Poker Maths - Headscratchers of the world unite

Benchmark

Okay, so there's 1000 chips in the pot. I need to bet 200 to call.

I have 8 outs on the river.

Pot odds 5/1 (200 chips to win 1000)

Card odds 8/46 = 5.75/1

Pot odds need to be greater than card odds to call. It's a fold.

However.... If the same cards are dealt 46 times, I should hit my outs 8 times and miss them 38 times, due to the laws of probability.

8 x 1000 (when I win) = 8,000 chips (hurrah!!!)

38 x 200 (when I lose) = 7,600 chips (boo!!!)

Soooo.. how come I win more than I lose , although the odds indicate it should be the other way around ???



Hopefully, I've made a simple mistake.

FeelGroggy

When you call the 200 the pot becomes 1200 chips which you need to win 1 out of 6 times to breakeven on your call ☺ Also I imagine you have implied odds and can get extra chips when you do hit. 

BorinLoner

Eight outs on the river isn't 5.75:1.

You're getting mixed up by 8/46 (eight divided by 46) and equating that to 8:46 (8 to 46). The second, 8:46, suggests there are 54 cards still in the deck. You need to be using 38:8, which is 4.75:1. There are 8 good cards and 38 bad ones.

BorinLoner

In Response to Re: Poker Maths - Headscratchers of the world unite:

When you call the 200 the pot becomes 1200 chips which you need to win 1 out of 6 times to breakeven on your call ☺ Also I imagine you have implied odds and can get extra chips when you do hit. 
Posted by FeelGroggy

This would be the way to calculate odds as a percentage or decimal. You'd say 200/1200 = 0.167 or 16.7%.

Using the old school odds, it's still 1000:200 or 5:1. 

Mostly people use a / to illustrate pot odds but they also use a / to indicate division... which is very confusing of them.

FeelGroggy

Yeah you seem to be getting confused with ratio and fractions. If there is 1 boy and 3 girls then 1/4 of the people are boys. The ratio of boys to girls is 1:3. A ratio of 1:4 would mean there's 1 boy and 4 girls. They aren't the same. I know it's a lame example but all I could come up with on the spot

Benchmark

Ahh... that now makes sense. I was confusing 1/5 meaning the same as 1:5.

TVM.

Benchmark

Okay, here's the rewrite..


There's 1000 chips in the pot. I need to bet 200 to call.

I have 8 outs on the river.

Pot odds 5/1 (200 chips to win 1000)

Card odds 38/8 = 4.75/1

Pot odds need to be greater than card odds to call. It's a call.

To prove.... If the same cards are dealt 46 times, I should hit my outs 8 times and miss them 38 times, due to the laws of probability.

8 x 1000 (when I win) = 8,000 chips (hurrah!!!)

38 x 200 (when I lose) = 7,600 chips (boo!!!)

I actually folded this hand earlier today. I guess it was a call after all. The 8 DID hit the river AND it was a correct call, even if it hadn't.

Not sure I could do the math again in 30 seconds...