Poker odds and probability?

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Poker odds and probability?

Postby WesleyGabriel » Wed Sep 14, 2011 3:57 am

Poker prob problems/?
After the turn (4th card on the board) find the odds of each, and the size the pot must be to
make a call of a $20 bet.
1. You have a four flush. What is your odds of making your flush?
2. You have two pair. What are the odds of making a full house?
3. You have three of a kind. What are the odds of making a full house or better?
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Re: Poker odds and probability?

Postby chenghao » Wed Sep 14, 2011 10:01 am

WesleyGabriel wrote:Poker prob problems/?
After the turn (4th card on the board) find the odds of each, and the size the pot must be to
make a call of a $20 bet.
1. You have a four flush. What is your odds of making your flush?
2. You have two pair. What are the odds of making a full house?
3. You have three of a kind. What are the odds of making a full house or better?


in Vacuum ( knowing no other information , like the range of opponent's hands , any exposed cards etc )

1. whats a four flush ? At turn , there are 3 cards of the same suit and you have like the Ace of that suit ?
If so + assuming your only chance of winning this pot is if the last card is the suit, giving you a flush. There are nine cards that you have not seen out of 46 in the deck (counting from the turn, not the flop) that will give you this flush, so you have about a 9/46 chance to hit on the river. Another way of putting this is that there are 9 cards that will make you win, and 46-9 = 37 cards that will make you lose. The odds are therefore 37 to 9, or just about 4:1. If there is more than four times as much in the pot as it costs you to call, you should continue, since you have a profitable situation!

4 times as much in the pot ? so 4 times $20 would give us $80 . $80 has to be in the pot for it to be a break even call ( its ok to call , its ok to fold)

2) you have two pair , there are 4 more cards that can come out of 46 that can make you your full house.
The assumption made here is that you know your opponent has a flush / straight and the only way to win the pot is to improve to a fullhouse.

so the chances are 4/46 or about 11.5:1
11.5 times as much in the pot ? so 11.5 times $20 would give us $230.

3) you have three of a kind. ( either set - 2 on hand , 1 on board or trips - 1 on hand , 2 on board )
The assumption made here is that you know your opponent has a flush / straight and the only way to win the pot is to improve to a fullhouse.

there are 10 cards that improve your hand to a fullhouse or better.
so the chances are 10/46 or about 4.6:1
4.6 times as much in the pot ? so 4.6 times $20 would give us $92.
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Re: Poker odds and probability?

Postby Afternoon » Wed Sep 14, 2011 7:50 pm

very clear.

thank you chenghao, you are the best.
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Re: Poker odds and probability?

Postby Phuturist » Thu Sep 15, 2011 2:24 am

chenghao wrote:
WesleyGabriel wrote:Poker prob problems/?
After the turn (4th card on the board) find the odds of each, and the size the pot must be to
make a call of a $20 bet.
1. You have a four flush. What is your odds of making your flush?
2. You have two pair. What are the odds of making a full house?
3. You have three of a kind. What are the odds of making a full house or better?


in Vacuum ( knowing no other information , like the range of opponent's hands , any exposed cards etc )

1. whats a four flush ? At turn , there are 3 cards of the same suit and you have like the Ace of that suit ?
If so + assuming your only chance of winning this pot is if the last card is the suit, giving you a flush. There are nine cards that you have not seen out of 46 in the deck (counting from the turn, not the flop) that will give you this flush, so you have about a 9/46 chance to hit on the river. Another way of putting this is that there are 9 cards that will make you win, and 46-9 = 37 cards that will make you lose. The odds are therefore 37 to 9, or just about 4:1. If there is more than four times as much in the pot as it costs you to call, you should continue, since you have a profitable situation!

4 times as much in the pot ? so 4 times $20 would give us $80 . $80 has to be in the pot for it to be a break even call ( its ok to call , its ok to fold)

2) you have two pair , there are 4 more cards that can come out of 46 that can make you your full house.
The assumption made here is that you know your opponent has a flush / straight and the only way to win the pot is to improve to a fullhouse.

so the chances are 4/46 or about 11.5:1
11.5 times as much in the pot ? so 11.5 times $20 would give us $230.

3) you have three of a kind. ( either set - 2 on hand , 1 on board or trips - 1 on hand , 2 on board )
The assumption made here is that you know your opponent has a flush / straight and the only way to win the pot is to improve to a fullhouse.

there are 10 cards that improve your hand to a fullhouse or better.
so the chances are 10/46 or about 4.6:1
4.6 times as much in the pot ? so 4.6 times $20 would give us $92.


1st scenario depends:
If you have [Ah] [Kh] and villian has [Ks] [Kc] , at turn u still have 34% chance of winning since u have 3 more outs.
but if it's [Ac] [As] vs your [Ah] [Kh] , then it's down to 27%.

2nd scenario:
also depends... i'm looking at specifically where you're always behind and need to catch up...
Hero: [Ah] [Kh] Villian: [As] [Ac]
Board: [Ad] [Ks] [2h] [7c] , and you will be drawing dead. Just highlighting an eg where the calculations above may not apply.

3rd scenario has been fully explained so no need to elaborate (since assumption is u r behind and need to make the boat to win!)
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Re: Poker odds and probability?

Postby tcs » Thu Sep 15, 2011 9:20 am

As always very helpful kaki. Thx chenhao.
I wanted to reply but lazy to explain lol
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Re: Poker odds and probability?

Postby chenghao » Thu Sep 15, 2011 10:01 am

Phuturist wrote:
1st scenario depends:
If you have [Ah] [Kh] and villian has [Ks] [Kc] , at turn u still have 34% chance of winning since u have 3 more outs.
but if it's [Ac] [As] vs your [Ah] [Kh] , then it's down to 27%.

2nd scenario:
also depends... i'm looking at specifically where you're always behind and need to catch up...
Hero: [Ah] [Kh] Villian: [As] [Ac]
Board: [Ad] [Ks] [2h] [7c] , and you will be drawing dead. Just highlighting an eg where the calculations above may not apply.


3rd scenario has been fully explained so no need to elaborate (since assumption is u r behind and need to make the boat to win!)


This is where reverse implied odds come in

implied odds = the amount of money you win from your opponent's stack if you hit your card

so Reversed implied odds = the amount of money you lose from your stack if you hit your card

so if a K comes in the River , then you are likely to lose your whole stack to your opponent ( assumption both are at least abc players)

another example to highlight this is

like you have [Ts] [Jh]

Your opponent has [Ad] [2d]

Flop comes

[Qd] [9d] [2s]

if these come : [8s] [8h] [8c] [Ks] [Kh] [Kc] your good as you make your straight

if these come : [8d] [Kd] , you look good , but your opponent looks great
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