Can anyone tell me why this math formula works?

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I'm an avid poker (texas hold'em) player, and calculating odds is a big aspect of a game.

There are certain situations where I can calculate the exact odds in my mind. Basically it's when I'm against one opponent, and there's one more card to come. In such a situation, there are 44 unknown cards.

So say I'm losing and there are 17 cards I can hit to win, my odds are 17/44. This is when I do the following calculation.

17/44 = 34/88
34/88 = 4.25/11

34 + 4.25 = 38.25 and 88 + 11 = 99 ====> 17/44 = 38.25/99

100/99 = 1,01010101010101....

So I do 38.25*1.0101010101...

Basically it's 0.38 + 0.25 on an endless loop, giving me the answer 38.63636363636363...% Or 38.64%

I tried it with several numbers, it always works.
I'm just baffled by the fact that my 34/88 + 4.25/11 math works, I have no idea how.

I'm confused. What are you trying to calculate?

I follow your logic and see how the odds are being computed quickly. I just can't explain why either

Why I would calculate this?
Poker is basically a statistics game.

Say I have 17 cards I can hit that help me, with 44 unknown. The other player moves all-in (in other words, bets all his chips.)
In such a case I have to calculate what my odds are. A 38.64% means a bit under a 4/10 chance, which means I'm a bit over a 3 to 2 underdog.

Which means the ratio of what I earn if I call his all-in, and what I have to put into the pot for me to make it a valid bet, has to be a bit over 3 to 2.

Anyway, FMX had it correct. I was wondering why that specific thing works.

Oh, so you're wondering why (34+4.25n)/(88+11n)=0.386? It's because you're keeping the ratio the same, FMX had it right. I'll explain it a bit more. So you start with 34/88=0.386. If you multiply 34/88 by one, you get the exact same number, as anything multiplied by one is equal to itself. So, (34/88)*1=0.386. Now, replacing 1 with what you had: (34/88)*((1+(n/8))/(1+(n/8))=0.386. (1+(n/8))/(1+(n/8)) is equal to one, since both the numerator and denominator are exactly the same. Once you multiply it out, you end up with the same equation in your original post, (34+4.25n)/(88+11n)=0.386. It's just different ways of expressing the same thing, multiplying by one doesn't change the expression at all. You could replace 1 with just about anything you want as long as it's still equal to 1, for example (34/88)*((950x+6758.56/x)/(950x+6758.56/x)) will still equal 0.386.


PS: Don't do that, the weird addition thing.

Poker

It seems that you have found a way of calculating the decimal value of 17/44 and wonder why it works. Now with 34/88 you have multiplied the numerator and denominator by 2, and with 4.25/11 you have multiplied them by 0.25. Combining them is the same as multiplying the original numbers by 2 + 0.25 = 2.25; i.e.: 17 x 2.25 = 38.25 and 44 x 2.25 = 99 and so on. You can do something similar if you end up with for example 98 as denominator, since 100 / 98 = 1.020408... If I needed to calculate 17/44 however, I would probably do 17/11 = 1 + 6/11 = 1.545454... and then divide by 4, which is the same as dividing by 2 twice: 1.54545454... / 4 = 0.77272727... / 2 = 0.3863636...