With the Chinese New Year around the corner, I thought I'll make a quick post about some of the popular New Year gambling games. To give credit where credit's due, this was mostly inspired by Changs and Colin.
In Between
The premise of the game is simple. Everyone gets dealt two cards. Some games allow everyone to be dealt cards before the game starts, others deal each player their cards by turn. After a player looks at his cards(which are open for all to see), he can, on his turn, make one of two choices:
1) pass, and forfeit his hand(and his ante)
2) draw a third card and play.
If he should so choose to play the game, he must bet an amount of money less than or equal to the amount of money already in the communal pot. The communal pot is built up from ante forfeits and lost bets by the players. If the player manages to draw a card that falls in between his two cards(Ace lowest, King highest), he is entitled to take from the pot the amount of money he bet. If the card falls outside the range, however, he puts the amount of money he bet into the pot. The worst case scenario is when he pairs his cards. If the third card pairs his hand, he has to put TWICE the amount of money bet into the pot.
As with every non-dealer, non-rake game, this game is a fair one. Meaning your value of playing the game is exactly 0. In the long run, playing as a rational player, you expect to break even. As you will see later, this makes the game a good one to play if you want to play in the New Year games. Other games are not quite as fair.
So how can we win a game with 0 value? Why would one even want to play this game? From an economical viewpoint, no rational person would play a game with no value. Here's a few reasons why, though
1) Value derived via entertainment
2) Value derived via lack of rational play from OTHER players
In other words, we play this game to perfection and hope others make mistakes. If you're starting to draw a relation to poker, you're absolutely right. In between is like a very simplified version of poker.
Here's the math behind it.
Your equity in any hand you bet is derived from the formula:
Equity = 1-(2X+Y)/D
X is the number of cards left in the deck that could pair your hand
Y is the number of cards left in the deck that falls outside your range(not inclusive of pairs)
D is the number of cards left in the deck
It may seem daunting to calculate your equity every hand, but a closer look at the formula reveals certain universal rules one needs to follow.
1) Never play any hand where you have a gap of 7 or less
2) Never play a hand where you have a gap of 8 unless Y or X has been reduced by cards dealt to others
3) Always play AK , AQ and 2K in early position.
With these 3 simple rules in mind, there Aren't really many hands where you have to get down to do the calculations. But it can't be hard to do the math either...the formula is so simple.
Let's say you're dealt 3K. That's a 9 gap. First thing you do is make a rough estimation of the deck. No need to be exact. Think in counts of 5s. 25/30/35/40/45 are really pretty much the only options. Now count the number of As and 2s that have appeared. Not hard right? Take 8 and subtract that number to get your Y. Now take 6 and subtract the number of 3s and Ks that have appeared(other than in your hand). Add your numbers together and divide it by the deck. If the resultant figure looks to be greater than 0.5, fold it. If not, bet.
Ok, math aside...I find it neccessary to talk a little on variance. In poker theory, we all know we should get all our money in the pot when we're ahead, no matter how little. One must bear in mind that in this game, the limits are not table limits, but pot limit. Obviously what I'm trying to say is, don't bet your whole bankroll on a single hand. 2 ways to look at this though.
1) The bet progression of a pot sized bet everytime you bet makes for a natural Martingale system. While mathematically correct, variance will eventually eat you up if you cannot support the bankroll. Another flaw of the system is that the Martingale breaks down if someone wins the pot before you do.
2) My personal recommendation : Pick a bet and stick to it. If you bet a constant amount through the game, always picking spots where you're ahead to put that amount in...you won't be one of the big pot winners everyone remembers, but you'll almost certainly be well off. You can expect on average to make about 10% of your bet. Meaning, you can expect to be up 10 dollars for every hand you play if you manage to make 100 dollar bets everytime you bet. I know, sounds pretty unglamorous...but that's what grinders do. Still, it's the new year, and if you can afford to pay 10k, go for the 5k pot when you have >50% equity if you want to. It's still mathematically correct.
Blackjack - Sg Home rules
The rules of this game is simple. Unlike the version played in the casino, cards are dealt to players face down, and the players then take turns to draw from the deck. Players need not declare when they bust. Once the players are done drawing, It's all up to the banker. At any point from here, he can request to open any player's hand and pay him off according to the strengths of their hands. The banker then procedes to draw and open cards until he is satisfied. He then opens the remaining hands and pays off the hands that beat him. If the banker busts, any unopened hands are paid off. In this way, the player can win even with a busted hand.
Different house rules are available everywhere, but here are a few common ones:
1) all players, including banker may fold without penalty if dealt 15 total
2) Pocket aces pay triple
3) Blackjack pays 2:1.
3) 5 cards below 21 gets paid 5:1.
All rules apply equally to the banker and player.
The strategy for playing a winning game of house rule blackjack is simple. Be the banker. Done. End of story. There is no winning player based strategy. Estimates put the banker's advantage at about 10%, and a much reduced risk of ruin than the player.
Blackjack - Casino rules
Casino rule blackjack is a game close to my heart. I have spent years studying the finer points of blackjack, reworking the mathwork calculated by many others before me. The rules are simple. The banker deals everyone 2 cards face up, and 1 for himself. He then proceeds to pay out blackjacks in a ration of 3:2, unless he holds an ace or a 10 value card. If he does, he proceeds to ask the blackjack player if he wishes to escape a push by taking 1:1 now. After this is done, the round of dealing to players commence. Any player who busts immediately loses his bet. This done, the banker draws his second card. If he does not make blackjack, he pays out in the form of 3:2 to anyone who has made a blackjack. If he does make a blackjack however, the player pushes. The dealer then proceeds to draw to 17 or higher. If he busts, he pays all remaining players. If he doesn't, hand strength determines the winners.
Lest be it thought to be a dull game for the player, a number of options are available during the drawing round to the player
1) The player may split any equal value card pair. Eg 77 or QK
2) The player may double up(and get only one more card) on any two starting cards that don't include an ace
3) The player may surrender any hand without drawing and lose only half his bet.
Blackjack played perfectly gives a 0.5% advantage to the dealer. As such, it is highly recommended that you take the dealer seat if it is available. You stand to gain more than 0.5% for 2 reasons:
1) Most people play horrible blackjack. Think of the worst poker player you've ever played with. He's almost certain to be a better poker player than a blackjack one.
2) Most people cannot take the variance because they tend to overbet. Martingale strategies users are also common. In the short run, most people run out of money to play, or simply stop playing out of disgust to "bad luck".
But there's an overriding reason to play the dealer here. You have a 0.5% advantage minimum. This is 0.5% of total bets placed. If each round gets 20 dollars worth of combined action, that's 10cents per round for the dealer. Multiply it by the 100 hands you play and you'll make a tasty 10 dollars. That's not including the value you get(quite substantial) from the above-mentioned dealer's reduced risk of ruin.
Anyway, good luck at the tables, and remember...those donkeys are your relatives=)
Monday, February 4, 2008
Saturday, January 19, 2008
This is why Doyle > Math
The usual after-game chat on thursday morning with Changs
set me thinking. For those of you who were there on
Wednesday night, you may recall the questionable hand where
I shoved pre-flop with AT and was called by Changs with
pocket nines.
Let's recap that hand.
The hand was min raised twice to me, and I min-raised it
again. Folded to Mike who calls the raise and Changs who
puts in 30 on top. I pushed him all in, and he reluctantly
calls, to flip over pockets nines. As mentioned before I
held AT of clubs.
Pot was about 25 dollars before Changs put in his 30, and I
had him covered for 83 and change more.
The results are irrelevant to this post, but I'll post it
anyway. I lucked out, spiking a ten on the first board and
an ace to secure the full pot on the second run.
What really set me thinking was my defence against Chang's
accusation of my apparent donkey shove.He feels that I
should not have shoved when he was apparently the favourite,
no matter how slight.(I'd told him I knew he had an
underpair before I shoved) I know many people would will agree with Changs here; shoving when you're behind, no matter how slight intuitively sounds like a -EV play.
Though I have poven it to be mathematically correct, this opinion of it being a donkey play bugged me for days. Why is it intuitively a bad move? After brushing up on my statistics and sorting through the 2+2 forums, I figured it out. It feels like a bad move because it IS a bad move.
So how can a move be mathematically correct, yet wrong at the same time? The answer lies in the underlying assumption that acts as a blindsight for most math based poker players. The advice "Make the right mathematical move every time and you'll end up winning in the long run" is flawed. What it doesn't mention is the risk of ruin and it's close cousin(which is relevent here), geometric cummulative variance.
Let's backtrack a little. What is bankroll management? It is money management in a sense so that you do not play with too much of your bankroll at any one time, exposing yourself to variance which can severely cripple, or ruin you. Most people can tell you bad management spells doom, no matter how perfect your poker math is. The reason this is a danger is a little something called risk of ruin. Risk of ruin predicts that the proportion which you risk in ratio with your bankroll is exponentially proportional to the chances of you going broke due to variance.The quirky part of it is, of course, that no matter how superb your management is, as long as you continue to risk a part(no matter how small) of your money playing games of variance, you end up with a possibility above 0 that you lose everything in time. Most people think casinos win because they have a slight edge in the long run(which is true). But in reality, it is this quirk of statistics that really help seperate the cash from the gamblers.
Why did i talk about the theory of risk of ruin? Well, it's an unwelcome opposing force to perfect mathamatical poker due to variance. I'm about to introduce you to another unwelcome variance concept: the geometrical cummulative.
I like what Mike offered as a compromise that night. He told me "It's not that it's a bad play. But you could have picked a better spot to put your money in". Wise Mike. He's absolutely right of course. When you're talking about putting all your money in, you hope to put it in when you're a clear favourite. But that's tourny Mike speaking. In tournaments, you only get one chance to go broke, so obviously waiting for a better spot is nicer. But in cash games, when the player can rebuy again(and the stakes are hopefully insignificant to his bankroll)...how does this work out to be right? After all, the right move in the long run always brings in the cash right?
Remember what I mentioned about how risk of ruin increases exponentially the more you expose yourself to variance? That was when variance was held as a constant. Now imagine if you will, the significance of the coeffecient in this equation, the variance. A small difference in variance will lead to a significantly larger difference in the probability of ruin.
Why does this matter? Well for starters, variance over the long run is not calculated by the normal averaging to find the mean of all variances(in all your hands). It's geometrically calculated. Meaning, instead of ADDING them together to find the total, you MULTIPLY. Big variance(big swings) mean the mean variance will end up much bigger.
Well that's the math part of it anyway. If you can't wrap your head around the math, here's another explanation. When you make a move based on math, the assumption that the long run will reap rewards only holds true if everything else remains on constant. This means, for example, that for any random play(let's take an example we see almost every game next), you must be assured that you will see that exact random play again in your lifetime. That is no easy feat. Let's see an example.
The pot is now 600 dollars. The flop is dealt, pending the river. Mike and Changs are both all in. Kelvin has 190 dollars in front of him with the nut flush draw. He puts neither on a set, meaning if his flush hits, it's very likely to scoop the pot. Mathematically this is a no brainer to call the all in right?
Here's what the math poker pros don't tell you. Mathematically, yes, it is correct. In the long run, you will always make money if you shove here. Here's the catch. For that long run to come true, you need to be sure that in your lifetime, you will encounter the exact situation two more times. That's what the long run means. That doesn't sound unlikely yet? Let's review this.
Let's say Kelvin holds AT of spades, flop is 4s8sKd. Changs holds KcAc and Mike holds 8d4d. Changs is in position of Mike who is in position of Kelvin. You will need these exact things to happen again twice more in your poker career. Let's list down the things that need to happen twice more:
1) Kelvin out of position to both Players A and B
2) Kelvin has to hold AT of a suit on a board of 48k, with 4 and 8 of the suit he holds
3) Player A in position of Player B, has to hold AK of another suit.
4) Player B in position of Kelvin, has to hold 84, with the 4 and 8 in the same suit as the king on the flop
5) both players have to go all in for exactly the total of 600 dollars
6) At this point, Kelvin must have exactly 190 dollars left in front of him
The likelyhood of the exact events replaying again the required number of times should influence how well you do in poker if you play with math. Imagine now, if Kelvin at another point in time encounters almost the exact situation, with 180 dollars left in front of him instead. If he shoves now, he is starting another cycle of hoping to catch another 2 exact situations, instead of fulfilling the above one. That's how sick it is. That's how unlikely it is.
I am reminded of the much overquoted quote:
"In the long run, we'll all be dead"
After all that ranting, what has this got to do with my AT vs 99 hand? Well, imagine my horror when I finally broke out of my bubble and realised what cummulative variance meant. How long do I have to wait for another hand as unlikely as an AT vs 99 all in pre flop cash game? Or to be more sadistic(since I won that one)....how long does CHANGS have to wait to balance out his variance call there? The upside of course, is that he only needs for it to happen once more because he was getting coinflip odds.
You're right Mike. We both could have chosen better spots.
set me thinking. For those of you who were there on
Wednesday night, you may recall the questionable hand where
I shoved pre-flop with AT and was called by Changs with
pocket nines.
Let's recap that hand.
The hand was min raised twice to me, and I min-raised it
again. Folded to Mike who calls the raise and Changs who
puts in 30 on top. I pushed him all in, and he reluctantly
calls, to flip over pockets nines. As mentioned before I
held AT of clubs.
Pot was about 25 dollars before Changs put in his 30, and I
had him covered for 83 and change more.
The results are irrelevant to this post, but I'll post it
anyway. I lucked out, spiking a ten on the first board and
an ace to secure the full pot on the second run.
What really set me thinking was my defence against Chang's
accusation of my apparent donkey shove.He feels that I
should not have shoved when he was apparently the favourite,
no matter how slight.(I'd told him I knew he had an
underpair before I shoved) I know many people would will agree with Changs here; shoving when you're behind, no matter how slight intuitively sounds like a -EV play.
Though I have poven it to be mathematically correct, this opinion of it being a donkey play bugged me for days. Why is it intuitively a bad move? After brushing up on my statistics and sorting through the 2+2 forums, I figured it out. It feels like a bad move because it IS a bad move.
So how can a move be mathematically correct, yet wrong at the same time? The answer lies in the underlying assumption that acts as a blindsight for most math based poker players. The advice "Make the right mathematical move every time and you'll end up winning in the long run" is flawed. What it doesn't mention is the risk of ruin and it's close cousin(which is relevent here), geometric cummulative variance.
Let's backtrack a little. What is bankroll management? It is money management in a sense so that you do not play with too much of your bankroll at any one time, exposing yourself to variance which can severely cripple, or ruin you. Most people can tell you bad management spells doom, no matter how perfect your poker math is. The reason this is a danger is a little something called risk of ruin. Risk of ruin predicts that the proportion which you risk in ratio with your bankroll is exponentially proportional to the chances of you going broke due to variance.The quirky part of it is, of course, that no matter how superb your management is, as long as you continue to risk a part(no matter how small) of your money playing games of variance, you end up with a possibility above 0 that you lose everything in time. Most people think casinos win because they have a slight edge in the long run(which is true). But in reality, it is this quirk of statistics that really help seperate the cash from the gamblers.
Why did i talk about the theory of risk of ruin? Well, it's an unwelcome opposing force to perfect mathamatical poker due to variance. I'm about to introduce you to another unwelcome variance concept: the geometrical cummulative.
I like what Mike offered as a compromise that night. He told me "It's not that it's a bad play. But you could have picked a better spot to put your money in". Wise Mike. He's absolutely right of course. When you're talking about putting all your money in, you hope to put it in when you're a clear favourite. But that's tourny Mike speaking. In tournaments, you only get one chance to go broke, so obviously waiting for a better spot is nicer. But in cash games, when the player can rebuy again(and the stakes are hopefully insignificant to his bankroll)...how does this work out to be right? After all, the right move in the long run always brings in the cash right?
Remember what I mentioned about how risk of ruin increases exponentially the more you expose yourself to variance? That was when variance was held as a constant. Now imagine if you will, the significance of the coeffecient in this equation, the variance. A small difference in variance will lead to a significantly larger difference in the probability of ruin.
Why does this matter? Well for starters, variance over the long run is not calculated by the normal averaging to find the mean of all variances(in all your hands). It's geometrically calculated. Meaning, instead of ADDING them together to find the total, you MULTIPLY. Big variance(big swings) mean the mean variance will end up much bigger.
Well that's the math part of it anyway. If you can't wrap your head around the math, here's another explanation. When you make a move based on math, the assumption that the long run will reap rewards only holds true if everything else remains on constant. This means, for example, that for any random play(let's take an example we see almost every game next), you must be assured that you will see that exact random play again in your lifetime. That is no easy feat. Let's see an example.
The pot is now 600 dollars. The flop is dealt, pending the river. Mike and Changs are both all in. Kelvin has 190 dollars in front of him with the nut flush draw. He puts neither on a set, meaning if his flush hits, it's very likely to scoop the pot. Mathematically this is a no brainer to call the all in right?
Here's what the math poker pros don't tell you. Mathematically, yes, it is correct. In the long run, you will always make money if you shove here. Here's the catch. For that long run to come true, you need to be sure that in your lifetime, you will encounter the exact situation two more times. That's what the long run means. That doesn't sound unlikely yet? Let's review this.
Let's say Kelvin holds AT of spades, flop is 4s8sKd. Changs holds KcAc and Mike holds 8d4d. Changs is in position of Mike who is in position of Kelvin. You will need these exact things to happen again twice more in your poker career. Let's list down the things that need to happen twice more:
1) Kelvin out of position to both Players A and B
2) Kelvin has to hold AT of a suit on a board of 48k, with 4 and 8 of the suit he holds
3) Player A in position of Player B, has to hold AK of another suit.
4) Player B in position of Kelvin, has to hold 84, with the 4 and 8 in the same suit as the king on the flop
5) both players have to go all in for exactly the total of 600 dollars
6) At this point, Kelvin must have exactly 190 dollars left in front of him
The likelyhood of the exact events replaying again the required number of times should influence how well you do in poker if you play with math. Imagine now, if Kelvin at another point in time encounters almost the exact situation, with 180 dollars left in front of him instead. If he shoves now, he is starting another cycle of hoping to catch another 2 exact situations, instead of fulfilling the above one. That's how sick it is. That's how unlikely it is.
I am reminded of the much overquoted quote:
"In the long run, we'll all be dead"
After all that ranting, what has this got to do with my AT vs 99 hand? Well, imagine my horror when I finally broke out of my bubble and realised what cummulative variance meant. How long do I have to wait for another hand as unlikely as an AT vs 99 all in pre flop cash game? Or to be more sadistic(since I won that one)....how long does CHANGS have to wait to balance out his variance call there? The upside of course, is that he only needs for it to happen once more because he was getting coinflip odds.
You're right Mike. We both could have chosen better spots.
Tuesday, December 18, 2007
Beginnings
Ah, the blog is finally up. When I first got the idea of starting one, I had grand plans for it. I registered for a domain name and got myself pretty good hosting, convinced the traffic would soon outgrow my capacity. Five years of procrastinating later, I'm finally starting. My domain may have expired(and been added to some unethical domain farmer's portfolio), but it's finally off the ground.
Anyway, for the handful of you who will read this, I intend to post whenever a stray thought hits me, so check back here regularly for my contribution to internet clutter, and I'll see if I can't burn a few minutes of your free time with my rantings on the world in general.
Anyway, for the handful of you who will read this, I intend to post whenever a stray thought hits me, so check back here regularly for my contribution to internet clutter, and I'll see if I can't burn a few minutes of your free time with my rantings on the world in general.
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