Poker: Winning Tips

 

 Make the figures speak for themselves:

If you had not already noticed, the probabilities play a huge part in the game of Texas Hold'EM. For example, there are a total of 2,598,960 possible hands in one pack of 52 cards, but there are only four royal flushes. If the average poker player is dealt a total of 100,000 hands during their lifetime, they will probably never hold more than 4% of the total possible combinations of hands! Quite amazing really!

Calculate the odds of your hand:
In calculating the possible combinations of cards, we forward the Odds of the Cards as the most revealing information and of the most interest. For example, how many straight flushes will you be able to manage in a lifetime? In order to calculate this probability, the number of hands that will be dealt to you in a lifetime is calculated as follows: 10 full hands of poker/hour x 5 hours/ game x 50 games/ years x 40 years/ poker career= 100,000 hands of poker in a lifetime. This estimation is fairly high, because the majority of players will not see as many hands through to the end, but it can serve as a reference point. By basing your play at this level, the number of specific hands that you will receive during your lifetime is calculated as follows:

Distributed Cards: Number of Hands Served:

No pairs 50,000
One pair 40,000
Two pairs 5,000
Three of a kind 2,000
Suits 400
Colours 200
Full 170
Four 25
Straight flush 1.4
Royal flush 0.15

Statistically, you should find a straight flush on your first 5 distributed cards, only once or twice in a lifetime. For the most part, the average player will never see any. Poker players often talk about a "good series" or "run". Except that mathematically speaking this kind of chance does not exist. Cards do not hold a memory and once they have been re-shuffled they will not work on the basis of what cards have been previously dealt- maybe one day this type of pack will be invented, but it is not for the 21st century.
Poker players use the odds of the cards to take good decisions for each hand that they play. A decision made without bearing in mind the odds of the cards amounts to a play based solely on divination. The chances of getting colours or suits, the probability of finding an "over card" (supplementary card), the percentage of occurrences where you will flop a card which will complete a useful par etc, should all be considered. All this data is extremely useful for the good poker player.

Statistical knowledge is the key to victory in poker:
Here are some calculations that you should learn and then be able to recollect when playing games of poker:

You need an additional card to form colours at the Turn or the River: 35%

The probability that you will get dealt suits at the Turn or River: 31.5%

Probability of getting connection cards: 23.5%

Probability of getting three or four of a kind at the flop, given that you already hold a pair: 11.8%

Probability that you will get a pair at the flop if you hold two un-assorted cards in hand: 32.5%

Probability of being dealt a pair of aces: 0.45%

Probability that no-one has a potential hand, in taking into account the number of players, assuming that you do not hold these cards:
2- 84.5%
3- 70.9%
4- 59%
5- 48.6%
6- 39.7
7- 32.1%
8- 25.6%
9- 20.1%
10- 15.6%

Probability that no-one holds an Ace, and assuming that you do not hold an Ace, by number of players:
2- 88.2%
3- 77.5%
4- 67.6%
5- 58.6%
6- 50.4%
7- 43%
8- 36.4%
9- 30.5%
10- 25.3%

How are the odds calculated?
Let us consider an example with 4 outs (you need 4 cards to complete your hand). You hold the six of clubs and the seven of diamonds in hand. At the flop the cards dealt are the nine of spade, ten of hearts and the king of clubs. In this case you need an eight to complete your run. Because there are four eights in a game of cards, you have four outs.

The odds that a card will come at the River:
To calculate the odds with only one card to come is relatively easy. If you are looking to make a continuation, you have four outs. There are a total of 46 unknown cards (52 cards minus your two cards, minus the three flop cards, minus one card at the Turn). Of the 46 cards that remain, there are 42 cards which will not help you and 4 that will. 42 divided by 4 is roughly 10% and this is your chance of getting the required card.

The odds with two cards to come at the Turn or River:
In order to calculate the probabilities with two communal cards to come, you should firstly determine the number of possible combinations of two cards that can come after the flop. The most simple calculation you can undertake is to multiply the number of cards available at the Turn (47) and divide it by two 47x46/2= 1081. Thus, a certain number of combinations of two cards will hold the cards that you are looking for, but it is necessary to carry out two additional calculations in order to determine the exact probability.

Let us take the example that we are looking for an eight at the Turn and the River. One of the remaining eights could appear at the Turn. If this happens, there leaves three possible eights at the River. If you multiply four by three and then divide it by two, you will see that there are six unique pairs of eight.

If one eight comes at the Turn, there remains 46 hidden cards, but you are no longer interested by the three remaining eights, therefore you can remove them from your calculations. This leaves 43 hidden cards that will make unique pairs with one of the eights. You need to multiply four (the number of eights in the game) by 43 (the number of hidden cards) to arrive at the number 172.

To finish off the calculation, 172 add 6 equals 178, that is the number of total combinations of two cards that can contain at least one eight and at most two.
Of the 1081 possible combinations of two cards that may be dealt at the Turn and River, 178 of these combinations can help you to complete your hand. Then you need to establish the number of combinations that will not complete your hand (1081-178=903).

The probability of you getting your hand is 903:178 or roughly 20%.

What are the cards that the other players hold?
Do you know why the private cards and the cards that are burnt out are never taken into account when trying to calculate what the remaining hidden cards are?

The reason is that you only need to consider the unseen cards. If you know the burnt out cards or that one of your opponents reveals their hand, you will know that these cards will not be dealt. As we do not know these cards, they cannot be taken into account differently to the unseen cards.

For example, taking a standard 52 card game where you receive two Aces and you burn out 25 cards. If you are dealt the next card, what are the chances that it will be an Ace? That will be 2/50 (two Aces remain in the 50 unseen cards). The calculation will not be 2/25 just because you have burnt half the deck, as these cards are not known.

Take the example again, only this time you are going to look at the burnt cards, and there are no Aces. Now your odds are 2/25 because there remain two Aces in the 25 unseen cards that remain.

You will find that you will be able to remember, in most circumstances, the number of useful outs, but there exists an easy method for estimating the probabilities without passing through complicated scientific calculations.

Which hands will win the pot?
The following classification retakes the most profitable hands in Texas Hold'EM. The graph accounts for a game of poker involving, on average, between $5-10. The results are based on a simulation that takes account of 5,000,000 hands of poker. The percentages show how many times the particular hand will be able to win the pot:

Two pairs= 31%
Pair= 27%
Three of a kind= 12%
Suit= 9%
Colours= 9%
Full= 9%
Higher= 2%
Four of a kind= 1%
Straight flush= <1%
Royal flush= <1%

What are my chances of victory?
Let us consider the chances of winning the pot with a specific hand. What are the chances of completing a series?

Private Cards Distribution Percentage
Assorted cards 680,351 23.56%
Connection cards 454,220 15.73%
Assorted connection cards 114,304 3.96%
Ace-Ace 13,010 0.45%
King-King 13,182 0.46%
Queen-Queen 13,122 0.45%
Jack-Jack 13,069 0.45%
10-10 12,886 0.45%
9-9 13,092 0.45%
8-8 13,046 0.45%
7-7 13,111 0.45%
6-6 13,130 0.45%
5-5 13,173 0.45%
4-4 13,015 0.45%
3-3 13,075 0.45%
2-2 13,076 0.45%
Ace-King assorted 8,717 0.30%
Ace-King un-assorted 26,051 0.90%

How much can I expect to win?
The starting hands posses an average probability based on the "large" type of round at Texas Hold'EM with a limit of $5-10.

Ace-Ace- $34.19
King-King- $24.13
Queen-Queen- $17.36
Jack-Jack- $12.08%
Ace-King assorted- $11.63
Ace-King Un-assorted- $8.65
Ace-Queen assorted- $8.32
10-10- $7.72
Ace-Jack assorted- $5.69
Ace-Queen un-assorted- $5.47

Probability of private cards:
Any pair- 16:1
Assorted cards- 3:1
Ace-King- 82:1
Connecting cards assorted- 24:1
Ace-Ace or King-King- 110:1
Ace 5- 3:1

After the flop:
Pair of Jacks or better- 55:1
No improvement of a pair by a pair- 2.7:1
Improvement of a pair to three of a kind- 8:1
Flop that gives three of a pair- 391:1

The River:
Ace-King which finds an Ace or King- 2:1
Queen- Queen vs. Ace-King that finds an Ace or a King- 2:1
Finding the fifth card to complete colours- 2:1
Complete a series by 2 cards- 3:1
Three of a kind that becomes full house- 3:1
Pair that becomes three of a kind after the flop- 12:1

Supplementary statistics:
5 players, an Ace at the flop. The chances that another player has an Ace- 2:1
4 players, an Ace at the flop. The chances that another player has an Ace- 2.1:1
3 players, an Ace at the flop. The chances that another player has an Ace- 3:1

What are the odds of the pot?
The relative odds of the pot serves as a way of analysing the current amount compared to the future amount of the bets or raises. The calculation of odds of the pot allows you to be able to make some good decisions; to follow, to raise or to fold...

Example; there is $200 in the pot and a final bet of $10 comes to you. You are looking to complete your flush of which is missing one card. The rapid calculations give you a 1:4 or 25% chance. In order to win in a regular manner, you need to know how to beat the odds, and especially not to over-bet. If the odds of the pot are 25% (you have four heart cards and you are missing one to complete the series), and if you should only wager 5% of the actual pot ($10 as a percentage of $200) to see the following card, you are in a good position. From the calculation of the odds of the pot for this hand, it is possible to rise up to 25% of the pot due to the possibility of you getting a heart at the River.

In any case, if your bet is smaller than your chances of winning the hand, you are effectively buying the following card at a discount. The key is to look at the odds of the winning hand and compare it to the odds of the pot.

Too many beginners play a series of suits or colours with too much consideration. It is only necessary to judge the chances of being dealt suits or colours relative to the situation, but the common error is to buy the supplementary cards at a much inflated price. When the bets are rising at a statistically exuberant level, you should give up the ghost.

But, however if you have the Nuts (the best possible hand), each time you bet, you are taking a certain level of risk. In the heart of the battle. You do not always have the time to take out your calculation tables in order to evaluate the probabilities. Thus, you can see the odds of the pot as another fashion of evaluation. It is enough to ask yourself if there is enough money in the pot to justify the level of your bet.

The probabilities surrounding the pot are useful for knowing how many victories are needed in order to make money.
Taking the example that there is $100 in the pot and that it costs $10 to enter into the game. You need to win one hand in eleven in order to break even. If you play 11 times, that will cost you $110, but when you win, you will win $110.

Another useful advantage of calculating the odds comes when it is a question of comparing the odds of the pot with the odds of the hand. For example, you know that in a situation where colours are dealt, the odds of you hand in realising colours is 2:1 or 35%. Say you are in a hand with colours being dealt at the flop and you have $5 to pay, should you follow?

If there is $15 in the pot, plus $5 from your opponents, you get 20:5 or 4:1 or 25% for the odds of the pot. This means that you have to win one time out of five in order to break even. Except that with your colours, your odds of winning are 1 in 3! Thus, you should realise fairly quickly that you are in a profitable situation in terms of your financial position if the game goes to your advantage. The margin of profit, in theory based on a repetition of 100 times from the flop that will be checked at the river:

Total costs of play= 100 hands x $5= $500

Value of the pot= $15 + $5 + $5 to come= $25

Chances of victory= 2:1 or 35% (after the flop)

Full number of hands won= 100 x 35% = 35 victories

Net profit= cost of net play + (number of total victories x value of the pot).

The fundamental point to know is of the odds of the pot > the odds of the card= profit.

 

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