One card Royal

Here's my first Royal Flush, albeit only a one card.

Party Poker 3/6 Hold'em (10 handed)

Preflop: Hero is SB with 8d, Jd. MP3 posts a blind of $3.
3 folds, MP1 calls, 1 fold, MP3 (poster) checks, 2 folds, Hero completes, BB checks.

Flop: (4 SB) Ac, Qd, Kd (4 players)
Hero bets, BB folds, MP1 calls, MP3 folds.

Turn: (3 BB) Ad (2 players)
Hero bets, MP1 calls.

River: (5 BB) Td (2 players)
Hero bets, MP1 folds.

Final Pot: 6 BB

Results below:
Hero has 8d Jd (straight flush, ace high).
Outcome: Hero wins 6 BB.

This is really dumb

Here's another one I found:

http://www.lowlimitholdem.com/StartingHands_2.htm

I'll repost the hand here:

For some reason it's 12 handed. Hero is dealt red aces. Four people limp and Hero raises. a player folds, LMP 3-bets, two callers, button caps, blinds call, everyone calls.

11 to the flop for 44 SB. Flop is Th 2h 6d.

Checked to hero who checks. LMP bets, two callers, button raises. Everyone calls, Hero 3-bets, calls, button caps, everyone calls

11 to the turn for 44 BB. Turn is Qc.

Checked to you, you bet, everybody calls.

11 to the river for 55 BB.

7d.

SB bets, two calls, three people vanish (??), hero calls, a fold, two people vanish (??), button raises. Everyone calls.

The website says that calling the first bet on the river was the mistake. Despite getting 57 to 1. And STILL having an overpair to the board. And lack of resistance on the turn. And people suddenly disappearing on the river is disconcerting too.

Unbelievable. The line they gave was perfect. I can't believe they are using this as an example to fold on the river for one bet in a huge pot.

Critique

I haven't personally written anything lately, just putting up interesting posts by other people. I thought it would be interesting to write a critique of some strategy I randomly found on the internet:

http://boardgames.about.com/od/poker/a/holdem_strategy.htm

It depends in part on how many players are in the game, but a general rule is that you should seriously consider folding before the flop if you have two non-pair cards, both less than 10.

Not a bad rule to give beginners. Advice I gave to someone who was learning the rules just an hour before he was to play in his first game of Hold'em ever, I suggested that he fold hand where both cards weren't ten and higher, except for pocket pairs.

A more conservative player might fold if just one of the cards is less than 10;

This is actually extremely loose advice. A conservative player would fold A7 or A9 in a heart beat, and would only play AT if the conditions were perfect.

a more aggressive player might stay in with, for example, an 8 and 9 of the same suit (because those cards give you decent possibilities for a straight or a flush).

I contend with the word aggressive player here. A loose player might come in with a suited connector more often than a passive player, but that has no bearing on how aggressively they play. (I guess an aggressive player might try to raise a suited connector, but this doesn't seem to be the point they are making.)

If the big blind (a forced bet designed to ensure that every hand has a pot) is low enough, it may be worthwhile to pay in so that you can see the flop even if you don't have particularly strong cards in your hand.

This advice is somewhat correct but doesn't give you enough detail and could get you into trouble. The absolute value of the big blind is irrelevant. All that is relevant is the size of the big blind relative to future bets, and in a tournament situation, how large they are compared to the number of total chips in the tournament.

In Las Vegas, they have 4/8 games where the blinds preflop are 1/2, although a raise brings it to 6 total. In those games, you can come in with a lot of crap since the implied odds are very high, since the betting size effectively doubles on the flop. But at the same time, the raise is by so much that in an aggressive game preflop, you still have to be positionally aware, or you'll end up being forced to fold your limps too often to the raises. And I still wouldn't come in with offsuit crap in these games, but I think you can play nearly any two suited in position with a lot of limpers, and suited stuff with at least one high card in early position.

In a tournament, you actually should play extremely tight when the blinds are small, and much looser then the blinds are large. That is because you come in with very little overlay for those times you don't have the best hand. If you play hands like KTo that easily can make a second best or dominated hand, you will have some hard decisions when people start to overbet the tiny pots.

With seven players at a table, two pair or better will generally be the winning hand.

I think this advice is dangerous as it seems to try to tell you not to showdown with less than two pair. Top pair will win more than it's share, and you should usually not fold top pair for only one bet.

If you don't have the high pair after the flop (e.g. if the flop is K-9-5, the high pair would be two Ks), and you're not in good position for a straight or a flush, you should probably get out of the hand.

I guess this is a good start for beginners, but in practice far too weak. This, like most bad poker advice, ignores the size of the pot. Play loose in large pots and tight in small pots. He should also really differentiate between a gutshot straight draw vs. an open ended straight draw, as they are wildly different creatures.

If you're first to bet after the flop, don't be afraid to check. This can work to your advantage in two ways. First, if your hand is on the weak side, you might be able to see one more card without having to put more into the pot. Second, if your hand is strong, you could convince an opponent or two that it's weaker than it really is.

Now the author decides to give some random betting advice. Unfortunately I think this advice alone will be more harmful than saying nothing. It is only one small piece of a larger betting strategy, and a newcomer to the game will think that in early position, checking is always correct. He is suggesting that you should check both your strong and weak hands.

Clearly it is not correct to bet a weak hand. A marginal or strong hand has a better argument for betting especially in small pots. In large pots a checkraise may be in order to protect it.

I disagree strongly with him mentioning the second point. If he means deception through slowplaying, then this is terrible advice to give a beginner. Slowplaying is very rarely correct in loose, small stakes games that the beginner is probably playing. If he means deception through check raising, more detail is needed on good check raising situations or the advice is completely meaningless.

After fourth street, don't stay in the pot hoping for a straight or flush, unless you can do so on a check (that is, without putting more chips into the pot). Although there will be times when you would have drawn the straight or flush, they will be outweighed by the times you wouldn't.

Terrible, terrible advice. In limit poker the flush draw is almost always drawing until the river because it is rare that you don't get the required 4 to 1 plus implied odds to draw profitably. You are certainly an underdog to make your flush, but the original author seems to have completely no grasp of equity, odds or pot size. Often, open ended straight draws will be getting the right odds to draw as well.

Is he talking about no-limit poker? Maybe this advice has a lot more merit when people are making pot sized bets to drive you out of the hand.

But as general advice (don't draw to a straight or flush until the river) is terrible in limit poker, and bad in no-limit, as there are many situations where you want to take one more off because of the odds situation.

That said, there is a point where the investment you've already made virtually dictates that you hang in there. It's useful to measure this in terms of percentage of your chips. For example, if you've already committed 40% of your chips to the pot, another 5% isn't that much. This is a gray area, so once again the best advice is to be cautious.

This seems to suggest that he was talking about no limit poker all along. If only he had stated that earlier, there would be far less confusion. His advice was far too loose preflop for NL, and gives some strange general advice.

Now he is talking about being pot-committed, but gets it horribly wrong. It is irrelevant how many chips you have invested in the pot. All that matters is how much is in the pot at the time of your decision. Now he is saying this is a grey area, when really the math makes this usually a fairly clear decision based on odds.

In conclusion, this is an example of the terrible advice on the internet for how to play poker, and why a lot of people can lose a lot of money to good players very quickly. It is clear that the writer knows very little about poker, and doesn't realize how dangerous advice like this really can be, when people will gamble real money based on it.

Yay for hand quizzes

http://www.cgtv.com/games/column/042904/
http://www.cgtv.com/games/column/052604/
http://www.cgtv.com/games/column/063004/
http://www.cgtv.com/games/column/072804/
http://www.cgtv.com/games/column/082504/
http://www.cgtv.com/games/column/092104/
http://www.cgtv.com/games/column/102004/

Ed Miller on Jim Brier's CardPlayer article

I had lunch with Jim today. He told me what he was referring to with the "won't bet unimproved overcards" assumption. He has logged a number of hours at a local $4-$8 game recently (since reading SSH) to play with some of the concepts. He observed that a fair number of the local Vegas regulars play an incredibly weak-tight and predictable game... and among their tendencies, they don't bet unimproved overcards.

Basically, he's right. Vegas is the world capital of weak-tight hold 'em play... and many of the regular small games players are the worst offenders.

I told Jim that a lot of this play is really limited to Vegas... that online and in LA these super weak-tight small players aren't nearly as ubiquitous.

What Jim has been saying about this stuff definitely has value. Namely, he is absolutely right that raising middle pair is no longer correct if you are almost certain your opponent is betting a better hand. All of these "raise your marginal hands" plays assume that there is SOME CHANCE YOU HAVE THE BEST HAND (or can get the one with the actual best hand to fold). Now because the bet size is small compared to the pot size, that chance need not necessarily be large to make raising correct... often 10% is plenty. But if you are playing against someone whose bet means with certainty that he has a better hand, then raising becomes no longer correct.

From Gambling Theory and Other Topics

pg 33

(1) E = W * N/100

W - Winrate (BB/100h)
N - Hands
E - Expected Win (BB)

Now 99.7% of results are within 3 standard deviations from the mean. So we
can calculate a worst/best case result.

So your results will be within:

W-3*S < R < W+3*S

W - Winrate (BB/100h)
S - Standard Deviation (BB/100h)
R - Results (BB/100h)

These are the worst/base case possibilities


pg 45

The number of hands to assure a profit is:

W*N - 3*S*sqrt(N) = 0

W - Winrate (BB/100h)
S - Standard Deviation (BB/100h)
N - 100's of hands to assure a profit.

Solving for N:

N = (3*S/W)^2

Smallest bankroll so we don't go broke.

B = ((3*S)/(2*W))^2

W - Winrate (BB/100h)
S - Standard Deviation (BB/100h)
B - Smallest bankroll needed to not go broke

BruceZ on Std Deviation

Here's a repost of a detailed and simple explanation of standard deviation which I posted some time ago. Mason has an essay in the essay section which shows you how to compute it when your sessions are different numbers of hours. Later, I will update this thread with detailed information on how to construct an Excel spreadsheet to compute this easily, as well as a derivation of Mason's formula, and an alternative form of the formula. There is a thread in the probability forum right now that explains EV.

The formulas in the essay section may look fearsome, but I'll give a ridiculously simple example to illustrate what is really being computed.

Suppose you play three 4 hour sessions.

In the first session you win $200.
In the second session you win $400.
In the third session you lose $300.

Your average win or EV for these sessions is ($200+$400-$300)/3 = $100/session or $25/hour.

In the first session, you won $100 more than average.
In the second session you won $300 more than average.
In the third session you won $400 less than average.

Now take the SQUARE of these 3 differences from your average (100, 300, -400) to get

100^2 = 10,000
300^2 = 90,000
(-400)^2 = 160,000.

Note that it doesn't matter whether your differences are positive or negative since we are squaring them.

Now average these numbers to get your variance per session.

session variance = (10,000+90,000+160,000)/3 = 86,667.

Take the square root of this to get your standard deviation per session denoted by the Greek letter sigma.

session sigma = sqrt(86,667) = 294

Normally people refer to their standard deviation for 1 hour. A session here is 4 hours, but you cannot divide 294 by 4 to get your standard deviation for 1 hour. You have to divide it by the square root of 4 or 2, because your standard deviation increases as the square root of the number of hours you play. So your standard deviation for 1 hour is:

sigma = 294/2 = $147 for 1 hour.

An equivalent way we could have computed the variance is to simply average the square of our actual wins, rather than the square of our differences from our average, and then subtract from this the square of our average win.

session variance = (200^2 +400^2 + 300^2)/3 - 100^2 = 8667 as before.

I glossed over an important point that is often misunderstood. Many people refer to their standard deviation in units of bb/hr. This is incorrect, and they really mean that this is their standard deviation for exactly 1 hour as we computed here. Standard deviation does not have units of bb/hr, because if it did that would imply that you could simply multiply this number by the number of hours played to get your standard deviation for any number of hours. You actually must multiply it by the square root of the number of hours, so it has units of bb/sqrt(hr) or bb/hr^.5. You don't normally see it written this way, but you can see from the above that this is correct. The variance we computed has units of dollars^2/hr, so the standard deviation, which is the square root of the variance, has units of dollars/sqrt(hr). So if our true standard deviation were $147, and if we are going to play for 100 hours, and we want to know our standard deviation for that period of time, it is sqrt(100)*147 = 10*147 = $1470. The standard deviation only increases by a factor of 10 in 100 hours, but our average win increases by a factor of 100 to 100*$25 = $2500. So our average win increases faster than our standard deviation. This is why gambling "works" when you have an edge. In the beginning, your average win will be small compared to fluctuations caused by luck. Over time, your average win will grow relative to the fluctuations, and your results will be determined primarily by your edge, and the effect of luck will be proportionately smaller. The effect of luck will still be larger in absolute dollars, but it will be a smaller proportion of your win which will also be larger in absolute dollars.

Note in this example that your average win for 100 hours is already greater than your standard deviation for 100 hours. When your average win becomes exactly equal to your standard deviation, you will be ahead more than 84% of the time. This is because your results will lie within +/- 1 standard deviation from average 68% of the time, so 32% of the time they will lie outside this +/- interval. 16% of the time they will lie more than 1 standard deviation below the average, and 16% of the time they will lie more than 1 standard deviation above average. Assuming $147 represents your true standard deviation for 1 hour, after 100 hours your average win will be $2500/$1470 = 1.7 standard deviations. From a table of the standard normal distribution, or from Excel, we can determine that you will be ahead nearly 97% of the time at the end of this period. This is not a very realistic example for most people, and with a different standard deviation this situation could be much different.

To determine how long it will take for your average win to be 1 standard deviation, divide the square of your standard deviation for 1 hour by the square of your hourly rate.

hours to break even 84% of the time = (sigma/ev)^2.

This is one way to define the "long run". To find out how long it will take for your hourly rate to equal let's say 1.6 standard deviations, this is simply

hours to break even 95% of the time = (1.6*sigma/ev)^2.

At this point you have a 95% probability of being ahead.

When you use your standard deviation for 1 hour to compute your swings for longer lengths of time as the other posters have described, the results will be more accurate than when you only use it to estimate your swings for 1 hour. The reason is that in the long term, your results will closely resemble a normal or Gaussian distribution (bell curve), but in the short term this is not exactly the case. For example, a true normal distribution has tails that go off to infinity and minus infinity. You can't actually win or lose infinity in 1 hour, or even close to infinity The result is that the extra probability that would normally be in the tails of the curve get pushed in, making the tails thicker. This means that your swings for short periods of time are likely to be a little larger than what your standard deviation would suggest. If your results were truly normal, your swings would lie within +/-1 standard deviation of your average 68% of the time, and within +/- 2 standard deviations 95% of the time. Your average swing, which I computed recently on the probability forum, will be +/- 0.8 standard deviations. Your median swing, which is the swing you exceed exactly half the time, will be +/- .67 standard deviations. These estimates can give you a rough sense of how you are doing without a lot of calculations. Just remember that results in the short term are just crude estimates, and they are less reliable for reasons that have to do partly with statistics, and partly with your particular circumstances, such as being in a particularly wild game.

Now the above calculation does not produce your true standard deviation, but rather an estimate of it. 3 sessions is obviously not enough for this estimate to be very accurate, and in reality you would compute it over many more sessions. The more sessions you use, the more accurate this estimate will become. On the other hand, it takes relatively few sessions to determine an accurate estimate for your standard deviation compared to the number of sessions required to determine an accurate estimate of your hourly rate. This is a good reason to compute this statistic. While your average win may be somewhat uncertain, there is really no good reason we cannot have an accurate estimate of our standard deviation after a relatively small number of sessions.

Notice above that when I computed the variance, I divided by the number of sessions. Sometimes you will see people divide by the number of sessions minus 1, and sometimes by the number of sessions + 1. These have to do with different types of estimates, and these different estimates have different properties. These differences need not concern you, since the difference is small after the number of sessions becomes large. The estimate used in the essay section is intended to be a "maximum likelihood" estimate of the standard deviation given the data.

Here we have assumed that all sessions are the same length. The formula in the essay section allows you to adjust for variable length sessions. You simply need to log your win and the number of hours played for each session. We have assumed constant length sessions here for the purpose of clearly illustrating what standard deviation means. Namely, it is the "square root of the average of the squares of the differences from your average", or sometimes called a "root mean square" or rms average. Perhaps you have heard of rms voltage, or rms power on stereo speaker specs, the latter of which is actually something of a misnomer. The 120 volts AC you hear about is an rms average of the voltage used in the US. It is actually the standard deviation of the voltage, which is a sine wave with peaks at +/- 170 volts.