Advanced Holdem Strategy Using Odds

In the first part of our strategy for  Texas Holdem online poker we drew a distinction between Big Hands and Drawing hands when considering our pocket cards and advised that a High Ranking  pair would be enough to win the majority of hands against a small number of opponents but not against a large number hence the need to raise pre-flop with Big Hands to deter the other players from continuing. The following table clearly shows the relative chances of winning a hand with different pairs and different numbers of players assuming all of the players played to the end of the hand.

It can be seen that a pair of Aces will win 88% of the time in a 2 player hand  but only half as often in an 8 player hand.

So as the number of players staying in the hand after the flop increases more of hands are won by Drawing Hands so we need to be able to judge how likely we are to win a particular hand and whether or not we would on balance benefit from the risk. We do this in two stages, the first is to calculate the probability of getting a winning hand and the second stage is to calculate the risk to reward ratio of  our betting to win a particular pot. For instance if we are are likely to draw a winning hand, our stake is small and the pot large it is worthwhile. If we are not likely to draw a winning hand our stake is large and the pot small we should obviously fold.

Outs and Hand Odds

We covered on the Poker Strategy page which pocket hands we should take into the flop so while some professional players calculate odds pre-flop we shall content ourselves to being far ahead of the game by knowing which pocket cards to take into the flop by using the guidelines of Poker Strategy and just calculating the odds of winning on the turn and river.

We do this by working out the probability of drawing the card we need to make up a winning hand on the turn and river as follows :

After the flop you will know what 5 of the 52 cards are, leaving 47 unknown.

An out is a card that would make up your winning hand from amongst those 47.

Add up the number of outs.

Subtract the number of outs from the 47 unknown cards.

The ratio of the remaining cards to the outs is the probability of drawing a winner.

For example 1) If we have 4 clubs from the community cards and our pocket cards and need one more to make a flush we have 9 outs (13 clubs in the deck minus the four we already have).

47 minus 4 is 43.

43 to 4 is the same as odds of 11 to 1 (divide the 4 into 43 to reduce it down).

For example 2) If we have a pair of 8's we would need a third to have a realistic chance of winning so since there are two 8's outstanding we have 2 outs.

47 minus 2 is 45

45 to 2 is approx the same as odds of 23 to1 (divide the 2 into 45 to reduce it down).

For example 3) If we have an open ended straight draw (4 consecutive cards) we would need an extra card at either end of the set of cards. There will be 4 possibilities (on from each of the 4 suits) for each end making 8 outs in total.

47 minus 8 is 39

39 to 8 is approx the same as odds of 5 to 1 (divide the 8 into 39 to reduce it down).

For example 4)  If we have a straight draw with the card still needed in the middle of the set of cards there will be only 4 outs (the required card from each of the 4 suits)

47 minus 4 is 43

43 to 4 is approx the same as 11 to 1 (divide the 4 into 43 to reduce it down).

The procedure is the same at the river except that since we now know what 6 cards (our 2 pocket cards + 3 flop cards+ 1 turn card = 6), there are only 46  unknown to us so we subtract our outs from 46 instead of 47.

Pot Odds

We now calculate the pot odds this is simply the pot to our bet ratio.

For example 1) If the pot is £80 and on a £5 / £10 limit game we call and need to put £10 in the pot. The odds will be 80 to 10 or 8 to 1.

For example 2) If the pot is £120 and £10/ £20 limit game we have been raised by a player before us in the round of betting ( an earlier position ) we would have to put £40 in the pot. The odds will be 120 to 40 or 3 to 1.

For example 3) If the pot is £140 and in a £10/£20 limit game you need to put £20 in the pot the odds will be 140 to 20 or 7 to 1.

For example 4) If the pot is £230 and on a £5/£10 limit game you have been raised you will need to bet £20. The odds will be 230 to 20 or approx 12 to 1.

Bet or Fold

To decide whether to bet or fold we compare the Hand odds to the Pot Odds, if the hand odds are smaller and therefore better ( shorter ) than the Pot odds we should bet. If the Hand Odds are larger than the pot odds we fold.

So if we compare the respective four examples we can see that :

Examples 1) Hand Odds = 11 to 1 and the Pot Odds are 8 to 1 so since the probability of drawing your winning card are worse than the risk to reward ratio of the Pot Odds you would fold.

Examples 2) Hand Odds = 23 to 1 and the Pot Odds are 3 to 1 so again the probability of drawing your winning card are worse than the risk to reward ratio of the Pot Odds so you should fold.

Examples 3) Hand Odds = 5 to 1 and the Pot Odds are 7 to 1. This time the Hand Odds are smaller than the risk to reward ratio of the Pot Odds so you should bet.

Examples 4) Hand Odds = 11 to 1 and the Pot Odds are 12 to 1. The Hand Odds are still smaller than the risk to reward ratio as represented by the Pot Odds so you should bet.

Don't get into the frame of mind that since you have already put money into the pot you somehow have a vested interest, anything in the pot is no longer yours. Make each betting decision separately and anew.

As you become practiced at calculating odds and experienced at how hands unfold you may be able to estimate the final pot odds which is the ratio of what you estimate the final pot will be without your contribution to the sum of your bets until the end of the hand. Comparing the final pot odds to your hand odds can help you think ahead. Obviously this needs a lot of experience to be accurate enough to be of use and is not for beginners but if you continuously calculate the odds at the turn and river over time you will be able to estimate well enough to help you decide on marginal calls.

So you have drawn your winning card, if you have three of a kind (at a chance of 50 to 1 of getting) or a better hand you should be home and dry so milk away. If you have two pairs (at a chance of 20 to 1 of getting) and you are playing against several players you are not as sure to win. It is less likely than 20 to 1 however that another player has a better hand since you are in possession of some of the outs so you should bet to win especially since you will only get a hand this good or better once in every 21 hands. If the number of hands played is an average of 10 per hour you will only get a two pair hand or better once in  every two hours  of play so make the most of it!

Remember to practice your new strategies in Gamguru's free online poker rooms or at least at the low stake tables before stepping up to the higher limit tables.