How to calculate expected return for a serie of spins?

Cokekiddy, if I'm not mistaken (tell me if I am) you're looking at column D on your link and determining that your probability of losing a given spin decreases based on past losing spins. This is not the case. It's showing that the probability of losing N spins, starting at spin #1 decreases as N goes higher. That is true; the chance of losing 10 spins in row is (19/37)^10 = 0.01275%. However, if you've just lost 9 spins in a row the chances of losing the next spin is still 19/37 = 51.35%. That's why column G stays at -2.7%.

Your expected return will always be [Bet] * [House Edge]. There's a few ways of using that. For a single spin of $10 the expected return is $10 * -2.7% = -$0.27. If you bet $5, then $10, then $20, then $40 your average bet for the series is 5+10+20+40 = $75 and your expected return for the series is $75 * -2.7% = -$2.02. To determine the expected value for a system simply find the average bet for a system and multiply it by the house edge. To determine the expected value for a particular series with a system, add all of the bets in the series together and multiply the sum by the house edge.

Thank you for eyplaining this,

But how do you explain column E? ("Average bet") from the link?
By using your formula I'm geting different results then those in a table (column E) from the link.

thats driving me nuts. what mean those numbers from column E? I have to know that otherwise I wont sleep :)

Thank you.

Average bet is the total amount you bet divided over the number of spins. This times column "G" gives column "F" - expected loss per spin. You need to multiply it by number of spins to get the expected total loss (it should be (2^n-1)*0.027 - total bet times house edge).

Ok,
I've done some testings in excel and here is my conclusion (correct me if am worng)

Column E "Average bet" is amount of chips needed multiplied by expected value (column G) so that Expected return will be equal to column F "Bet units" which acctualy IS Expected return :D.

However (lol),
when using this formula for non even-money bets then "Average bet" gets negative because expected return is positive.
so to solve this sign must be changed (for both average bet and expected return) to get right result!
finaly to prove these results, quotient of these result must be Expected value(house edge).

Haha :D
Thank you guys!
If you have some better way/ formula to achive this please advise me!


Kind regards!

OK, so, I just now finally actually went to the webpage in the link. The formulas are in the last line, aren't they? The n-case line tells you exactly how the values were derived...

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Sally

Quote: mustangsally

...This can not be correct.
I have to disagree with this statement and results.
$75 can not be the average bet for the 4 steps.
We need to know the weighted average so we can then multiply it by the house edge...

I understand what you're saying but I think you misunderstood what I was saying due to a very bad slip when I typed that up. Allow me to rephrase it:

If you bet $5 then $10 then $20 then $40 your TOTAL bet for that series is $75. At a house edge of -2.7% the expected return is -$2.02. That is true when looking at that particular series. It's not true, as you stated, when looking at the betting system as a whole or trying to find the average expectation.

I see your point about finding the weighted average bet per spin and appreciate seeing the math.

Quote: mustangsally

We need to know the weighted average so we can then multiply it by the house edge.

This is the sum of the product of each value or the weighted averages (one can use the SUMPRODUCT function in Excel)
or longhand
=$5*1 + $10*0.513513514 + $20*0.263696129 + $40*0.135411525

avg bet = $20.82551873 * (times)
house edge = -1/37
expected value = -0.562851857

Why?
100% of the time we make the first step wager of $5.
The $5 wager loses with a probability of 0.513513514, so we make the $10 wager 0.513513514 of the time
The $10 wager loses with a probability of 0.513513514, so we make the $20 wager 0.513513514*0.513513514 (p^2) of the time
The $20 wager loses with a probability of 0.513513514, so we make the $40 wager 0.513513514*0.513513514*0.513513514 (p^3) of the time
The $40 wager loses with a probability of 0.513513514 and so on

another way to calculate the expected value (return)
=(0.930464352*$5)+(0.069535648*-$75)
Sally

This is freak'n awesome!!
I'm Finaly geting right results in excel :D

Thank you Sally a lot! All your help is much appreciated!

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