Hold Em Poker odds and poker values for starting hands.

This is the second page of a Hold Em poker article by Tex Canuck. Can poker odds and other poker skill overcome luck and is long term luck the same for everyone.
This is a good time to define what a poker game is.

The game, like life itself, is about making decisions based on the information available at the time of the decision. Your success or failure depends on how well you can interpret and act on this information.

Hold Em Poker is usually played with up to a total ten players. Often played for money poker players enter a game with their own cash stake and try to increase the size of that stake by winning pots. A winner is any player that, at the time they leave the game (or the game ends), has with more money than they brought to the table.

Poker tournaments are designed to be played until one player accumulates all the other player’s chips. N.B. All other “in the money” players are winners in a monetary sense.

Let us look at poker math or poker odds for the first two “hole cards” dealt to each player to start a hand. There is a long-term mathematical probability a standard deck of playing cards that are shuffled and randomly dealt will, in the long run, result in all players receiving each card combination the same number of times. For example, there are 169 possible two card combinations consisting of pairs, suited and unsuited combinations that are possible from a standard deck of fifty-two playing cards. There are no more and no less. Each of these combinations will, in the long run, be dealt at a predictable mathematical poker odds rate to each player albeit the rate is non linear. The poker odds, for each combination, will be the best hand when all the board cards are dealt and all of the players see the river is also mathematically predictable. In a limited or relatively short number of deals this poker odds predictability is not necessarily apparent which leads to many, especially new or infrequent players, to develop many misconceptions related to their own or another players luck. Look at Texas Hold Em starting hand combos.

In all poker situations, on all streets, there is a finite mathematical outcome governing how often a hand will be the best hand at the end and are the poker odds. This fact helps those players that are able to estimate their chances of winning a hand, at any stage, to compare those chances against the pot odds available to guide them in their decision-making. What they are able to do by using this mathematical outcome combined with other, mostly human, factors is to insure that the payoff odds they receive when a hand wins are greater than the odds of actually winning. e.g. if the poker odds of winning are 3 to 1 and the pot is paying 4.1 they must make a profit in the long run by playing the hand. This advantage is the edge and is no different to the edge that a Casino or Sports book rely on for their profits. This skill is very difficult to acquire but when highly developed completely wipes out the element of luck over the long haul. I have never heard of Casinos or Sports book being referred to as gamblers and from this point of view, a skilled poker player is not a gambler either. Do yourself a favor and learn the poker odds and skills that will overcome the luck of the draw and make you the Casino or Sports book sitting at your table. For those that argue that they have very good skills but are still losers (because of the luck factor) should look at how they utilize poker odds and the other skills they have.

It is my hope, that if you can stay to the end of this exercise, you will have at least picked up some information that will make you a better player. My main intention is to promote, in a positive way, the idea that poker is a game worthy of being recognized and respected as primarily a game of skill. Here we go.

Using Texas Turbo Limit Hold Em poker software version 6 from Wilson Software I ran a poker simulation, using deal number 500, where each player was dealt a million hands. A player occupied each seat that I created called Dopey Dave who never folds but checks or calls all single bets all the way to the river. This type of player is the ultimate poker fish and the biggest loser. He (she) can also put many players on tilt at those rare times when they are getting lucky and hitting their hand with infuriating regularity. This poker game simulation was run to prove that the software could randomly deal starting hands at the approximate long term expected mathematical frequency. Also other useful data was generated, such as hole card win frequency or poker odds, that will enlighten some people reading this, but more importantly the data generated can useful to Dopey Dave when he decides he wants to try to play smarter poker. Pre flop game strategy started by eliminating some of the worst of the unprofitable hands as indicated by the poker odds of winning.

One interesting hand is AA which is the best hole card holding that you can be dealt. The chances of winning with these cards under the conditions above, which are the worst conditions you will ever encounter, are about 30%. That is right, about three in ten or odds of about 2.33 to 1 and you are paid off at a rate of 9 to 1 when you win. The next time you lose AA five times in a row, in a game like the one above, instead of whining, just accept it as part of the overall win loss expectation and you will be a much happier player. View long term No Fold Em Texas Hold Em hole card win frequency chart.

The number of times each player received any given hand was in line with the mathematical expectation for that hand with each player receiving those hands an almost equal number of times. The wins for each player were roughly the same at 11.3%. You would expect to see a 10% win rate but when there is a split pot each player is given credit for a win hence the discrepancy.

Each player experienced lengthy losing streaks, oh, I am so unlucky is the mournful cry, the longest of which was 109 hands, for one player it was only 89 and the rest fell somewhere in between. The Longest win streaks were just seven hands oh boy, it is about time I had some luck because I deserve it.

Money won or lost by all players was an insignificant amount over the million hands. It should be noted however, that if a house rake of $2.00 per hand, which represents 10% of each pot, were taken each player would have lost roughly $200,000. Tokes to the dealer at $1.00 per hand would cost each player another $100,000. This brings up an interesting point, which is this. In a poker game, where the house levies a charge of some sort, if the players involved all have the same level of skill every player will, in the long run of course, lose money. This suggests that unless you are a player at the lowest point of the food chain you should avoid, whenever possible, playing in a game where you feel you are not one of the better players. Determining this fact is a skill rarely considered by most poker players even though the affect on earnings can be quite dramatic. That little tip is an aside and is not part of what my little study covers. Note: This poker odds simulation can be run many times with different deals and will always yield similar results.

Note: You can run these poker odds simulations many times with different deals. The results will always be similar.

Summary: So far, it seems that, according to the simulation, everyone has roughly the same luck in the long run.

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Tex Canuck

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