Hand Probability

[dobbs]

In Sklansky's book, "Hold 'Em Poker," at page 106 he states that when 9 cards will make your hand after the flop (2 community cards to come) and there are 47 unseen cards, that the probability of making the hand are 35% rather than 38.3%.

How does he get to 35%?

I calculate it as 9 chances in 47 on the first draw, and 9 chances in 46 on the second draw, or 9/47 + 9/46, or 38.7%. Since it doesn't matter whether you make the hand on the first draw or second draw, this should be the proper calculation.

[danderso8]

That method figures it a little high, because it double counts times on the river where you have already made your hand at the turn.

P(making hand)=P(making it on the turn) + P(making it on the river IF you did NOT make it on the turn)

P=9/47 +(9/46 * (47-9)/47)
P=34.97%
__________________________________________________ _____
But just so we're reminded of the ones who are held back,
Up front there ought 'a be a Man In Black.
--johnny cash 1932 -- 2003

[BruceZ]

Hi dobbs,

This has been coming up a lot lately. Here is a link to 3 different methods for computing the exact answer.

completing flush draw (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Board=probability&Number=326 125&Forum=probability&Words=BruceZ&Match=Username& Searchpage=0&Limit=25&Old=1month&Main=325790&Searc h=true#Post326125)

-Bruce

[Kurn, son of Mogh]

Your calculation is incomplete. All you've done is compute the individual probabilities of hitting your outs on each street. You now have to subtract out the probability of hitting your outs on *both* streets to avoid double counting.

[TheRake]

Some of you may already know this system, but when calculating odds in a game situation I use the "4&2 rule". It is much faster, easier and works with any number of outs you may have. So the hands you don't have memorized are much easier to figure odds on. It works like this...

Take the number of outs you have and multiply by (4) if you have (2) cards left to come and multiply by (2) if there is just (1) card to come. So for example if you have a four flush with 2 cards to come multiply 9(number of outs)x4=36%. If there is one card left it would be 9x2=18%. I know these are not exact numbers, but they are close enough to give a quick idea of where you are at in a hand without having to do complicated math in your head.

[Wake up CALL]

[ QUOTE ]
Some of you may already know this system, but when calculating odds in a game situation I use the "4&2 rule". It is much faster, easier and works with any number of outs you may have. So the hands you don't have memorized are much easier to figure odds on. It works like this...

Take the number of outs you have and multiply by (4) if you have (2) cards left to come and multiply by (2) if there is just (1) card to come. So for example if you have a four flush with 2 cards to come multiply 9(number of outs)x4=36%. If there is one card left it would be 9x2=18%. I know these are not exact numbers, but they are close enough to give a quick idea of where you are at in a hand without having to do complicated math in your head.

[/ QUOTE ]

Close enough???? OK the flop is 7 /images/graemlins/heart.gif 8/images/graemlins/heart.gif 2 /images/graemlins/club.gif I am holding the 9 /images/graemlins/heart.gif T /images/graemlins/heart.gif and my oponnent holds a pair of black 3's. That gives me 21 outs times 4 equals 82%. The true number is 71% anytime you can be off this far it seems like a risky method. Perhaps it is much closer when you have fewer outs. Let's see now I have AA and my oponnent has KK and the flop comes KK2, now your method says I have a 4% chance to win but it is closer to .1% this is off by a factor of 40! WOW! Well I'm sure it is correct somewhere in between these two extremes. At any rate it is still pretty easy to tell using the correct math.

[Flashy]

Gee - I am sure glad you set the record straight. I wouldn't want to mis-calculate the odds when I have a straight flush draw. Or to figure out that I am sunk when 2 kings flop and I hold AA. Yep, knowing the real odds will certainly help me play those hands better.

[Wake up CALL]

[ QUOTE ]
Gee - I am sure glad you set the record straight. I wouldn't want to mis-calculate the odds when I have a straight flush draw. Or to figure out that I am sunk when 2 kings flop and I hold AA. Yep, knowing the real odds will certainly help me play those hands better.

[/ QUOTE ]

Actually I doubt this is true, much more help would likely be required.

[TheRake]

[ QUOTE ]

OK the flop is 7 /images/graemlins/heart.gif 8/images/graemlins/heart.gif 2 /images/graemlins/club.gif I am holding the 9 /images/graemlins/heart.gif T /images/graemlins/heart.gif and my oponnent holds a pair of black 3's. That gives me 21 outs times 4 equals 82%. The true number is 71% anytime you can be off this far it seems like a risky method. Perhaps it is much closer when you have fewer outs. Let's see now I have AA and my oponnent has KK and the flop comes KK2, now your method says I have a 4% chance to win but it is closer to .1% this is off by a factor of 40! WOW! Well I'm sure it is correct somewhere in between these two extremes. At any rate it is still pretty easy to tell using the correct math.


[/ QUOTE ]

Is this what you do Wake up Call? you try and itimidate the new posters to make yourself feel better? Well alow me to retort...First of all if you are aware of the fact that you have 21 outs to begin with i would assume you would be aware of the fact that the pot odds are probably good enough to go ahead and...oh I don't know...Call that bet?... Secondly 21x4=84 (not 82 /images/graemlins/blush.gif) Einstein....Lastly, I didn't say this calculation was used to figure your chance "to win" a hand I only said it was used to roughly calculate odds of making your hand. Sometimes even when you make your hand you can't win...It's called drawing dead...A concept I am sure you are exceedingly familar with.

I apologize if I had the nerve to try and make it a little easier for people who are not mathamaticians, like yourself, to figure simple odds.

Good day sir

[Wake up CALL]

I apologize for trying to show the error of your method to prevent costly errors.

[Copernicus]

In situations where someone is really on the shelf about a play and needs to calculate pot odds he is most likely in the range of 4 to 12 outs, and the estimate isnt that bad. A far worse error is made in using "2 to come" odds when there is no chance of having proper odds to call when the first card doesnt hit.

[Flashy]

No doubt, like all nerds you over value your ability to calculate exact odds.

If you think your little tib bit on math contributed to anyone's knowledge of the game, your mistaken. Your examples were assine. More exact odds wouldn't change one's decisions in either example.

Next time you try to make a point, formulate better examples.

[Piiop]

I found WakeUp's post to be relevant in response to the previous post.
The question was about calculating probabilities, not whether or not one should call.
I think if you are going take the time to calculate probabilities, you should calculate exact numbers instead of estimates.
Especially in situations when estimates lead to inaccuracies of more than %10.
TheRake's method would be acceptable in certain situations, but not in others.
I think if you learn to know the numbers for a given situation,
it becomes a lot easier to make that on the spot decision.

Theres also really no need to namecall and flame someone for responding to a post with their own thoughts

[TheRake]

You are correct piiop. I took the post as sarcasm towards me. I hope this was not the intent. The point of the board is to exchange ideas. And i can see that maybe an apoligy may be in order here. I hope i did not offend wake up or any other people for that matter with my zealous response. Please accept my apologies...

[Flashy]

WakeupCalls examples were assine.

In a cardroom game, you don't have the time to figure exact odds unless your a math whiz. Even if you could, what is the big deal?

Are you really not going to bet a straight flush draw if the odds are only 71% instead of 84%?

If you have AA, you don't have a drawing hand. When KK flops, you are trying to figure out if the opponent has a king or not. You don't make a decision on drawing to a two outer.

Oh and by the way, if your openent had KK as in WakeupCalls example, you would be silly not to draw. Bad beat jackpots pay between $5,000 to $50,000 to Aces full beaten by quad kings. Let's see, on a $12 call, that's odds of about 400 - 4,000 to 1. Of course WakeUpCall, could tell me precisely what the odds are.

Don't confuse winning poker with a ability to calculate odds. You will never know if you are drawing dead or what the true implied or implict odds are. Knowing the approximate odds is usually good enough. Knowing how your opponents play is much more important.

The Rake was trying to pass on a good tip to begining players. WakeUpCall had to be rude to The Rake and me.
Frankly, he is the type of player I love having in my games.

[Piiop]

I find that once you have learned a probability for a certain situation, and actually played thru that situation many times, that you now know the probability by heart. There's no need to make calculations while you're at the table, because you already know the answer. It also doesn't take a math whiz to understand how to reach these answers, just a little knowledge of probability.
Certainly, a probability isn't going to be the only thing that brings you to a decision, but a lot of times it helps. It's also what the original poster was asking about.
And for someone trying to learn how to find a probability, I think it would be best to learn how to the exact way, and then be able to approximate.

As a side note, I don't know if playing and hoping you lose to get a bad beat jackpot is a very good strategy.

[Flashy]

"As a side note, I don't know if playing and hoping you lose to get a bad beat jackpot is a very good strategy."

The point was to show how poor the example was. However, if you had pocket Aces and knew you were up against quads, you would be stupid not to go for the 3rd Ace giving you the bad beat. Would you buy a lottery ticket that paid you $50,000 for $12 if you had a 5% chance of winning? Often Bad Beat jackpots get over $100,000 through promos. Even if the jackpot is only $5,000 your still getting tremendous odds.

When you have pocket Aces and a qualifying pair flops, remember if you spike the third Ace, the only likily hands that can beat you give you the jackpot.

I hope that advice wins you a jackpot some day!

If you want to know the exact odds, more power to you. I just don't think knowing the exact odds are going to help you that much.

How different would your decisions be knowing that your four flush has a 19.5% chancce of hitting on the next card versus an estimate of 18%?

[slider77]

I calculate the chances of not making a flush a subtract that number from 100%

So P(No Flush) = 38/47 * 37/46 = 65%

P(Flush) = 100% - 65% = 35%.

[Wake up CALL]

[ QUOTE ]
You are correct piiop. I took the post as sarcasm towards me. I hope this was not the intent. The point of the board is to exchange ideas. And i can see that maybe an apoligy may be in order here. I hope i did not offend wake up or any other people for that matter with my zealous response. Please accept my apologies...

[/ QUOTE ]

Allow me to apologize to you as well TheRake, I was just pointing out how inaccurate your method could be under some circumstances, never meant you to take it personally. In many forums many people take what they read as gospel and if BruceZ writes it this is rightly so. /images/graemlins/smile.gif

[Wake up CALL]

[ QUOTE ]
WakeupCalls examples were assine.

In a cardroom game, you don't have the time to figure exact odds unless your a math whiz. Even if you could, what is the big deal?

Are you really not going to bet a straight flush draw if the odds are only 71% instead of 84%?

If you have AA, you don't have a drawing hand. When KK flops, you are trying to figure out if the opponent has a king or not. You don't make a decision on drawing to a two outer.

Oh and by the way, if your openent had KK as in WakeupCalls example, you would be silly not to draw. Bad beat jackpots pay between $5,000 to $50,000 to Aces full beaten by quad kings. Let's see, on a $12 call, that's odds of about 400 - 4,000 to 1. Of course WakeUpCall, could tell me precisely what the odds are.

Don't confuse winning poker with a ability to calculate odds. You will never know if you are drawing dead or what the true implied or implict odds are. Knowing the approximate odds is usually good enough. Knowing how your opponents play is much more important.

The Rake was trying to pass on a good tip to begining players. WakeUpCall had to be rude to The Rake and me.
Frankly, he is the type of player I love having in my games.

Another of your posts to me:

No doubt, like all nerds you over value your ability to calculate exact odds.

If you think your little tib bit on math contributed to anyone's knowledge of the game, your mistaken. Your examples were assine. More exact odds wouldn't change one's decisions in either example.

Next time you try to make a point, formulate better examples.

And yet one more:

The point was to show how poor the example was. However, if you had pocket Aces and knew you were up against quads, you would be stupid not to go for the 3rd Ace giving you the bad beat. Would you buy a lottery ticket that paid you $50,000 for $12 if you had a 5% chance of winning? Often Bad Beat jackpots get over $100,000 through promos. Even if the jackpot is only $5,000 your still getting tremendous odds.

When you have pocket Aces and a qualifying pair flops, remember if you spike the third Ace, the only likily hands that can beat you give you the jackpot.

I hope that advice wins you a jackpot some day!

If you want to know the exact odds, more power to you. I just don't think knowing the exact odds are going to help you that much.

How different would your decisions be knowing that your four flush has a 19.5% chancce of hitting on the next card versus an estimate of 18%?




[/ QUOTE ]

My examples were perfect for their intent which was obvious to most posters here. That was simply to show the potential inaccuracies of the 2 card 4 card method. If I had been attempting to demonstrate useful calculations for daily play then you would be correct. Next time read an entire thread before commenting, take time to digest the content of the material and keep your useless insults to yourself
unless you have value to add to the thread.

I will comment on one particular statement you made: Are you really not going to bet a straight flush draw if the odds are only 71% instead of 84%? Yes there are times you should fold. I'll leave it to you to figure these times out for yourself. You do get two hints: Bankroll and No Limit.

[TaintedRogue]

Although odds are not always what one makes a decision on, it plays a very important role in playing smart poker. For one to sit a poker table without having the odds memorized is handicapping himself.
I will support that statement with two examples. These are actual hands I played in the past.
10/20 HE. I am dealt AA UTG and limp as the game has been really tight. I get 3 callers, one being the big blind. $45 in the pot. Flop: Ks,Ac,7d. I bet, and get 2 callers. $75 in the pot.
Turn: (Ks,Ac,7d)Td....I bet, 2nd player raises and 3rd player re-raises. There is now $195 in the pot. The read I get is that the re-raiser has a straight and the raiser doesn't seem worried that he's been raised. I think it's obvious that the raiser has a straight. I put the 1st player on the straight also. He appears ready to re-raise.
If I call the $40 and there are no more raises, I am chasing $215 with $40 and getting 5.37:1 pot odds plus what I get on the river if I fill my boat. I know the opponents, however, and they will call me less than 1/2 the time if the board pairs. They know me also. I think about it awhile and the lead raiser has now sold me on him having broadway also. I can count on him re-raising and the 2nd player capping it. So I will have to put up this $40 plus another $40. $295 in the pot is what I will be chasing with my $80. 3.68:1 pot odds. If you cannot add this up and divide in your head quickly you are handicapped in the game. The odds here are easy as I have 10 outs with 46 cards to come. 3.6:1. It's a coin toss here. Unless they call me on the river. I don't like playing razor sharp odds. I would have to be in this situation alot to see a tangible profit and fold. The players did raise back and forth after I folded and they did both have QJ.
The trick to keeping track of bets is counting them and dividing in half after the flop betting is done. 4.5 bets b4 the flop. the half is the small blind. 3 bets on the flop is 7.5 or now 3.75. The turn saw six bets before I had to make my decision, now 9.75 bets in the pot. If I call the two bets and the 1st player calls that's 10.75:2 or 5.3:1. There is no need to go past the tenth. If the 1st raiser re-raises and the 2nd player caps it, that's 4 more bets making it 14.75:4 or 3.68:1 Or you can take the 295/80 and drop the zero and divide 8 into 29.5. Practicing when you're not in the hand and you'll soon being doing it naturally.
The second example is where I had JJ in the big blind and 5 people limped, including the small blind. Knowing the crowd I'm playing with I would give you 4-1 odds that there is an ace, a king, and a queen somewhere in those hands. So if I don't flop a set and an overcard comes up, I'm done. I know that because I know the odds of tripping up by the river with a pair on the flop is 10.88:1 and the pot odds are not going to justify calling to see the river card. If I just call b4 the flop and everybody stays to see the river card and there is only one bet on the flop and turn that's 6*2/2 = 6 +5 bets on the turn = 11, and it's even money but we know everyone isn't going to pay to see the river so it's less than my odds of catching. So I have to catch on the flop and if I do, I am going to wish I had raised before the flop, so I do. I remember this hand well, because I won alot of money with it when they all called and the flop came J,9,5 rainbow and I bet and they all called, except the last guy who raised. He had limped in in the small blind with 95suited and filled his house on the turn with a 5. The flop did not justify me worrying about being outdrawn and I just called and a few others did also. There are many aspects to the game and knowing your odds are just as important as any of them.

[Copernicus]

flashy never said that igorance of the odds is acceptable, just that the approximation approach will rarely distort results enough to change the decision (ie the pot odds will either be short or exceed both the estimate and the exact calculation). I'll go a step further and add that if you make a "wrong" decision based on the estimate, that the pot odds are so close to those needed that the loss of EV wont amount to squat in EV over the long haul, and in the short run the variance of results even using the exact calculation overwhelms the minor errors that might occur.

I primarily use exact odds, because its easy for me...Ive done similar calculations nearly every day in my career, so I'm not an apologist for the short-cutters by any means. However, there are far more important things to think about in the time you have to take action than the difference between 3.7/1 and 3.9/1 pot odds.

[M.B.E.]

Good post, TaintedRogue. An interesting approach to preflop decision-making; I will give it some thought. Hope to see more of your posts here and on the "Mid- and High-Stakes Hold'em" forum.

I'm not sure about limping UTG with aces in a tight game, however (especially since your game seemed tight-passive).

[rayrns]

"The Rake was trying to pass on a good tip to begining players."

As a new player myself, I appreciate that someone would post a shortcut to learning. When it was shown how far off this type of shortcut can be, then I am glad that others would point out the error and post a more correct way of figuring these odds.

Remember as a beginner, I want/need to learn correct procedure.

[Copernicus]

"I know that because I know the odds of tripping up by the river with a pair on the flop is 10.88:1 and the pot odds are not going to justify calling to see the river card. If I just call b4 the flop and everybody stays to see the river card and there is only one bet on the flop and turn that's 6*2/2 = 6 +5 bets on the turn = 11, and it's even money but we know everyone isn't going to pay to see the river so it's less than my odds of catching. So I have to catch on the flop and if I do, I am going to wish I had raised before the flop, so I do."

An excellent example of why there are more important concepts than exact odds. With JJ pockets you have two strategies...raise to isolate against one other player, or lay low to keep as many in the pot as possible in case you make a big hand. With 5 limpers you have virtually no chance to isolate, so a raise is exactly the wrong thing to do on this hand. Projections of play through 3 additional rounds of play are so complex that an "implied odds approach" is too simplified and an EV calculation would really be called for....if you really needed it.

Also, in the context of the issue being debated, approximate vs exact odds, the 4&2 rule gives 4/1 vs the true 3.6/1. Most people using approximate odds would say thats a call, the same decision you make based on the 3.6875 odds you think you are getting. But what would the cost be if they made a mistake and folded? $1.52 for your $80 bet, or less than 2%, and that doesnt even take into account that your read could be wrong and youre ahead.

You also limp with AA because the table is really "tight", but then conclude that you have two limpers with QT and made straights? And the limp with QT, make a straight, but will fold to any pair on the board 1/2 the time? What are they limping for if they are going to fold a straight to a pair? If you even think its possible that on this "tight table" opponents will be limping with one gappers then slowplaying AA is a huge mistake to start with.

Sorry, it just doesnt make sense, and hand reading and thinking like this will cost far more than 2%.

[Flashy]

Below is a table which shows the probablities of hitting outs using TheRake's estimating method (Est) and the Actual (Act). Decide for yourself how inaccruate TheRake's method was.

I hope you realize that WakeUpCalls 40 fold error was inaccruate. First of all, it is an 80 fold difference. Second, he is comparing the odds of hitting a two out runner runner to the odds of hitting one out. The Rake never suggested using his approximation method to estimating the odds of hitting a perfect runner - runner.

If you want to memorize the exact odds, please go ahead. But if in the heat of the battle you not sure, TheRake's method won't steer you off course by much. Especially if you know it under estimate the odds by 2-3 percentage points.

Good luck!


This table is the percentage of hitting an out on the
-----------Turn---------River---------Combined
Outs-----Est--Act-----Est--Act------Est--Act
00001 2.0% 2.2% 2.0% 2.2% 4.0% 4.4%
00002 4.0% 4.3% 4.0% 4.4% 8.0% 8.8%
00003 6.0% 6.5% 6.0% 6.7% 12% 13.2%
00004 8.0% 8.7% 8.0% 8.9% 16% 17.6%
00005 10% 10.9% 10% 11.1% 20% 22.0%
00006 12% 13.0% 12% 13.3% 24% 26.4%
00007 14% 15.2% 14% 15.6% 28% 30.8%
00008 16% 17.4% 16% 17.8% 32% 35.2%
00009 18% 19.6% 18% 20.0% 36% 39.6%
00010 20% 21.7% 20% 22.2% 40% 44.0%
00011 22% 23.9% 22% 24.4% 44% 48.4%
00012 24% 26.1% 24% 26.7% 48% 52.8%
00013 26% 28.3% 26% 28.9% 52% 57.1%
00014 28% 30.4% 28% 31.1% 56% 61.5%
00015 30% 32.6% 30% 33.3% 60% 65.9%
00016 32% 34.8% 32% 35.6% 64% 70.3%
00017 34% 37.0% 34% 37.8% 68% 74.7%
00018 36% 39.1% 36% 40.0% 72% 79.1%
00019 38% 41.3% 38% 42.2% 76% 83.5%
00020 40% 43.5% 40% 44.4% 80% 87.9%
00021 42% 45.7% 42% 46.7% 84% 92.3%

[Flashy]

Correct table - assumes outs are independent
Outs-------Turn---------River---------Combined
--------Est--Act.-------Est.--Act.-----Est.--Act.
00001 2.0% 2.1% 2.0% 2.2% 4.0% 4.3%
00002 4.0% 4.3% 4.0% 4.3% 8.0% 8.6%
00003 6.0% 6.4% 6.0% 6.5% 12% 12.9%
00004 8.0% 8.5% 8.0% 8.7% 16% 17.2%
00005 10% 10.6% 10% 10.9% 20% 21.5%
00006 12% 12.8% 12% 13.0% 24% 25.8%
00007 14% 14.9% 14% 15.2% 28% 30.1%
00008 16% 17.0% 16% 17.4% 32% 34.4%
00009 18% 19.1% 18% 19.6% 36% 38.7%
00010 20% 21.3% 20% 21.7% 40% 43.0%
00011 22% 23.4% 22% 23.9% 44% 47.3%
00012 24% 25.5% 24% 26.1% 48% 51.6%
00013 26% 27.7% 26% 28.3% 52% 55.9%
00014 28% 29.8% 28% 30.4% 56% 60.2%
00015 30% 31.9% 30% 32.6% 60% 64.5%
00016 32% 34.0% 32% 34.8% 64% 68.8%
00017 34% 36.2% 34% 37.0% 68% 73.1%
00018 36% 38.3% 36% 39.1% 72% 77.4%
00019 38% 40.4% 38% 41.3% 76% 81.7%
00020 40% 42.6% 40% 43.5% 80% 86.0%
00021 42% 44.7% 42% 45.7% 84% 90.3%

[Flashy]

“My examples were perfect for their intent which was obvious to most posters here. That was simply to show the potential inaccuracies of the 2 card 4 card method. If I had been attempting to demonstrate useful calculations for daily play then you would be correct. Next time read an entire thread before commenting, take time to digest the content of the material and keep your useless insults to yourself unless you have value to add to the thread.”

Let’s see, you post a rude reply to TheRake, make a denigrating reply to my first post, make a half ass apology to TheRake for being rude, and but then maintain you were right after all.

Ok, I will apologize for using the word asinine. I should have used your word “useless.”

Here is one of your “perfect examples”

“Let's see now I have AA and my opponent has KK and the flop comes KK2, now your method says I have a 4% chance to win but it is closer to .1% this is off by a factor of 40! WOW!”

It would be a perfect example except the discussion was how to quickly figure out the odds of hitting an out, not how to figure out hitting a perfect runner-runner. To imply TheRake’s method was off by a factor of 40, when his method was never intended to calculate runner-runner Aces was just plain wrong!

It was also an insulting example because I don’t think anyone here would seriously thinks the chances on hitting runner-runner Aces to make quads is 4%. How dumb do you think TheRake is?

The estimate of 4% in hitting an Ace on the next card stacks up pretty well to the calculated odds of 2/47 or 4.3%. Those are the odd calculations most people want to make in that scenario. If you can divine your opponent has flopped quads, great! But in that case you are folding unless there are jackpot considerations.

Most people would agree that knowing that the exact odds of getting quad Aces is 0.1% is pretty useless information if you know your opponent flopped quads.

By the way, TheRake original post stipulated using this method for “game situations” for hands you “don’t’ have memorized.” He never suggested it as a substitute to memorizing the exact odds.

So I guess this statement agrees with my other points:

“If I had been attempting to demonstrate useful calculations for daily play then you would be correct”

I think I am correct in everything expect for using the word asinine. For which I will apologize.

[biggambler]

This method is used to approximate the chances of making a pat hand. It is pretty close.

Hand 1:

You have 9 hearts to make a flush and 8 cards to make a straight. 17 outs times 4 equals 68%. Thats pretty close to the 71% actual. When would you fold a hand that has a 68% chance of winning that you wouldn't fold if you had a 71% chance?

Hand 2:

You can't use this method because there is no card to give you a pat hand. Therefore you can't do any calulations.

The method is used to play hands for us non-math types. It is not used to get a rocket to the moon.

[Wake up CALL]

Flashy I have no trouble with you calling me assinine. I do have trouble with you calling me incorrect when not only have I proven otherwise but you have as well.

The clear point of my post was to state TheRakes method was inaccurate. It is inaccurate as you have agreed and proven. We may disagree as to how inaccurate or even how important the inaccuracy becomes during a single hand. Therefore you are certainly incorrect and have proven yourself so even while arguing otherwise. It is up to each individual to determine if they wish to continue to make mistakes playing poker or learn how to improve. Personally I think they should at least know the choice exists rather than take every shortcut written as gospel.


So you did not like my examples, that's life. They were used as extremes and it was obvious to all but you.

TheRake took my apology as sincere which is the manner in which it was offered. As to how you feel about it I could give a Sh*t.

[Flashy]

Obviously you do give a "Sh*t" or you would not bother replying. By this reply, so must I.

My first post to you was an easy, although pointed, push back at what I thought was a rude post. You took exception and insulted my abilities as a player. Although you and I have never played so you would have no way of knowing how good or bad I am. ALthough if you ever sat at a table with me I would be more than happy to tell you what a horsesh*t player I am.

When you fire at people, don't be so shocked if they take exception and fire back.

Finally, I would never agree that you examples proved anything, or that everyone but me got the point. There are at least three to four posts expressing pretty much the same opinion as mine.

Ignorance is bliss. Let's leave each other in our own blissfull state.