Theory of Poker - Pot Odds and Chances of Winning

[Gambler101]

I would like someone to clarify the calculation of pot odds

for me. If I need to call $10 in a $50 pot, are my pot odds

$50 - $10(5-1), or $60 - $10(6-1). So, would I rather have

high odds against me(6-1) or lower odds(2-1)? According to

my logic, I would rather put in $10 to win $60 than to win

$20. Please explain.

What is the chance of winning? Is this based upon a

player's judgment or solved by means of calculations?

The following question concerns Texas Hold'em:

I hold AK(suited hearts). The flop is: 2 9 J // 2 & 9 hearts

Since there are 52 cards in this heads-up match, my chances

of drawing another heart are (52 - 4(my pocket hearts +

hearts on the flop). My chances are then 48-9, which ~ 5-1.

Is this rationale correct?

[avatar77]

I have been doing a lot of hold'em reading lately and this is how I understand it.

You are given 5:1 pot odds because you are putting up your $10 to win $50.

Assuming that you will win with your nut flush, you have 9 outs - the four remaining hearts. There are 47 cards remaing though, the 52 less your hole cards and the flop cards. Since we do not know what the opponents hold, we assume that there are random cards as well.

Your odds of hitting your flush by the turn are 9 in 47 which gives you a 19.15% chance or 4.2:1 odds.

Your odds of hitting your flush by the river are 35% or 1.9:1.

In other words, you are a clear favorite to win with a flush just over 35% of the time with slightly better than 2:1 odds but you are getting 5:1 pot odds so it would be correct for you to bet or call the $10.

You want pot odds as high as possible - b/c this increases your pot winnings if you win and you want your implied odds based on outs to be as low as possible.

Over the long run, you will theoritically come ahead if you bet $10 into a $50 pot but always with a better than 1 in 5 chance of winning each time.

You can also expand this further with the following points:
-You can also account for implied odds which accounts for the actual size of the pot (i.e. how many more callers will you have if a heart flush is on board)
- you can argue that you have actually 15 outs because you have two excellent overcards - the Ace and King - both giving you top pair, top kicker. If you feel that you can win with either an ace or king on the turn or river, then your odds of winning are even greater.

[MEbenhoe]

Close but not exactly. There are 52 cards in the deck. 13 of which are hearts. You can see 5 cards, 4 of which are hearts. Leaving the possibility of 9 hearts in the other 47 cards that you don't see. So with two cards to come the probability of hitting your heart on the very next card is 9/47=19.1% or approximately 4.23:1 which means if you call $10 into a $50 pot, completely ignoring the river you'll win 1 out of 5.23 times thus making it a good bet. Now if the turn doesnt make your flush there are now 9 hearts in 46 cards left making the possibility of your card hitting on the river 9/46=19.6% leaving you with 4.12:1 odds on the river to hit your flush, so basically same situation. However the one which really concerns you is the odds of hitting your flush on either the turn or the river. You'll miss the flush on the turn 80.9% of the time and then hit the flush on the river 19.6% of that 80.9% which equals an additional 15.9% of hands you'll hit the flush on. 19.1%+15.9% = 35%. This means 1.85:1 odds of hitting your flush overall.

However if for example you are playing in a limit game, to see both cards you will not only have to call the bet on the flop, but also the bet on the turn if you don't make your flush on the turn, in order to see the river card. Seeing how you'll only make your flush on the turn about 20% of the time that means the other 80% you'll have to be throwing in an extra double bet. So for example if you're playing in a $10/$20 game and you have a 4 flush on the flop. There's $20 in the pot and your opponent bets $10 into you. So the pot is laying you 2:1, however when you factor in the fact that 80% of the time you're going to have to call an additional bet on the turn when its likely you still won't hit. Essentially the majority of the time you're putting in $30 to win a pot of $20. So in this rare case you'd prob throw your hand away. However in a NL game these types of odds can't be figured out because there is no structure to the betting. So in NL I would look for the pot to be laying you at least 4.23:1 (odds of hitting on the turn alone) to continue with your flush draw.

This discussion of course ignored implied odds, but this post is already growing long so I think I'll cut it off here, as implied odds is a topic that generally isn't for beginners.

If you have any further questions please feel free to ask.

[Jezebel]

[ QUOTE ]
However the one which really concerns you is the odds of hitting your flush on either the turn or the river.

[/ QUOTE ]

In limit poker, you should rarely if ever use the "two card to come" odds when deciding whether or not to continue. Take it one street at a time. Figure out what your immediate pot odds are and add implied odds to come to your decision. The two card to come odds are useful if your opponent or yourself is all-in on the flop and for deciding whether or not you can raise for value with a draw on the flop. Most players would be better off forgetting that they even heard about "2 card odds" since it can cause many mistakes.

[ QUOTE ]
However if for example you are playing in a limit game, to see both cards you will not only have to call the bet on the flop, but also the bet on the turn if you don't make your flush on the turn, in order to see the river card.

[/ QUOTE ]

Why MUST we see the river card? There are many situations where it is correct for us to call a flop bet but fold to a turn bet if we do not improve. If you figure your draws with 2 cards to come you will be folding on the flop too frequently, because the results of the two card odds calculation will say that is incorrect for us to continue to the river, which it may be, BUT it may be correct to see the turn. This is usually the case with gutshot draws and middle pair type hands. As a side note, it is almost never correct to fold a flush draw until it busts on the river.

[ QUOTE ]
This discussion of course ignored implied odds, but this post is already growing long so I think I'll cut it off here, as implied odds is a topic that generally isn't for beginners.


[/ QUOTE ]
You must include implied odds in your calculations to have any real meaning. To say that implied odds are some sort of advanced concept that beginners don't need to use is just wrong.

[MaxPower]

[ QUOTE ]


What is the chance of winning? Is this based upon a

player's judgment or solved by means of calculations?

The following question concerns Texas Hold'em:

I hold AK(suited hearts). The flop is: 2 9 J // 2 & 9 hearts

Since there are 52 cards in this heads-up match, my chances

of drawing another heart are (52 - 4(my pocket hearts +

hearts on the flop). My chances are then 48-9, which ~ 5-1.

Is this rationale correct?

[/ QUOTE ]

You calculate the chance of making your hand based on the unseen cards. After the flop, there are 47 unseen cards (the other 5 cards are the two in your hand and the 3 on the board). Of the 47 unseen cards 9 are hearts, so there are 38 cards which will not give you a flush and 9 that will.

So your odds against hiting a flush on the next card are 38:9, which is about 4:1.

However, an Ace or a King may also be an out in your example. So that adds 6 more outs. The problem is that you won't win every time that you hit one of these outs. In some cases you will not need to hit any outs and your AK will win unimproved.

So your odds of winning are a combination of determining how many outs you have and your judgment of how often your hand will win if you hit your outs. You also have to consider the fact that you might already have the best hand.

As far as pot odds go, it is just the total amount of money in the pot when it is your turn to act compared to how much you have to call. So if the pot is $50 and your opponent bets $10, you are getting 6:1 to call. If the pot is $50, someone bets $10 and there are 2 caller before you, you are getting 8:1 to call.

[MEbenhoe]

[ QUOTE ]

In limit poker, you should rarely if ever use the "two card to come" odds when deciding whether or not to continue. Take it one street at a time. Figure out what your immediate pot odds are and add implied odds to come to your decision. The two card to come odds are useful if your opponent or yourself is all-in on the flop and for deciding whether or not you can raise for value with a draw on the flop. Most players would be better off forgetting that they even heard about "2 card odds" since it can cause many mistakes.

[/ QUOTE ]

I made this statement in an attempt to help the poster who asked the original question, not for more advanced players. This is because most beginning players won't have the discipline to simply call one the flop and then fold on the turn.

[ QUOTE ]
Why MUST we see the river card? There are many situations where it is correct for us to call a flop bet but fold to a turn bet if we do not improve. If you figure your draws with 2 cards to come you will be folding on the flop too frequently, because the results of the two card odds calculation will say that is incorrect for us to continue to the river, which it may be, BUT it may be correct to see the turn. This is usually the case with gutshot draws and middle pair type hands. As a side note, it is almost never correct to fold a flush draw until it busts on the river.

[/ QUOTE ]

The reason I advocate this system for beginning players is for the following common occurence that will happen in a limit game. ex: You're playing a $10/$20 limit game. You have a 4 flush on the flop and there is $40 in the pot. First player bets out and you call leaving $60 in the pot. You don't make your flush here either and again you are bet into. Here's the problem most beginners will make the incorrect call here rather than fold, and in the long run this is a losing bet. If you go by the two cards to come rule and think about it as putting $30 in to win a $40 pot you'll fold and save yourself the extra bets, and in the long run this will be a winning play. This idea is even discussed in Super System (which I consider to be a pretty good authority). Again like I said this is for the beginning player.

[ QUOTE ]

You must include implied odds in your calculations to have any real meaning. To say that implied odds are some sort of advanced concept that beginners don't need to use is just wrong.

[/ QUOTE ]

No this isn't wrong at all. Most beginning players are not advanced enough in their play to be worrying about implied odds.

My original post was made under the assumption that someone asking about what pot odds mean and how to use them was a beginning player and thus made my post in that respect.

[Jezebel]

[ QUOTE ]
The reason I advocate this system for beginning players is for the following common occurence that will happen in a limit game. ex: You're playing a $10/$20 limit game. You have a 4 flush on the flop and there is $40 in the pot. First player bets out and you call leaving $60 in the pot. You don't make your flush here either and again you are bet into. Here's the problem most beginners will make the incorrect call here rather than fold, and in the long run this is a losing bet. If you go by the two cards to come rule and think about it as putting $30 in to win a $40 pot you'll fold and save yourself the extra bets, and in the long run this will be a winning play.

[/ QUOTE ]

This is wrong way to think about pot odds and you are costing yourself money if you play flush draws this way. In your example you are getting 4-1 odds on a 4-1 shot. Folding is poor option and costing you tons of money in the long run.

[MEbenhoe]

I never said I play flush draws this way. I only recommend the fold on the flop play to people who are beginners in understanding pot odds and implied odds. Also, its not a true 4:1 shot its 4.23:1 of hitting on the turn and 4.13:1 on the river. So if you call every time the pot lays you 4:1 your actually costing yourself money in the long run.

[Gambler101]

According to the Theory of Poker, a player should

bet if his chances at winning are greater than the pot

odds.

Using my previous example, my outs are the 3 Aces, 3 Kings,

and 9 Hearts. 32 cards will not help me, assuming that I do

not pair my Ace or King, and I do not complete my flush.

The chances that I will win are 15-32 for the turn, and 15-

31 for the river.

If the pot odds are 5-1, and my odds of winning on the

turn are 15-32(50%), how am I able to determine whether

that bet is a wise, or foolish decision concerning my

initial writing regarding the chances of winning exceeding

the pot odds?

Thanks.

[pudley4]

[ QUOTE ]
(on the turn) Here's the problem most beginners will make the incorrect call here rather than fold,

[/ QUOTE ]

How is the turn call any more correct/incorrect than the flop call?