Betting on World Series of Poker final tables is stupid. Don't do it. There's just no way you can possibly have enough information to make an intelligent decision. The books feel the same way, which is why the vig on the Bodog line is a horrendous 50% - they have no clue how to handicap it and want to make sure they don't get burned if someone going off at low odds winds up winning.
Seriously...Shulman has twice as many chips as Ivey, but is at the same price. This would suggest that the public thinks Ivey is twice as good as Shulman. If you think that, you haven't seen Jeff Shulman play.
Most of the others are even less known. Just because someone is not well known doesn't mean they can't play. On what basis would we handicap the chances of these players?
Just don't waste money on these kinds of bets. It's football season. Bet on the Bucs to lose instead.
Saturday, October 24, 2009
Friday, October 23, 2009
Poker Punditry Fail
Amy has one of the better, more readable poker blogs, and she's very good with investment stuff, but maybe she should avoid writing about important Civil War battles, especially if she can't even get the name right.
It's Donelson, not Donaldson.
If she had just posted this, I'd assume it was one of those "there/their" type errors that writers often make. But the article was published a couple years ago on PokerPages. Did no one point out the mistake to her?
But let's get to the non-nitpicky shit:
Grant did not have a weak hand at all. His initial approach to Fort Donelson was done with 15,000 available troops (versus 12,000 to 17,000 Confederates at Fort Donelson), but the total Union forces in the immediate area vastly outnumbered the available Confederate troops. Indeed, another 10,000 troops arrived a couple days later to reinforce Grant. The Union also controlled the lower Cumberland River and all of the Tennesse River, had cut the railroad to the south, and had split the two main Confederate forces in the area. The strategic, numerical and logistical situation overwhelmingly favored the Union. Grant knew that, and so did the Confederate commanders, who debated the merits of even trying to defend the fort before deciding they couldn't let the Union capture Nashville that easily.
If you want a poker analogy, look at is this way: the purpose of advancing on Fort Donelson was to protect the Union's stronger hand and not let the Confederates draw out with a weaker holding.
There are many examples in military history of going into battle with the weaker hand and winning. This just doesn't happen to be one of them.
Update: In fairness to Amy, calling the place "Fort Donaldson" was a common error in reports of the time. It might be spelled that way in Grant's memoirs, too - I don't have a copy hand to check. But the proper name is nevertheless Fort Donelson.
It's Donelson, not Donaldson.
If she had just posted this, I'd assume it was one of those "there/their" type errors that writers often make. But the article was published a couple years ago on PokerPages. Did no one point out the mistake to her?
But let's get to the non-nitpicky shit:
In his attack against Fort Donaldson Grant said, “I was impatient to get to Fort Donaldson because I knew the importance of the place to the enemy and supposed he would reinforce it rapidly. I felt that 15,000 men on the 8th would be more effective than 50,000 a month later.” Grant knew his opponent was weak. He realized that his best chance was to try take the pot with a weak hand rather than to wait for a better one, when his opponent might be stronger and less uncertain.Emphasis mine.
Grant did not have a weak hand at all. His initial approach to Fort Donelson was done with 15,000 available troops (versus 12,000 to 17,000 Confederates at Fort Donelson), but the total Union forces in the immediate area vastly outnumbered the available Confederate troops. Indeed, another 10,000 troops arrived a couple days later to reinforce Grant. The Union also controlled the lower Cumberland River and all of the Tennesse River, had cut the railroad to the south, and had split the two main Confederate forces in the area. The strategic, numerical and logistical situation overwhelmingly favored the Union. Grant knew that, and so did the Confederate commanders, who debated the merits of even trying to defend the fort before deciding they couldn't let the Union capture Nashville that easily.
If you want a poker analogy, look at is this way: the purpose of advancing on Fort Donelson was to protect the Union's stronger hand and not let the Confederates draw out with a weaker holding.
There are many examples in military history of going into battle with the weaker hand and winning. This just doesn't happen to be one of them.
Update: In fairness to Amy, calling the place "Fort Donaldson" was a common error in reports of the time. It might be spelled that way in Grant's memoirs, too - I don't have a copy hand to check. But the proper name is nevertheless Fort Donelson.
Windows 7
Ever since I started working with computers around 1970 or so, first as a tech support elf and later as a programmer and systems analyst, my philosophy about upgrades and new releases has been to let some other sucker find the bugs.
That's especially true with operating system upgrades. If you upgrade, say, a word processor and it doesn't work, you can use a different program or go back to the older version. And the bad program is extremely unlikely to affect the other functionality of your system.
But if you install an operating system upgrade and it doesn't work, nothing works, and going back to the old version is usually a complete reinstall that could take hours if not days. That's assuming you have proper backups, which almost no one does.
So with Windows 7, I'm going to let the large institutional users with professional IT support departments (and, often, a direct line to Microsoft) test-drive it first. There's no reason for the great majority of home users and small busineses to rush into it.
That's especially true with operating system upgrades. If you upgrade, say, a word processor and it doesn't work, you can use a different program or go back to the older version. And the bad program is extremely unlikely to affect the other functionality of your system.
But if you install an operating system upgrade and it doesn't work, nothing works, and going back to the old version is usually a complete reinstall that could take hours if not days. That's assuming you have proper backups, which almost no one does.
So with Windows 7, I'm going to let the large institutional users with professional IT support departments (and, often, a direct line to Microsoft) test-drive it first. There's no reason for the great majority of home users and small busineses to rush into it.
Thursday, October 08, 2009
Zzzzzzzzz.......
At this rate, I won't live long enough to know the outcome.
One problem is the multitabling. There comes a point, especially in heads-up play, where much of the wait time is not thinking time, but thinking-at-another-table time. This is obvious when you watch these guys play. It would be hard to model without actually trying it, but I suspect they would get nearly as many hands in if they played just two tables rather than four. More importantly, they wouldn't get so tired so quickly and could play longer sessions. I don't care how sharp and fit you are, four-tabling high-stakes PLO is going to quickly turn your brain into a raisin. Hence, the mostly short sessions.
Of course, the other problem is that this has obviously become a 0 EV proposition for both players. There are golden sheep to fleece in the regular ring games, and both of these players are passing up much bigger +EV opportunities any time they sit down to resume the Challenge. Furthermore, when this first started, Dwan wasn't all that well-known. Now his name and face are all over the place, the endorsement deals and appearance fees are pouring in, and despite never having won anything important, not even his own Challenge, he has actually convinced a lot of not-real-bright people that he deserves to be nominated at the age of 23 to the Poker Hall of Fame. So the main objective of the Challenge - to get Durrrr some publicity without having to prove he can beat someone not name Laliberte - has been accomplished, and at this point the only reason to continue is so people won't think he's a quitter. Arguably, it's in his best interest to drag this out as long as possible, until he gets all the contracts inked, in case he winds up losing.
One problem is the multitabling. There comes a point, especially in heads-up play, where much of the wait time is not thinking time, but thinking-at-another-table time. This is obvious when you watch these guys play. It would be hard to model without actually trying it, but I suspect they would get nearly as many hands in if they played just two tables rather than four. More importantly, they wouldn't get so tired so quickly and could play longer sessions. I don't care how sharp and fit you are, four-tabling high-stakes PLO is going to quickly turn your brain into a raisin. Hence, the mostly short sessions.
Of course, the other problem is that this has obviously become a 0 EV proposition for both players. There are golden sheep to fleece in the regular ring games, and both of these players are passing up much bigger +EV opportunities any time they sit down to resume the Challenge. Furthermore, when this first started, Dwan wasn't all that well-known. Now his name and face are all over the place, the endorsement deals and appearance fees are pouring in, and despite never having won anything important, not even his own Challenge, he has actually convinced a lot of not-real-bright people that he deserves to be nominated at the age of 23 to the Poker Hall of Fame. So the main objective of the Challenge - to get Durrrr some publicity without having to prove he can beat someone not name Laliberte - has been accomplished, and at this point the only reason to continue is so people won't think he's a quitter. Arguably, it's in his best interest to drag this out as long as possible, until he gets all the contracts inked, in case he winds up losing.
Labels:
heads up play,
PLO,
poker celebrities,
Pot Limit Omaha
PLO: Benyamine Finds Five Extra Outs
I was railbirding a 200/400 game on Full Tilt last night when David Benyamine, in the big blind, got it all in on the flop here:
Benyamine: Jd 9c 5s 4d
Flop: 8d 5d 2h
Benyamine's opponent (the small blind) bet the flop, and both players kept raising until the money was all in. His opponent had Ks 8h 7s 5h and his two pair held up.
There was some chirping from the railbirds about Benyamine giving his money away, but as the cards stood, he was a 436:384 (53:47) equity favorite. He has the only flush draw, his two overcards give him five clean outs for a bigger two pair (the 9d gives him a flush), and he has some backdoor straight potential.
Yes, in the bizarro world of PLO, top two pair can be an underdog to second button with no nut draws.
Against a big overpair - say Ks Kh 7s 5h - Benyamine is in even better shape, with 477 wins and 343 losses (58:42). This is why big pairs are kind of crappy unless you flop a set or a decent draw to go with them.
The hands that hurt him the worst are those containing a bigger diamond draw or a set. Against Kd 8h 7d 5h, Benyamine is a 664:156 (81:19) dog. But heads-up, there's only about an 11% chance that an opponent playing a random hand would hold bigger diamonds. That percentage goes up somewhat if you assume your opponent is not playing random hands and/or is not automatically c-betting, but it's still unlikely that Benyamine's opponent had bigger diamonds. Similar math and logic applies to the likelihood of his opponent having a set.
So all in all, it wasn't a terrible play. I wouldn't have done it because risking $40K to protect $800 in pot equity on a coin flip just isn't my style. I think maybe Benyamine thought he could push his opponent off the pot with a raise on the flop, because the guy had min-raised preflop and had been playing fairly tight, but once he got three-bet there was so much money in the pot that Benyamine had no choice but to push the rest in. Even so, I think he's better off, with the money as deep as it was and the non-trivial possibility that he's in bad shape to a set or a bigger flush draw, just calling on the flop and seeing what happens. He does have position, and if his opponent was c-betting with little or nothing, Benyamine will likely pick up the pot with a bet on the turn anyway, and still have some outs if he gets called.
The main point I want to make here, however, is how much value those two live overcards added to Benyamine's hand. Five outs twice was enough to push the hand from equity dog to equity favorite. I think Benyamine is a good enough player to know those outs were probably live, and his play was based at least partly on that knowledge.
Simulations run here.
Benyamine: Jd 9c 5s 4d
Flop: 8d 5d 2h
Benyamine's opponent (the small blind) bet the flop, and both players kept raising until the money was all in. His opponent had Ks 8h 7s 5h and his two pair held up.
There was some chirping from the railbirds about Benyamine giving his money away, but as the cards stood, he was a 436:384 (53:47) equity favorite. He has the only flush draw, his two overcards give him five clean outs for a bigger two pair (the 9d gives him a flush), and he has some backdoor straight potential.
Yes, in the bizarro world of PLO, top two pair can be an underdog to second button with no nut draws.
Against a big overpair - say Ks Kh 7s 5h - Benyamine is in even better shape, with 477 wins and 343 losses (58:42). This is why big pairs are kind of crappy unless you flop a set or a decent draw to go with them.
The hands that hurt him the worst are those containing a bigger diamond draw or a set. Against Kd 8h 7d 5h, Benyamine is a 664:156 (81:19) dog. But heads-up, there's only about an 11% chance that an opponent playing a random hand would hold bigger diamonds. That percentage goes up somewhat if you assume your opponent is not playing random hands and/or is not automatically c-betting, but it's still unlikely that Benyamine's opponent had bigger diamonds. Similar math and logic applies to the likelihood of his opponent having a set.
So all in all, it wasn't a terrible play. I wouldn't have done it because risking $40K to protect $800 in pot equity on a coin flip just isn't my style. I think maybe Benyamine thought he could push his opponent off the pot with a raise on the flop, because the guy had min-raised preflop and had been playing fairly tight, but once he got three-bet there was so much money in the pot that Benyamine had no choice but to push the rest in. Even so, I think he's better off, with the money as deep as it was and the non-trivial possibility that he's in bad shape to a set or a bigger flush draw, just calling on the flop and seeing what happens. He does have position, and if his opponent was c-betting with little or nothing, Benyamine will likely pick up the pot with a bet on the turn anyway, and still have some outs if he gets called.
The main point I want to make here, however, is how much value those two live overcards added to Benyamine's hand. Five outs twice was enough to push the hand from equity dog to equity favorite. I think Benyamine is a good enough player to know those outs were probably live, and his play was based at least partly on that knowledge.
Simulations run here.
Thursday, September 24, 2009
The Two-in-a-Row Problem Rears Its Ugly Ahead Again
The exact same set of numbers were drawn twice in a row in the Bulgarian lottery this month. This has generated a number of newspaper articles and blog threads about the probability of this happening, and as usual, the discussion is a whole lot of stupid.
The exact same thing comes up when people talk about the probability of being dealt aces two hands in a row in Hold'em. Someone will say it's 1/221, and someone else will say it's 1/48,841. But unless we specify the total number of hands dealt in that same sequence, these numbers are meaningless.
If you play exactly two hands of Hold'em, the probability that both will be aces is 1/48,841. But if you play 200 hands, the probability of getting aces at least two hands in a row at least once is about 60%. If you play 2,000 hands, it approaches 100%.
Given the large number of state-run lotteries around the world, how long these have been in existence, and how often the drawings take place, it's just not that big a longshot that sooner or later the same numbers would come up two drawings in a row in the same lottery somewhere in the world. But that doesn't stop the "experts" from stating odds based on the assumption that these were the only two lotto drawings in the whole history of the human race.
Another problem here is that mathematical probability is only a theoretical model, and one which assumes complete randomness. In the real world, a bunch of ping pong balls getting bounced and banged all over the place inside a bingo blower are not going to have precisely equal chances of being selected. This is why the better-run lottos and kenos frequently change blowers and ball sets, typically using some other method to randomly select which blower and which ball set will be used for a particular drawing. They can't make the results purely random, but they can make them impossible to predict, which is really all that matters.
The point being that the particular numbers that came up in the Bulgarian lottery might in fact have had a somewhat better chance of being selected than the pure mathematical probability would suggest, because in the real world, ping pong balls get scratched and scuffed in bingo blowers.
Or it could have been rigged, but I find that unlikely. If you have the capability of rigging the outcome, the last thing you want to do is make it look anything other than random. Cheats are often very stupid and/or convinced that they are way smarter and cleverer than anyone else, but I think in this case even the stupidest and most egotistical cheat would pick some numbers other than those guaranteed to raise eyebrows. If it was a non-random result, the most likely explanation is something wrong with the ball set and/or blower.
The exact same thing comes up when people talk about the probability of being dealt aces two hands in a row in Hold'em. Someone will say it's 1/221, and someone else will say it's 1/48,841. But unless we specify the total number of hands dealt in that same sequence, these numbers are meaningless.
If you play exactly two hands of Hold'em, the probability that both will be aces is 1/48,841. But if you play 200 hands, the probability of getting aces at least two hands in a row at least once is about 60%. If you play 2,000 hands, it approaches 100%.
Given the large number of state-run lotteries around the world, how long these have been in existence, and how often the drawings take place, it's just not that big a longshot that sooner or later the same numbers would come up two drawings in a row in the same lottery somewhere in the world. But that doesn't stop the "experts" from stating odds based on the assumption that these were the only two lotto drawings in the whole history of the human race.
Another problem here is that mathematical probability is only a theoretical model, and one which assumes complete randomness. In the real world, a bunch of ping pong balls getting bounced and banged all over the place inside a bingo blower are not going to have precisely equal chances of being selected. This is why the better-run lottos and kenos frequently change blowers and ball sets, typically using some other method to randomly select which blower and which ball set will be used for a particular drawing. They can't make the results purely random, but they can make them impossible to predict, which is really all that matters.
The point being that the particular numbers that came up in the Bulgarian lottery might in fact have had a somewhat better chance of being selected than the pure mathematical probability would suggest, because in the real world, ping pong balls get scratched and scuffed in bingo blowers.
Or it could have been rigged, but I find that unlikely. If you have the capability of rigging the outcome, the last thing you want to do is make it look anything other than random. Cheats are often very stupid and/or convinced that they are way smarter and cleverer than anyone else, but I think in this case even the stupidest and most egotistical cheat would pick some numbers other than those guaranteed to raise eyebrows. If it was a non-random result, the most likely explanation is something wrong with the ball set and/or blower.
Thursday, September 17, 2009
One of the Great Riddles of Our Time...
...is how seriously David Caruso takes himself.
I figure the only way anyone can put on a performance like this week in and week out is either (a) he knows it's campy and the fans love it and it's putting money in his pocket, so he plays it up; or (b) he's completely oblivious to just how bad he is and truly believes he is a Serious Actor.
I figure the only way anyone can put on a performance like this week in and week out is either (a) he knows it's campy and the fans love it and it's putting money in his pocket, so he plays it up; or (b) he's completely oblivious to just how bad he is and truly believes he is a Serious Actor.
Playing for EV vs Playing for the Pot
This hand from a $25 five-handed PLO game is an example of a situation where you should be asking yourself, "Do I have positive EV?" rather than, "How can I win this pot?"
Stacks:
Small Blind = $15.45
UTG = $29.30
Button (moi) = $28.10
Preflop:
UTG raises to $0.85, I call on the button with Qh Jh 9d 7d, SB reraises to $3.65, BB folds, UTG calls, I call.
Flop: Qc 9s 3h
SB bets $10.65, UTG calls, I raise to $24.45 all-in, both call.
Aside - I know a lot of people would three-bet my hand here before the flop, because I have a double-suited rundown on the button and the raiser is a bit of a nutcase, but the play in these games is so horrible postflop, and the rake is so brutal (basically 5% to infinity) that I think you're better off seeing the flop cheap and hoping to pick up a bigger edge in the postflop play, especially when you're up against another fairly big stack. 85 cents from a $28 stack is a trivial investment, whereas getting it all in preflop with a hand like mine often means you're taking the worst of it, and are usually generating a lot of variance but only a little profit when you have the best of it. In a high-stakes game where the rake is trivial and/or there's an ante and the money is often much deeper and the players tend to play better postflop (e.g., the deep-stack $25/$50 games on FullTilt), the case for three-betting three-flop is much stronger.
Once SB three-bets the pot out of position, I'm definitely just calling, as he for certain has AAxx (he was that type of player).
Anyway, on to the flop, which is the where the money got all in. I was pretty sure from my experience with these two opponents that I had the best hand on the flop. I just knew SB had AAxx and I was pretty sure UTG had something like KJTx. UTG was the sort of player who would have raised all-in with top two or any set here. But I don't have much in the redraw department, so I guessed my equity to be around 40-45%. That's more than one-third of the pot, so against three opponents I'm making money. And heads-up against UTG for the side pot, I figured I was probably around 55-60%, which is more than half the pot, so again I'm making money.
The point I want to make is that even though I have positive EV in the main pot, I will lose the pot more often than I win it. This is why you often have to think about whether you have positive EV rather than worrying about whether you're going to win or lose the pot. You're leaving a lot of profit on the table in situations like this if you don't get your money in.
Was I right? I turns out SB was a little better than I thought - As Ah Kh Th - and UTG was quite a bit worse - Kc Jc 7c 5d. In the main pot, however, I had 44.29% pot equity (vs 33.78% and 21.92% respectively), and in the side pot I had a whopping 87.50%. UTG (of course) backdoored a 7 and K to beat me, but over the long haul I'm going to come out way ahead.
Stacks:
Small Blind = $15.45
UTG = $29.30
Button (moi) = $28.10
Preflop:
UTG raises to $0.85, I call on the button with Qh Jh 9d 7d, SB reraises to $3.65, BB folds, UTG calls, I call.
Flop: Qc 9s 3h
SB bets $10.65, UTG calls, I raise to $24.45 all-in, both call.
Aside - I know a lot of people would three-bet my hand here before the flop, because I have a double-suited rundown on the button and the raiser is a bit of a nutcase, but the play in these games is so horrible postflop, and the rake is so brutal (basically 5% to infinity) that I think you're better off seeing the flop cheap and hoping to pick up a bigger edge in the postflop play, especially when you're up against another fairly big stack. 85 cents from a $28 stack is a trivial investment, whereas getting it all in preflop with a hand like mine often means you're taking the worst of it, and are usually generating a lot of variance but only a little profit when you have the best of it. In a high-stakes game where the rake is trivial and/or there's an ante and the money is often much deeper and the players tend to play better postflop (e.g., the deep-stack $25/$50 games on FullTilt), the case for three-betting three-flop is much stronger.
Once SB three-bets the pot out of position, I'm definitely just calling, as he for certain has AAxx (he was that type of player).
Anyway, on to the flop, which is the where the money got all in. I was pretty sure from my experience with these two opponents that I had the best hand on the flop. I just knew SB had AAxx and I was pretty sure UTG had something like KJTx. UTG was the sort of player who would have raised all-in with top two or any set here. But I don't have much in the redraw department, so I guessed my equity to be around 40-45%. That's more than one-third of the pot, so against three opponents I'm making money. And heads-up against UTG for the side pot, I figured I was probably around 55-60%, which is more than half the pot, so again I'm making money.
The point I want to make is that even though I have positive EV in the main pot, I will lose the pot more often than I win it. This is why you often have to think about whether you have positive EV rather than worrying about whether you're going to win or lose the pot. You're leaving a lot of profit on the table in situations like this if you don't get your money in.
Was I right? I turns out SB was a little better than I thought - As Ah Kh Th - and UTG was quite a bit worse - Kc Jc 7c 5d. In the main pot, however, I had 44.29% pot equity (vs 33.78% and 21.92% respectively), and in the side pot I had a whopping 87.50%. UTG (of course) backdoored a 7 and K to beat me, but over the long haul I'm going to come out way ahead.
Monday, August 31, 2009
Don't Play Results
Let's play a coin-toss game. You get up to three tosses, depending on how the previous tosses turn out. Here are the scenarios allowed by the rules (I know they're a little complicated, but bear with me).
Winning scenarios:
W1: Win the first toss.
W2: Lose the first toss, win the second toss, win the third toss.
W3: Skip the first toss, win the second toss.
Losing scenarios:
L1: Lose the first toss, lose the second toss.
L2. Lose the first toss, win the second loss, lose the third toss.
L3: Skip the first toss, lose the second toss.
Assuming it's a 50:50 coin, should you take the first toss or skip it?
The answer, of course, can be determined mathematically. The probabilities of the various winning outcomes are:
W1: 1/2 = 50%
W2: 1/2 * 1/2 * 1/2 = 1/8 = 12.5%
W3: 1/2 = 50%
Skipping the first toss (W3) gives you a 50% chance of winning. But taking the first toss gives you two ways to win - either W1 or W2 - for a total 62.5% chance. So you you should take the first toss.
Now let's fiddle with the probabilities. Let's say the chance of winning the second toss is 90%. Does this change the strategy? Well, do the math:
W1: still 50%
W2: 50% * 90% * 50% = 22.5%
W3: 90%
Now it's better to skip the first toss.
Finally, let's suppose the chance of winning the first toss is about 70%, and the second toss about 90%. One more time...
W1: 70%
W2: 30% * 90% * 50% = 13.5%
W3: 90%
You're still better off skipping the first toss entirely, even though the chances of winning it have gone up.
Note that when you increase the probability of W1, you decrease the probability of W2, albeit at a slower rate.
I'm bringing this up because there has been a bit of controversy surrounding Sunday's Tampa Bay - Detroit game. The Rays were ahead by 2 runs at the bottom of the ninth. The Tigers had one man on base and two outs. The Rays pitcher, Grant Balfour, claims he was ordered to "pitch around" the next Tigers batter, Granderson. As a result, Granderson walked, putting two men on base. Balfour then gave up a three-run home run to the next Detroit batter, Polanco, who up that point had been 0-18 in the three-game series. Balfour thinks he shoudl have been allowed to challenge Granderson.
The coin toss game is a simplified version of various possible outcomes of the game. It doesn't begin to cover all the possible winning/losing scenarios. However, even in this simplified form, you get some idea of the math.
The key here is that Polanco had been hitting so badly against the Rays (0-18) that the chances of getting Granderson out would have had to been much higher than they probably were. Of course, this isn't allowing for the objectively verifiable fact that MLB relief pitchers are headcases. One problem with applying stats to baseball is that the psyches of a lot of players are pretty fragile. In a situation like the ones the Rays were facing, you have to consider whether your pitcher will keep his shit together with two men on base and the winning run at the plate.
In any case, I'm not trying to second-guess Joe Maddon here, just pointing out that withotu considering other hard-to-quantify factors, the math appears to support pitching around Granderson.
Winning scenarios:
W1: Win the first toss.
W2: Lose the first toss, win the second toss, win the third toss.
W3: Skip the first toss, win the second toss.
Losing scenarios:
L1: Lose the first toss, lose the second toss.
L2. Lose the first toss, win the second loss, lose the third toss.
L3: Skip the first toss, lose the second toss.
Assuming it's a 50:50 coin, should you take the first toss or skip it?
The answer, of course, can be determined mathematically. The probabilities of the various winning outcomes are:
W1: 1/2 = 50%
W2: 1/2 * 1/2 * 1/2 = 1/8 = 12.5%
W3: 1/2 = 50%
Skipping the first toss (W3) gives you a 50% chance of winning. But taking the first toss gives you two ways to win - either W1 or W2 - for a total 62.5% chance. So you you should take the first toss.
Now let's fiddle with the probabilities. Let's say the chance of winning the second toss is 90%. Does this change the strategy? Well, do the math:
W1: still 50%
W2: 50% * 90% * 50% = 22.5%
W3: 90%
Now it's better to skip the first toss.
Finally, let's suppose the chance of winning the first toss is about 70%, and the second toss about 90%. One more time...
W1: 70%
W2: 30% * 90% * 50% = 13.5%
W3: 90%
You're still better off skipping the first toss entirely, even though the chances of winning it have gone up.
Note that when you increase the probability of W1, you decrease the probability of W2, albeit at a slower rate.
I'm bringing this up because there has been a bit of controversy surrounding Sunday's Tampa Bay - Detroit game. The Rays were ahead by 2 runs at the bottom of the ninth. The Tigers had one man on base and two outs. The Rays pitcher, Grant Balfour, claims he was ordered to "pitch around" the next Tigers batter, Granderson. As a result, Granderson walked, putting two men on base. Balfour then gave up a three-run home run to the next Detroit batter, Polanco, who up that point had been 0-18 in the three-game series. Balfour thinks he shoudl have been allowed to challenge Granderson.
The coin toss game is a simplified version of various possible outcomes of the game. It doesn't begin to cover all the possible winning/losing scenarios. However, even in this simplified form, you get some idea of the math.
The key here is that Polanco had been hitting so badly against the Rays (0-18) that the chances of getting Granderson out would have had to been much higher than they probably were. Of course, this isn't allowing for the objectively verifiable fact that MLB relief pitchers are headcases. One problem with applying stats to baseball is that the psyches of a lot of players are pretty fragile. In a situation like the ones the Rays were facing, you have to consider whether your pitcher will keep his shit together with two men on base and the winning run at the plate.
In any case, I'm not trying to second-guess Joe Maddon here, just pointing out that withotu considering other hard-to-quantify factors, the math appears to support pitching around Granderson.
Tuesday, July 14, 2009
It's Not About Poker
Police raided a euchre game last summer in Ohio. The trial starts this week.
The right to play poker, or euchre, or any other game for money, is a civil liberties issue. It's not about whether poker is a game of skill. Unfortunately, the PPA emphasis has been to argue for some right of poker to be played, as if a game had rights, rather than for your right to be free of unwarranted government intrusion in your personal finances and activities.
(h/t John Cole)
The right to play poker, or euchre, or any other game for money, is a civil liberties issue. It's not about whether poker is a game of skill. Unfortunately, the PPA emphasis has been to argue for some right of poker to be played, as if a game had rights, rather than for your right to be free of unwarranted government intrusion in your personal finances and activities.
(h/t John Cole)
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