Help trying to understand probability in 2-7 triple draw

I wouldn't go about it this way. I have been playing for a long time and I dont know the answer to these questions. Try to find a way to learn pre-draw ranges and go from there.

Ha, fully agree with this / me too

Yes and no. If you knew the math answer would that tell you whether the hand is playable or not? If you make a 7 25% of the time with a certain starting hand is that good enough? 15%? You can figure out a probability calculation but it wont tell you the answer to can you play the hand. I would suggest you look at studflopdraw.com which is very math / equity based tools for draw games (among others).

I get what your saying but I would still like to know. Do you know how to do it??

For a D1 hand like 2347, the math is fairly easy to do yourself. On the first draw, there are 48 cards to draw from, and 8 of them make your hand. So 8 out of 48 you make it on the first draw. 40 out of 48 you do not. Of those 40 you do not, there are 47 cards to draw from, and 8 make your hand. Etc.

For the D2 hand like 237, now you have to start dividing this into the times you hit both cards on the first draw, hit one card on the first draw, and hit zero on the first draw. It branches out quickly, and is messy to do by hand. I do not know any method to do this more easily.

Do you know anywhere that shows it the long way by hand. I like seeing the maths and trying to understand it

You might enjoy this very old forum post: https://fullcontactpoker.com/poker-forum...

Hopefully the poster has gotten better at formatting since then!

It's actually 47 cards to draw from because the 5th one you discarded isn't generally coming back (unless there aren't enough cards left in the stub because of many players still in the hand, which rarely happens).

Exactly what I'm looking for but wow it's hard to understand.

Yeah, math is hard!

How are you thinking about the game without knowing the maths of drawing?? It seems to be like you have to put your opponent on a hand and then see if you think can outdraw him.

Like I've said before. I'm brand new to the game. But to me it looks like you have to put your opponent on a range and then workout if you can outdraw him. And to know if you can outdraw him would require some understanding of the math. But maybe I'm wrong. How are you making decisions in a hand??

I've played millions of hands of the game. I know when I have a four card 7 draw I should almost never fold it, I know when I have a rough 87 draw when I should fold it and when I shouldn't. Yes these things are based on math, no being able to calculate the math exactly would not help me. You can use an equity calculator to see how you are doing hand vs range, or range vs range. I've met a lot of students that view things the way you do, all I can say is you are focused on a tree and ignoring the forest 😀

Occasionally you will be in a close spot on the last draw where you are against a pat hand will think: OK I need a 4 or a 6 to win almost for sure and I will assume say 6 of them are live depending how the hand played out, and then if I hit an 8 I expect to win half the time so I will count that as 2 outs...so I reckon I have 8/45 or 18% equity or so. Check the pot, factor in some implied odds if you hit, and decide whether or not to continue.
Thats about the only time its ever needed imo.

I think this math is wrong.

You are adjusting the numerator without adjusting the denominator. If you are counting the opponents blocking your outs, you have to also count the cards they have that are NOT blockers.

In your example, you get 8/45. Your odds are better than that.

It looks like you are using 7532 as your hand. Let's assume you are drawing one. From your own perspective, you have seen at least 3 other cards if you were D1 from the start. Unless your opponent is snowing, they have other cards that block your pair outs as well, or if you prefer reduce your denominator.

Say their hand is a pat 86432, so they block 2 of your outs. Let's also assume this is heads up, so we don't have to worry about the other players folded cards.

My final answer is...we have seen 7 cards, and our opponent is holding 5 cards as well, so the denominator is at most 40. In more realistic scenarios, your opponent has probably drawn; you might have started with a D2. Say it was D2vs D1 and you opponent was pat after the first draw, and you were down to D1. Now the denominator is down to 38. The numerator might need to go down a little as well, as the opponent may have had a pair of the cards you needed, but that effect isn't particularly likely.

The clumping factor (or whatever it is called) probably adds another tiny bit. At a 6 handed table, if you are heads up predraw, your cards will be a bit more live; if 4 people saw the draw, your cards will be more dead, on average...

This is more work than one candidate do at the table, but is useful for honing your intuition when looked at in retrospect.

Math is hard. Apparently most players don’t know math! Boycott WSOP Circuit! With tournament rake over 20% even in $300+ events is proof of fact! All WSOP circuit should be boycotted! I don’t know how anyone thinks they can beat 20+% tournament rake, the pro and semi pro’s are losing the most money. Why don’t pros form a union and boycott the high rake? I’ve met too many players who gladly pay 25% WSOP rakes and they violently defend it when I present my opinion!!! Are poker players really desperate gambling addicts or simply dumb???