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I have a seemingly simple problem but I can't work it out. Say I start with a bank of £20 - I would like to work out how much I should bet take my bank to £25 (assuming a win).

In this case we'll assume odds of 2.00. Since the amount I want to win is £5 I could bet £5/2.00 = £2.50 however, if the bet won my final bank would be £22.50 and not £25.

Can anyone point out what I'm missing here?

Thanks, Matt

Matt Griffiths
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  • won't you get £10 back at 2:1? (you win £2 for every £1 staked, plus your stake back giving you a bank of £30) – JMP Sep 15 '16 at 10:09
  • I assume you mean you are betting on the favored side. But if a bet of $X$ returns a profit of $\frac X2$ all you need to do is to solve $\frac X2=5$. – lulu Sep 15 '16 at 10:13
  • @JonMarkPerry Thanks for your response - the odds are expressed in decimal format. This means that if you bet £2.50 at 2.00 - you're return is £5. Your stake is included in the £5. – Matt Griffiths Sep 15 '16 at 10:17
  • @lulu This might be related to Jon's point. If I was to solve that equation I'd get £2.50 as the amount I should bet. This'll be taken of my bank at the time of the bet (now it's £17.50). If I win, my winnings (including my stake) are £5 - this means my total bank is now £22.50 and not the £25 I want have. – Matt Griffiths Sep 15 '16 at 10:21
  • The solution to $\frac X2=5$ is $X=10$. – lulu Sep 15 '16 at 10:30
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    It isn't clear to me which side you are betting on! You just say "the odds are $2.00$ but you don't say for or against. The fact that your profit is lower than your bet, in your example, is consistent with your betting on the favored side. That is, you are betting on the side that $\frac 23$ of the bettors think will win (ignoring the house spread and such). Assuming that's correct, then I agree your bet of $5$ will get you a profit of $2.5$, so a bet of $10$ will get a profit of $5$, which was your goal. Or have I misunderstood the way you are quoting the odds? – lulu Sep 15 '16 at 10:35
  • @lulu It's only a for/againts ambiguity when the odds are expressed in US format (2-1). When the odds are expressed in European decimal format there is no such ambiguity. For example 2-1 against is $3.00$ and 2-1 for is $1.50$. Anyway OP should really clarify here as there are like 3 different interpretations here. As I understand it $2.00$ is an even money bet so betting $2.5$ would only win you $2.5$ bringing the bank up to $22.5$ – Winther Sep 15 '16 at 10:46
  • @Winther thanks. I guess I've seen that system before, but it never fails to confuse me. So....you just state what the total return is on a bet of $1$? Of course, in that case you are correct that decimal odds of $2$ should mean an even money bet. – lulu Sep 15 '16 at 10:52
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    @lulu The for/against thing confuses me even though it's just two options. I always have to look up the definition. Exactly; its the total return. The way to convert it if the odds is $a$ - $b$ with $a>b$ then in decimal this is just $\frac{a+b}{a}$ (for) or $\frac{a+b}{b}$ (against). So 4-1 is $1.25$ (for) and $5.00$ (against). – Winther Sep 15 '16 at 11:00
  • I'm sorry for the lack of clarity on this, and I appreciate your comments. – Matt Griffiths Sep 15 '16 at 18:23

1 Answers1

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Your mistake is that $£5:2.00=£5$ profit, not $£2.50$ as you say, so your bank would be at $£25.00$, as you wanted.

If the odds are $d$ and you make a stake of $s$, then your profit $p$ is:

$$p=s(d-1)$$

So for a profit of $p$, you should stake;

$$s=\frac p{d-1}$$

JMP
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