Your Questions About Poker Odds Outs

Betty asks…

Whats a quick way to work out pot odds in a game of Texas Holdem Poker?

I have trouble calculating pot odds quickly in live play, does anyone have any tips on being able to do this quickly and easily?

admin answers:

Yes, simply make sure you learn the odds of hitting your hand FIRST. You should know these back to front and inside-out. Here’s some help:

Once you have those memorised, you simply work out what’s in the pot and compare what it costs to call versus the odds of making your hand. The thinking MUST be more automatic than manual though. Otherwise you will struggle.

Like this:

„Odds of making my flush on turn or river are 2-1. There’s $50 in the pot and it costs $10 to call, so I’m getting 5-1. Easy call.“

Ken asks…

poker percentages/pot odds?

what are the odds of three out of the five community cards being hearts?

admin answers:

If you meant AT LEAST 3:

Disregarding your hole cards:
(13 * 12 * 11) / (52 * 51 * 50) +
3 * (39 * 13 * 12 * 11) / (52 * 51 * 50 * 49) +
6 * (39 * 38 * 13 * 12 * 11) / (52 * 51 * 50 * 49 * 48)

= 9.2767%

But if you meant EXACTLY 3:
(5 c 3) * (39p2 * 13p3) / (52 p 5) = 8.1543%

(note: 52p5 is a shorthand for 52*51*50*49*48)

Alternative scenario #1 — both of your hole cards are hearts:
(11p3) / (50p3) +
3 * (39 * 11p3) / (50p4) +
6 * (39p2 * 11p3) / (50p5)
= 6.4%

10 * (39p2 * 11p3) / (50p5) = 5.77%

Scenario #2 — 1 of your hole cards is a heart:
(12p3) / (50p3) +
3 * (38 * 12p3) / (50p4) +
6 * (38p2 * 12p3) / (50p5)
= 8.2247%

10 * (38p2 * 12p3) / (50p5) = 7.3%

Scenario #3 — neither of your hole cards is a heart:
(13p3) / (50p3) +
3 * (37 * 13p3) / (50p4) +
6 * (37p2 * 13p3) / (50p5)
= 10.3%

10 * (37p2 * 13p3) / (50p5) = 9%

If you need me to explain the method, just say so. There is also another method.

Your wish is my command, pdq! But do not mistake this as an admission of being your female dog!

The reason you can’t just do:
10 * (11p3 / 50p3)
is because not all ways of getting 3+ hearts are equivalent, there would be an error resulting from using the same denominator terms too many times and using too few terms in the denominator (getting a non-heart will change the denominator for the next heart, and will also insert an extra term into both the numerator and denominator). Doing the above pretends HHH is the same as XXHHH, which it is not. (11*10*9)/(50*49*48) is not equal to (39*38*11*10*9)/(50*49*48*47*46)

There are 3 different sets of permutations:
A) you can accomplish 3 hearts on the flop
B) you can accomplish them by the turn
C) you can accomplish them by the river

You’ll notice my 3 lines of work correspond to those 3 sets. There is only 1 way to get them all on the flop: HHH. There are 3 ways to get them by the turn: HXHH, HHXH, and XHHH. There are 6 ways to get them by the river. Mathematically, every individual permutation belonging to the same category is equal to one another. For instance, P(hxhh) = P(xhhh). So that’s why you can just multiply by 3 and 6.

As a way to check my work, notice: P(exactly 3) + P(exactly 4) + P(exactly 5) = 6.4%
(using my method for exactly N hearts)
And my method for exactly N hearts is simple: there MUST be exactly 5-N non-hearts. Those appear in my answer as the „39p2“ aka 39*38. And all 5 cards must be accounted for, so there has to be 5 terms in the denominator (so you go from 50 to 46, hence 50p5).

And actually, look again: James‘ answers agree with mine, not yours 😛

Carol asks…

Odds of one person winning in poker?

What are the odds of one person out of nine being delt a winning hand using a standard 52 card deck in Texas Hold em Poker? That is with everything being equal and no pot involved. How often should one person be delt a winning hand?

admin answers:

>Here ya go for an answer:

Lisa asks…

pot odd and outs poker help?

how does 2 to 1 turn into 1/3 then to 33%

i dont get it what is the math in it thanks

admin answers:

2:1 odds is 2 chances to lose vs 1 chance to win.

Count all chances, and you have 3 total outcomes. 1/3 is a win, 2/3 is a loss.

1/3 = 33.33/100 or 33.33%

Take 1/3 = x/100 then (1 * 100) / 3 to get 33.33

To change fractions to a percentage, it’s easier to use a calculator. If you’re sittin‘ at a table, you just estimate.

Now, when you are checking pot odds vs hand odds, you have to do both kind’a quick in your head.

Say you have a 4s 9s and a 2s Js 10d come up on the flop. You now have the other spades, which you need one of to get your flush, so you have 9 outs. 13 total of any suit – 4 that you have showing. The easy way to get an estimate on hand odds is to take outs*4 after flop, and outs*2 after turn. So, after the flop you have 9 outs, 9*4 is 36% chance to hit your flush.

Now, there’s 300 in the pot,and the person beside you bets 100. Now, the pot has a total of 400, and to call you need to put 100 in. 400/100 = 4, and 100/4 = 25. Pot odds is 25%, which means that to call, your hand odds should be at least 25%. Since your hand odds is 36%, it’s higher than the 25% pot odds, and you should call.

Hopefully you get what I’m tryin‘ to put out there. I ain’t sure how much easier I can explain it.

Richard asks…

what is the formula for calculating both POT ODDS and OUTS in texas hold em?

I am new to poker and would appreciate your help.

admin answers:

First you figure out your „Outs“. From there you can calculate your „Pot Odds“.

You don’t „calculate“ your Outs, you just count them. First you need to come to some guess as to what your opponent has. Let’s take an example where you called a pre-flop raise in position with A-6 of spades. The flop is 10-spades, 6-hearts, 2-spades. Your opponent puts out a big bet and you figure for sure he has either pocket Jacks, pocket Queens, or pocket Kings.

So you like that you flopped the nut-flush draw, but you KNOW that so far you are beat in this hand. You are positive that a spade will win the pot, and you are quite positive that if you hit your Ace you’ll win, or if you hit a third Six you’ll win.

So count it up: Not knowing your opponents cards you have to figure EVERY card besides the 5 that you see are available. (2 in your hand and 3 in the Flop.) So there are still 9 spades left out of all the unknown cards. (13 spades in the deck, minus the 4 you’ve seen.) PLUS, you think there are 3 Aces out there that could help you. PLUS, there are 2 more SIXES that can win it for you, too!

So…that is a total of 14 „Outs“ for you to win, provided that you’ve read your opponent correctly. (If it turns out that he flopped trip 10’s, then you only have the 9 spades to win, and that’s only if he doesn’t get a full-house!)

So that is 14 ways to win out of 47 UNKNOWN cards. This is important after you’ve figured out what your Pot Odds are.

Let’s say at this point there is $100 in the pot. Your opponent bets $50 on the flop. The pot is now up to $150, and you have to call a $50 bet. Your Pot Odds at that moment would be 3 to 1.

I’m not going to go into the math, but I’ll tell you that your chances of winning the pot by the end of the hand are a little bit better than 1 to 1! (In fact, even if he has pocket Kings you have about a 51.62% chance of winning!!!)

So this would tell you that it’s an easy call to make.

Now let’s say the turn comes and it’s a 3-clubs. No help to you, and now you really need some help. You STILL have just as many outs, but now you’re down to only 46 unknown cards, and only ONE MORE CHANCE to hit one of those 14 outs!

There is $200 in the pot now, and THIS TIME your opponent bets $200. So there is now $400 in the pot and you would have to call $200. You are getting pot odds of 2 to 1 on your call. HOWEVER, this time your odds of hitting your card with only ONE chance remaining are only around 31.82%! At a 33.33% chance, that would be 2 to 1 against you and barely worth a 2 to 1 pot odds bet. At 31.82%, you are not getting enough „POT ODDS“ to justify a call. (Almost, but not quite enough.)

HOWEVER, HOWEVER, HOWEVER…I would still make the call because of something that is MUCH more important than Pot Odds. In No-Limit Texas Hold ‚em, you worry much more about „IMPLIED ODDS“. I could go on for 10 more paragraphs about „implied odds“, but I won’t. In a nutshell – you’re thinking not about JUST what’s in the pot. You’re also thinking about what’s in your opponent’s stack! If he still has $1,000 left in his stack, you’ve got to think to yourself, „That could be mine, too!“ The only way it would be right to fold in my final part of this scenario is if your oppenent went „All In“ for his last $200. Then it would be a small mistake in the long run to call. (A very small mistake since it’s really so close to the correct „Pot Odds“.)

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