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 Originally Posted by Thunder
Spoon,
Thx for your explanation. I read what you wrote and though it makes sense in the context of your post, it doesn’t make sense in relation to mine and the maths I am using. Now, I have gone over my workings out numerous times, with differing examples, and it always adds up! I will detail various maths examples so hopefully you can spot the mistake I am making – because I cannot.
Just to cover the obvious and where I am coming from: 1 IN 10 is written as 1/10 and equals 9 TO 1 (which is written as 9:1).
The simple way to remember is that "IN" is always one more than the "OUT".
So 1/10 is 9: 1
1/20 is 19:1
1/7 is 6:1
1/4 is 3:1
So far so good. I don't think anyone will disagree so far.
And if this is true then 10/25 (or 1/2.5) equals 1.5:1 and not 2.5:1.
Example 1
So calling $10 to win $40 is 10/40 or 1/4 (1 IN 4). We know this is 3 TO 1. And if we do the calculation 1/4 x100 we get 25%. Out of 100 percent, the ratio to 25/75 and that is 3:1 – which is what I said at the start of this example. And so, as you can see, my maths is correct as this example proves that 1 in 4 is 3 to 1.
Now, if this example is true then by the same token, the OP setup of calling $10 to win $25 means that it is 10/25 (10 "IN" 25) or 1 in 2.5 And this, by the maths above, is 1.5: 1 not 2.5:1 as has been written. So first off, why do you say it is 2.5: 1 when the maths here shows that it’s 1 IN 2.5 and that this equates to 1.5:1?
Secondly, by my working out, the bet is 40% of the pot (as Stacks already said). We know it’s about that anyway without doing any maths because it’s just short of half the pot – and thus just short of 50%. So again, I cannot see how it works out that a near 50% bet equates to 28.5%. And if we show as a ratio then 40% is 40/60. 40 fits into 60 exactly one and a half times and is thus, as said, 1.5 to 1.
And just to test my maths once more, here is an even more obvious example. Let’s make the villain bet $10 into a $20 pot, exactly half the pot. This is 10/20 or 1/2. 1 in 2 is 1:1. And if we do the actual working out we get 10/20 x 100 = 50%. And 50% is 1/2 because you have a 1 in 2 chance of winning. A 1/2 chance means you win one and lose one, and this is, as already mentioned, 1:1.
Can you see where I am apparently going wrong here? I have no idea and every test I run works out exactly.
Help mucho appreciated.
Thunder, there's nothing wrong with your calculations, your problem is your starting assumptions. Calling $10 in a pot that already has $40 in it is 10 in 50, or 1 in 5, or 4:1. It is NOT 1 in 4.
Perhaps the best way to illustrate this is your last example. Lets say you have a $10 pot on the river, and villain bets pot. So you the option to call $10 into a $20 pot. If you call and lose, you're down $10. If you call and win, you're up $20 (the pot not including your call). So therefore you only have to win more than 33% of the time for this to be profitable or 1 in 3 times. Or put another way, your pot odds are 2:1.
Does that help?
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