if you are thinking or organising a game you have to be prepared to lose a bit in the short term

[ukanonymous]

The prizes are as follows:
50% lose
1% chance to win 0.52
3% chance to win 0.7
1% chance to win 0.72
45% chance to win 1.0

I am getting a game takings of 500 but winnings of 483.4 This is not correct right?

1000*.01*.52=5.
1000*.03*.7=21
1000*.01*.72=7.2
1000*..45*.72=450

therefore your total winnings = 483.4

BUT you have 50% chance of winning prizes more than what you played with so it should be MORE than 500. What is wrong with this?

[fiction-factory]

Your figures are right for the payout over 1000 plays - your expected pay out is £483.40 and your takings are £500

[ToraToraTora]

OK the figures are 500 in and 483.4 out (96.68%) for a sample of 1000 you cannot say that will happen for certain. The larger the sample the closer you will get to the 96.68% payout but for small samples you could be paying out more (that's how fruit machines work (smaller payeout %tage mind)), so you could lose for small samples. eg if the first 5 people in your game win which is entirely feasable then you are down, it will come back if you get the numbers of players.

[fiction-factory]

>BUT you have 50% chance of winning prizes more than what you played with so it should be MORE than 500. What is wrong with this?

Think of it this way. If you paid out 51p to 50% of entries you would make a loss as the gamesmaster of 1p each time- but that is insignificant compared with the 50p profit in the other 50% of plays

[jim360]

I don't think uka has a problem with the figure being less than 500 per se, merely he's confused why is should be less in the case when half of the time you are winning more than your stake -- as in, why if you win half the time and lose half the time don't you get back what you started with?

To which the answer is no, because 5% of the times the winnings made are less than the stakes lost when you did lose. Consider as an absurd example a game in which half the time you lose everything but the rest of the time you win back your stake plus 1%. Then each win only recuperates 1% of the money lost in the other half of the games, which is never going to be enough to recover the total losses on average.

[Old_Geezer]

This will not tab correctly but this is what I get:

stake (non-refundable) £0.50
number of bets 1000
total staked £500.00

520 0 0
10 £0.52 £5.2
10 £0.70 £7
10 £0.72 £7.2
450 £1 £450
Total £469.4

So the player stakes £500 and is expected to win £469.4 for a net loss of £30.6 (which is effectively won by the organiser).

[Old_Geezer]

Oh, percentages are being changed from the original are they ?
Ho hum ...

[ukanonymous]

Jim I am not a HE.

Lets say we have a game
50% chance of winning 2
50% chance of winning 0

then after 1000 games player takes 1000 and game takes 1000

So from the last %'s you have 50% of winning equal or greater than .52

Therefore the player after 1000 games should take minimum 520. But if you calculate it like this:
1000*.01*.52=5.
1000*.03*.7=21
1000*.01*.72=7.2
1000*..45*.72=450

therefore your total winnings = 483.4

It is not right. Why?

[fiction-factory]

I'll leave it to you jim. I think we're going round in circles or there is a misunderstanding somewhere