Lesson 1: What's my chance of getting a Jack on the turn? You need to just figure out the number of outs and divide it by the number of cards in the deck. There are 2 more Jacks. There's 47 more cards since you've seen five already. The answer is 2/47, or .0426, close to 4.3%.
Lesson 2: No luck on the turn, how about the river card? Still 2 Jacks left, but one less card in the deck bringing the grand total to 46. What's 2/46? That's .0434, which is also close to 4.3%.
Your chances didn't change much.
Lesson 3: Forget just getting just one Jack! I want them both! What are my chances?
Since we're trying to figure out the chances of getting one on the turn AND the river, and not getting one on EITHER the turn or river, we don't have to reverse our thinking. Just multiply the probability of each event happening. Chances of getting that first Jack on the turn was .0426, remember? The chance of getting a second Jack on the river would be 1/46, because there'll only be one Jack left in the deck. That's about .0217, or 2.2%.
To get the answer, multiply them. .0426 X .0217 is about .0009! That's around one-tenth of a percent. I wouldn't bank on that one.
Lesson 4: Hey, what were my chances of getting a pair of Jacks anyway?
To figure that out, think of it as getting dealt one card, then another. What are your chances of the second card matching the first one? There will be 3 cards left like the one you have. There's 51 cards left in the deck. 3/51 is .059 or 5.9%. What the chance that 55 it'll be Jacks? Well, there are 13 different cards. So, .059/13 is about .0045, a little less than half a percent.
Lesson 5: What were my chances of getting a Jack on the flop? Now you do have to ?think in reverse? as in the previous example.
Figure out the chances of NOT getting a Jack on each successive card flip. First card you have a 48/50 chance (48 non-Jack cards left, 50 cards left in the deck), second card is 47/49, third card is 46/48.
Those come out to .96, .959, and .958. Multiply them and get .882, or an 88.2% chance of NOT getting any Jacks on the flop. Invert it to figure out what your chances really are and you get .118 or 11.8%. This will be your chance to get one or two Jacks.
Example #2 ?The straight draw?

THE POCKET

You start with a Jack of Spades and a Ten of Spades. You get a Rainbow flop with a Queen of Spades, a Three of Diamonds, and a Nine of Clubs. You've got a straight draw.

THE FLOP

Lesson 1: What are my chances of hitting it on the next card? Same as before, but with different outs. A King or an Eight will complete your hand. There is presumably four of each left in the deck. You've got 8 outs. The chance of getting one of them on the turn is 8 over 47, because there's 47 cards left in the deck. That comes out to about .170, or around 17%.
Lesson 2: I didn't get it on the turn! What are my chances now? There are still 8 cards left in the deck that'll help you, but 46 cards left in the deck. That's 8 over 46. It changes to .174. It's improved to a whopping 17.4%! Lesson 3: I should of thought about my total chances first, I'm such an idiot. What are my chances of getting that card on the turn OR the river? Once again we'll have to calculate the chances of a King or Eight NOT appearing, so we can do it like the last problem (in this case, {39/47} X {38/46}). Or, since we've already figured out our chances in the previous two lessons, we can just invert the probabilities and multiply them. You had a .170 chance on the turn, and a .174 on the river. By inverting, I mean subtracting them from one. Now we've got .830 and .826! Multiply and get .686! That's our chance of NOT hitting our card at all. So invert it again and get .314, or 31.4%.
Example #3 ?Top Two Pair?

THE POCKET THE FLOP

You get dealt a King of Diamonds and a Nine of Hearts. The flop is looking' pretty good for you with a King of Spades, a Nine of Clubs, and a Four of Clubs. Top Two Pair! Lesson 1: What are my chances of getting a Full House on the turn? To get a Full House, you need another King or Nine to pop up.
There is two of each left in the deck. So you've got 4 outs. After the flop there's always 47 cards unaccounted for. 4/47 is around .085 or an 8.5% chance of you getting the Full House.
Lesson 2: What are my chances of getting a Full House on the river? If it didn't happen on the turn, your chances usually don't change all too much, but let's check. You've still got 4 outs and now 46 58 unseen cards left. 4/46 is about .087 or around an 8.7% chance of hitting it on the river. A .2% difference.
Lesson 3: How about the chances of getting the boat on the turn OR the river? Like the previous examples, to figure your chance of something happening on multiple events, you need to calculate the chance of it NOT happening first. On the turn it won't happen 43/47 times.
On the river it won't happen 42/46 times. 43/47 is .915, and 42/46 is .913. Multiply them and get .835, or 83.5% chance of it not happening. Invert that and you get a 16.5% of getting at least a full house by the showdown.
Lesson 4: What do you mean by ?at least? a Full House? Since we figured the chances to NOT get dealt a Full House, the chances are built in if the turn and river are two Kings, two Nines, or a King and a Nine. If you are dealt two cards both of either King or Nine, it'll be four-of-a-kind and not a King and Nine 33% of the time. Think of it as being dealt one card then the other. What are the chances of the first card matching the second? Whether it's a King or Nine, there will be only one unaccounted for, but two of the other. That's 1/3, or 33%.
Lesson 5: Then what are my chances of getting four-of-a-kind? This one requires a little more thought. It doesn't matter which card we're hoping for. We need to first get a Full House on the turn.
According to lesson #1, the chance of that happening is .085. The chance of getting the same card we got on the turn is 1/46. There's only one out, and the usual 46 unseen cards. 1/46 is around .022, or 2.2%. Multiply the two probabilities (.022 X .085) and get .002 or 59 one-fifth of a percent. It will be Kings half of the time and Nines the other half Is this making any sense? If you really want to be a master of calculating odds, you need to see these calculations in action, over and over. Like anything else, practice makes perfect. In online games especially with very few if any tells (shown cards), statistical knowledge becomes the main factor when choosing whether to bet, call, or fold.
If you do have a hand that you know can�t lose � you have the nut.
Bet like crazy.
While there is a lot more to Texas Hold�em poker than this - this should open your eyes to more things about the game of poker than just the cards and their statistics.
Yes - You DO need to know your general chances of pulling what types of hands - but if you learn to study your opponents, they will tell you their hands and you'll be able to beat them without even knowing yours.

RETURN ON INVESTMENT (ROI)

When the stakes required to play a game of Texas Hold�em increase, there is not a proportional increase in the average winnings or money flow because most players, especially at the start of play, play tighter at higher stakes.
Here�s how that works.
Higher stakes cause players to be more cautious. Pots do not grow proportionately as the stakes and blinds increase. Your return on investment will therefore decrease as the minimum blind goes up.
Max Bet Pot Size $ 2 Max 28 - 37 $ 4 Max 25 - 35 $ 6 Max 20 - 22 $ 10 Max 10 - 28 $ 20 Max 6 - 7 $ 50 Max 12 $ 60 Max 7.6 $ 100 Max 6.11 $ 200 Max 5.5 Most major online casinos release data on hands played (for a price) on a regular basis. A recent study (June 2004) from one of the largest online casinos, based on several million actual hands of Poker played, revealed that the return on investment varies quite a bit based on the maximum bet.
In the $2 games, the value of the winning pot varied from 28 to 37 times the Big Blind (BB) � the most you would have to invest to see the flop (short of Raises). The average pots were in the $60 range.
With the right cards, you could expect a return of 3000% on a winning hand.
As you can see in the chart above, this ratio falls as the Blinds go up. In the $200 game, with pots averaging $600-1200, the ratio averages 5.5:1. Sure, greater overall winnings - but much greater risk based on the investment you have to make to see the flop.
Also notice the volatility or variance of this ratio. On the high stakes tables, play is very tight and often Passive, so the ratio remains very narrow � pots are predictably 5-6 times the Big Blind.
At the smaller stakes tables, there is considerably more volatility, indicative of a lot of looser players and more aggressive playing styles.
The $1/$2 tables are the loosest with pots ranging from 28-37 times the Big Blind.
Are Low Stake Tables Faster? Not necessarily. Texas Hold�em is the king of fast play. Several $1000 plus pots were played in less than a minute and ranged as long as 6 minutes � the same range for the small stake tables. Over all, the average length of an online Poker game today is just over one minute or 50-60 hands per hour.
In higher stakes games, one thing is quite clear. There are a higher percentage of tighter and aggressive players at these tables than at the small stake games. That means there are more sharks at the big tables and a much better chance that you will be one of the fish.
The smart thing to do here is to say away from these kinds of tables.
Given the fact that the return on investment is lower at the high stake games, that the average level of play is much more aggressive and that a much larger stake is required, there is very little opportunity to be a consistent winner on tables with $50 and up blinds.
�All of the recent research points to $5/$10 Limit tables as ideal combination of risk and reward.� Insider Tip FACT! When the average loose gambler loses, he or she keeps on playing in an attempt to recover the loss. This is irrational and unplanned play and can be very expensive.
On the other hand, when most innate gamblers win, they forget all about their losses and conclude incorrectly that they have finally learned how to win - or that their luck has finally changed. They express what is an irrational optimism at this point � a totally unfounded and undeserved optimism that keeps them in the game until they revert back to a losing streak.
Sharks exploit this irrational playing style in gamblers to generate a continuous income.
OUTS ODDS CHART Outs Holding Hand Drawing To 2 to come 1 to come 21 98 % 83% 20 98 % 77% 15 open straight flush draw straight, flush, Straight Flush 85% 48% 14 96% 44% 13 92% 39% 12 gutshot straight flush draw straight, flush, Straight Flush 82% 35% 11 71% 31% 10 54% 28% 9 four flush flush 54% 24% 8 open straight straight 46% 421% 63 draw 7 39% 18% 6 32% 15% 5 26% 12$ 4 gutshot straight straight 20% 9% 3 14% 7% 2 pocket pair 3 of a kind 9% 4% 1 3 of a kind 4 of a kind 4% 2% POCKET CARD ODDS Hole Cards Dealt Dealt Percent Expected Percent Suited Starters 680,351 23.56% 679,596 23.53% Connected Starters 454,220 15.73% 453,064 15.69% Suited Connected Starters 114,304 3.96% 113,266 3.92% Paired Starters AA Dealt 13,010 0.45% KK Dealt 13,182 0.46% QQ Dealt 13,122 0.45% JJ Dealt 13,069 0.45% TT Dealt 12,886 0.45% 99 Dealt 13,092 0.45% 88 Dealt 13,046 0.45% 77 Dealt 13,111 0.45% 64 66 Dealt 13,130 0.45% 55 Dealt 13,173 0.46% 44 Dealt 13,015 0.45% 33 Dealt 13,075 0.45% 22 Dealt 13,076 0.45% All Paired Starters 169,987 5.89% 169,899 5.88% AK Suited Starters 8,717 0.30% 8,713 0.30% AK Offsuit Starters 26,051 0.90% 26,138 0.90% All AK Starters 34,768 1.20% 34,851 1.21% THE RULE OF FOUR �TWO The rule of four-two is an easier way to figure the odds for any situation where you know your outs. It is not completely accurate but it will give you a quick ?ballpark? figure of your chances for making a hand.
Here is how it works.
With two cards to come after the flop you multiply your number of outs by four. With one card to come after the turn, you multiply your number of outs by two.
This will give you a quick figure to work with.
If you have a four-card flush after the flop you have nine outs.
With two cards to come, you multiply the nine by four and you get 36 percent chance of making the flush.
The chart shows the true odds at 35 percent. With one card to come you multiply nine by two and get 18 percent. The chart shows that the true figure is 19.6. It is not completely accurate but it is pretty close, and it is an easy calculation to do in your head How to calculate hand odds (the longer way): Once you know how to correctly count the number of outs you have on a hand, you can use that to calculate what percent of the time you will hit your hand by the river. Probability can be calculated easily for a single event, like the flipping of the river card from the turn. This would simply be: Total Outs / Remaining Cards. For two cards however, like from the flop to the river, it's a bit more complicated. This is calculated by figuring the probability of your cards not hitting twice in a row. This can be calculated as shown below: Flop to River % = 1 - [ ((47 - Outs) / 47) * ((46 - Outs) / 46) ] Turn to River % = (47 - Outs) / 46 The number 47 represents the remaining cards left in the deck after the flop (52 total cards, minus 2 in our hand and 3 on the flop = 47 remaining cards). Even though there might not technically be 47 cards remaining, we do calculations assuming we are the only players in the game. To illustrate, here is a two overcard draw, which has 3 outs for each overcard, giving a total of 6 outs for a top pair draw: Two Overcard Draw = 1 - [ (47 - 6) / 47 * (46 - 6) / 46 ] = 1 - [ (41/47) * (40/46) ] = 1 - [ 0.87 * 0.87 ] = 1 - 0.76 = 0.24 = 24% Chance to Draw Overcards from Flop to River