I am reading Owen Gaines, poker math that matters and on chapter, Equity Versus a Range, I read the chapter and thought I got everything but no

I am stuck on the question 2:

Hero: JA

Villains range:QQ, KK, 55, 44

Board:54T

What is hero's equity assuming we're all in?

I don't know how he gets 45% equity for the hero against villains big pairs range and he gets 25% equity for the hero vs the villains set ranges. How the heck did he do that?

You basically need to count up how many cards can help you versus what redraws he has.

With AJss, any spade or Ace (so 12 outs or so) will improve you to beat QQ/KK. If you hit the ace, they have two outs for a set. If you hit the spade, they need the spade to have paired the board or it be their set card, and then redraw to a full house on the river. This is unlikely, so you have basically all 12 of your outs good and you get 45% (12*4 = 48% from the rough from flop rule, minus the 3% for redraws). Runner-runner jacks is unlikely enough to neglect.

If villain has a set, your ace is no good (not even runner runner!). You need to hit a spade to win, giving you at most 9 outs (he might have one if he has 55 so then 8 outs). If you hit the spade and he has 44, you need to discount the 5s since it gives him a full house. If it is not the 5s, he now has 10 outs on the river to hit the boat and beat your flush. The same occurs with 55, you just sometimes have all 9 outs on the turn.

9 outs = 36%, with a 10 out redraw which multiplies this by 0.8 giving ~28%. Take away 3% for the potential for him having the 5s or 44 (when you hate the 5s), which takes away about 3/4 outs. This gives you 25%.

Thanks for the nice explanation max, I will try it and get back if I have any questions.

Awesome post from a 'newbie' above ...

There are a lot of poker odds apps that you can put on your phone or look at online. Most of them will show you 'the math' and outs for any given situation. These are very good tools but most will only let you compare specific hands and not ranges of hands.

The simplistic rule is the rule of 4 and 2 ... You take your outs (to improve) and multiply by 4 if going to the Turn and by 2 if going to the River. As shown above, this doesn't directly discount 'bad' outs or 're-suck' outs your opponent may have if you hit the Turn.

It's best to keep these simple until you actually do consider comparing outs against a player's range, which may have a significant effect on 'clean' outs.

To take things further ... your 'total' equity can be figured out as well based on the possible combinations of holdings available to your opponent.

There are 6 combos of QQ and KK each .. so 12 total combos of pocket pairs
There are 3 combos of 44 and 55 each .. so 6 total combos of sets

So you face 18 combos here .. 67% and 33% ...

45%(67% of the time) + 25%(33% of the time) gives you a 'net' equity of about 38% to win here against this given range.

Just remember that all these numbers change once the Turn comes out. If you are all-in, no biggie, but if you still have chips behind you may not be able to just reduce these by half when looking to the River card. GL

PS .. You do have some runner-runner straights out there too, but in it's simplest form you don't really want to 'count' on those happening.

Runner-Runner draws are usually about one or two outs effective on the flop.

The runner-runner straight is variable (you may have more than one way to hit it) - in your case you need a Q and K, meaning the turn has 8 outs (6 if he has QQ/KK) and the river has 4 (2 if he has QQ/KK and the one he didn't have hit the turn). At best, this is ~16% * ~8% = 1.28%, or less than one out. Not usually worth mentioning, especially against a range which contains the cards you need.

Runner-Runner flush is a bit better - assuming villain does not have a flush card you have 10 outs on the turn and 9 outs on the river (your usual flush draw). This roughly equates to 20% * 18% = 3.6%, or a little bit worse than 2 extra outs overall. This makes a difference - an OESD with runner-runner flush is worth more than a naked flush draw using this approximation, while normally the flush draw gives you better odds.

I only count runner-runner flushes usually, and then usually only if I either need both cards or have the Ace (you get good implied odds against a K or Q high flush). If you have only one lower flush card be careful, since villain may have a better flush card negating your draw.

Hi everyone, I’m a bit confused about how to calculate equity.

Answer20 you say this:

“The simplistic rule is the rule of 4 and 2”
For a flush draw the equity will be 9*4=36 (turn) 9*2=18 (river)

but if I use another formula to calculate the equity the number is different, the common algorithm is the one used to calculate equity for a flush draw:
52-5=47 (cards in the deck)
47-9(cards to complete the draw)=38
38/9=4/1 in percentage 1/(4+1)=25% of equity which is weigh different compared to the algorithm mentioned before.
Which one is better to take in consideration?

Still,
“So you face 18 combos here .. 67% and 33% “

Can you please tell me how you calculate this percentage?

thank you

You have a few errors. For a flush draw on the flop the odds for hitting on the turn are 38/9= 4.22 to 1, which translates to a win probability of 1/5.22 = 19.2%. This compares to the approximate 18% given by the 2x rule.

NOTE: The 4x rule is used only for an all in bet on the flop.

1) The rule of 4 and 2 are shortcuts so you don't get lost in the deep sea of exact math. Yes, people over-use the rule of 4 since they generally are facing a Turn bet as well. The rule of 4 assumes that you 'will' see both the Turn and River cards.

2) You face 18 combos in the range you gave. 12 of them are QQ/KK combos .. or 67% of the 18 .. the other 6 combos (33% of 18) are the possible sets. GL

How are you getting 45% and 25%?

I must have punched the hand into my poker odds ap on my phone ...

WITH 2 CARDS TO GO ...

1) You are 45% to out draw KK or QQ with a clean Ace and a flush draw.

2) You are 25% to hit your flush/bd straight against a set

When you net these out against the potential combos you face it's 38% against the 'range' of hands used. GL