Mathematics
If you're holding the strongest starting hand possible, AA, how would you play it? There are a lot of variables to consider such as what position you're in, how many people are in the pot or sitting on the table and what kind of table (game) you're on. Position makes a difference because if you bet too little in early position (weak betting), more people will call. Betting too much will cause them to fold. In late position you get to see how others have bet giving you a general idea on their hand strength. A call will result in everyone seeing the flop. A weak bet will get calls from pocket pairs, over cards (face cards), 'A' anything suited and or maybe even any suited connectors depending on how loose the player is. Of course, at this point you have the strongest hand so, do you want more chips or less? You can slow play (betting weak to lure players into the pot) but that leaves the door open for chasers to 'make' something on you. A strong bet or all in (betting all your chips) will potentially get you less chips because the chance of a chaser calling your bet is smaller. Of course, if you can fold a big hand when faced with a dangerous flop you can always slow play first, but you leave yourself open to being bluffed or rivered (getting beat by the river card).
Pot Odds
So you're faced with a dangerous flop. What do you do? You have to able to muck your hand when the odds are no longer in your favor. In limit games, basically you can't force people to fold by betting big (either as a bluff or making the pot odds extremely unfavorable) as you could in no-limit or pot limit. What if you still have a strong hand? Then you need to be able to calculate your odds and the odds of your opponent(s), taking into account pot odds.
This when your hand is not that strong and has a chance to win but someone has bet or raised. Look at the amount in the pot, is it worth the risk. For example, if the pot is at $20 and it only costs you $1 to see another card. You should call because it's cheap. Whereas if the person bet $40, then you probably don't want to call since you have to bet more than you can win.
For example, to win the hand you determine that you must hit one card to win and the pot is $5 and someone has raised the pot $5 you basically have a 1 in 48 chance to hit your card. But you are betting $5 to potentially win $10 that's only 1:2 odds and you still need to hit your card to get it. So the next step is to compare your pot odds % to to your outs %. Your pot odds percentage is your bet in comparison with the pot. In our example, a $10 pot plus your $5 that you have to bet equals $15 so your pot odds % is 5/15 equals 1/3 which equals 33.33%. Now you have to compare that with your outs % to determine how you should act. Remember, this is only one set of factors you have to figure out all the other factors too, like kickers, opponents play style etc etc.
If you need help understanding this concept you can research this further online. You can even find a pot odds calculator online. Below is a chart referencing the number of 'outs' versus the percentage of hitting it.
Also in tournaments, when there are many people in the pot & you have a pocket pair, you should call if the pot odds are in your favor especially pre flop. Your opponents may be drawing dead or holding a smaller pocket pair. If your opponents (4) are holding the same cards (for example, they all have a single A) and you have a pair king, then you should win or at least not lose to a pair of A's. Or if only two of them have an A then their odds of hitting an A to beat you are the same as your odds of hitting a set (3 of a kind).
Implied Pot Odds
Implied Pot Odds are in essence and extension of pot odds.
If you have a medium hand that has a decent to high chance of improving
and winning but the pot odds may not be good enough for you to call, you
may want to calculate implied odds. You do this by calculating how
much more money will be in the pot after you call and the next card comes
down. If you are facing this dilemma after the flop you would want
to calculate how much more would be in the pot at the turn AND river
should you choose to take it to showdown.
This is most noticeable when against a short stacked
opponent. If the short stack is in the blinds, with any
reasonable hand, you can be sure their whole stack is
going into the pot. So before you put your money into the
pot, make sure you account for this. If your hand is
strong, you can slow play it because if you raise too big
the short stack may fold, the chances of the short stack
sticking their stack is greatest if you just call. If you
call, you may be able to trap the other players. Again
read your situation carefully.
Outs
To determine the odds you have to evaluate the board and how likely it is that the other player is holding the 2 cards that can beat you at this point. Here's where the principle of outs comes in. An out is a card that can help you make a hand. If the flop has scattered cards both in number and suit, then there is no way that they can beat you at this point unless they have made 2 pairs (remember, you are holding AA). What are the odds in that? Well to hit one pair they have a max of 3 out of 48 cards preflop (they're holding 2 cards of which there is one already and your opponent has 2 cards). So your opponent will have to hit twice since 1 pair cannot beat you. If by chance your opponent does have 2 pairs you need the board to pair (but not the ones your opponent has). So to make a set you only have 2 cards (2 more aces in the deck) or for the board to pair you have at least 3 cards, per card on the board. This is a very important concept. You must be able to understand the number of outs you have and how much it would cost you to stay in the game (remember to keep the pot odds in mind).
| Number of Outs |
% of Hitting on either Turn or River |
| 1 |
4.4 |
| 2 |
8.4 |
| 3 |
12.5 |
| 4 (inside straight draw) |
16.5 |
| 5 |
20.3 |
| 6 (two overs) |
24.1 |
| 7 |
27.8 |
| 8 (open ended straight draw) |
31.5 |
| 9 (flush draw) |
35.0 |
| 10 |
38.4 |
| 11 |
41.7 |
| 12 (flush draw + gut shot draw) |
45.0 |
| 13 |
48.1 |
| 14 |
51.2 |
| 15 (straight + flush draw) |
54.1 |
| 16 |
57.0 |
| 17 |
59.8 |
| 18 |
62.4 |
| Number of Outs |
% of Hitting on River |
| 1 |
2.2 |
| 2 |
4.3 |
| 3 |
6.5 |
| 4 (inside straight draw) |
8.7 |
| 5 |
10.9 |
| 6 (two overs) |
13.0 |
| 7 |
15.2 |
| 8 (open ended straight draw) |
17.4 |
| 9 (flush draw) |
19.6 |
| 10 |
21.7 |
| 11 |
23.9 |
| 12 (flush draw + gut shot draw) |
26.1 |
| 13 |
28.3 |
| 14 |
30.4 |
| 15 (flush draw + straight draw) |
32.6 |
| 16 |
34.8 |
| 17 |
37.0 |
| 18 |
39.1 |
* An open ended straight draw is if you have 4 connected cards already and you need the card on one end or the other to complete the straight. For example, you have 9T (pocket) and the flop hits J Q 2, you only need either a K or an 8 to complete the straight. A gut shot draw is if you the board hits J K 2 and you need the queen (a card in the middle) to complete your straight.
Another thing to analyze while calculating pot odds and outs is to make sure you're not drawing dead. Drawing dead means you are chasing an out that even if you hit it, your hand will not be good enough to win. For example, the board has a one card flush draw and you are chasing an open straight even if you make the straight, your opponent probably has the flush already.
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