Game theory in High Stakes Poker

I came across a great hand on the TV show High Stakes Poker.

The hand is from Season 3, Episode 12, and it features poker professionals Phil Ivey and Brad Booth (yes, the same Brad Booth who used some psychology and game theory in Poker After Dark).

Some background on the hand: Booth had appeared on High Stakes Poker before. This time he bought in for a cool million dollars, hoping to intimidate opponents with a big stack. This is one of Phil Ivey’s first hands on High Stakes Poker and he bought in for about 300,000.

Here’s how the hand went down. Keep reading for my analysis.

Youtube video: High Stakes Poker Brad Booth vs Phil Ivey

The pre-flop betting

The hand started routinely with a raise to $1,800. Brad Booth then re-raised to $5,800 with his weak hand of 2-4 spades, perhaps in an attempt to steal the pot.

But it was not a good time to try because Phil Ivey woke up with pocket kings. Ivey played his hand strongly and re-raised to $14,000.

The action folded around the table to Booth. While contemplating the decision, Booth asked Ivey how many chips he had. He was likely trying to get a read on Ivey and also deciding if the hand was worth pursuing.

Upon hearing Ivey had $300,000, Booth made the call because he stood to win a lot of money with the right kind of flop (in other words, he figured he had good implied pot odds).

On the flop

The flop comes 3-7-6 with two diamonds, missing both Booth and Ivey.

With no ace on the board, Ivey figures his kings are the best hand and he bets out $23,000, about 2/3 of the pot. Ivey probably wants to win the hand right there. He certainly doesn’t want Booth to catch up with a flush or straight draw.

It would seem that Booth would fold here. The flop was not good for him, and he’s seen Ivey represent a strong hand–with a big pre-flop re-raise and a continuation bet on the flop.

And this is where the hand gets crazy. Booth, with only a four high, announces that he’s all-in! He really is putting Phil Ivey all-in. He lays down three cash bricks, each one hundred thousand dollars, right on the table.

Ivey is completely caught off-guard by the bet. His face at 2:15-2:19 is priceless. He’s thinking, what the heck does Booth have?

Ivey understandably takes some time to figure out whether to call. He’s probably mulling over what Booth might have. Here are a few possibilities:

–Three-of-a-kind of 3s, 6s, or 7s: It’s possible Booth raised pre-flop with a low pair like 3s, 6s, or 7s, and he got lucky enough to his a set. Against one of these hands Ivey is a huge underdog, with only about a 13 percent chance of winning.

–An ace high-flush draw: An aggressive player could have raised with ace-queen, ace-jack, or ace-ten suited diamonds on the flop. But this is not a very strong hand even with the favorable flop. Ivey’s kings would still be a favorite with over a 56 percent chance of winning, which would give him the right odds to call $250,000 for a pot of $300,000. Still a gutsy call but one that Ivey might make.

–A pair of aces: This is another hand that could worry Ivey. Booth was fearless in the pre-flop betting and could have represented a strong pair. He also raised big here to possibly price out draws if Ivey were chasing. Against aces Ivey would have just a 13 percent chance of winning.

–A pair of jacks or queens: Ivey might also be putting Booth on a strong pair like queens or jacks. Booth’s pre-flop betting would be consistent with these hands. Ivey would be a huge favorite–over 90 percent–to these hands. He’d be in great position to double up, and it’s tempting to call.

It’s pretty much impossible to put Booth on the hand he actually has. After all, he’s betting $300,000 on a 4 high to win a $55,000 pot. Sure, betting is the only way he can win the hand. But there’s no need to chase this hand. He can pick a better spot, with a better hand, to play a big pot.

In the end, Ivey releases his hand and folds. I read somewhere that he was putting putting Booth on pocket aces, a reasonable rationale.

It’s debated whether Booth was being smart or reckless, but the commentator seems to believe it was a great move. He says that Booth played the hand for two reasons: “One, he doesn’t think Phil Ivey can call him with a pair of queens, kings, or aces. And two, he is advertising. He is showing that he is totally unpredictable and he expects this $300,000 bet here to pay dividends in the future.”

What do you think: was Booth’s all-in bet genius or stupid?



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  • http://ww.franchise-info.ca michael webster

    My sense is that Ivey thought Booth had put him on for Jacks, Queens, or Kings. And Booth played like he could beat any of those pairs.

    It looked like a masterful job of intimidation. I don’t know what Ivey had lost with before, it might make a difference.

  • http://www.quantitativepeace.com Michael Allen

    I originally started to learn game theory by playing poker as some of the foundational books covered in a basic manner. When I first start taking formal theory, it was quite easy for me to pick up thanks to my poker background.

    Booth’s bet is a bit odd here. Traditionally, if he was representing a pocket pair that hit its set, he would play more cautiously and try to milk Ivey for more money. Obviously, Ivey knows this and it goes back to “I know that you know that I know..” so the overbet of a made set might seem like the feigned overbluff to disguise the set.

    Since this is highlevel poker, it is playing on multiple levels as opposed to the $500 NL tables. Either way, Booth was able to play accurately enough to send the right signal at the right level to Ivey.

    A better example of game theory is this matchup between Ivey and Paul (one of my favorite to watch/show): http://www.youtube.com/watch?v=–Qap3VT_ZY Paul makes the mistake of not committing to the bet and reserving and out in case his bluff gets called, this is clear to Ivey and he is able to win the pot in an amazing sequence of hands. If Paul had went all in earlier, Ivey could not have called:

  • http://gd0t.com geoff

    What abotu 4-5 for the straight, or 8-9 diamonds for the fatty draw?

    I like this hand, but I am not sure this article has much information?

  • http://ww.franchise-info.ca michael webster

    @Michael;

    I thought of that also – why didn’t Booth slow play if he really had aces.

    But look at the body language through out this clip.

    Ivey is beat from the beginning, pre-flop. Booth just looks like a predator slowly figuring out how much he can take Ivey for. (The flop turns up nothing to help anyone hold jacks, queens or kings.)

    Ivey knows that Booth has made his hand. And Booth probably did.

    As the commentators say – great signal no matter how the hand turns out. Too bady Ivey didn’t ask to Booth to turn over a card!

  • Julie

    I think both players made mistakes.

    Before the flop, Booth raised and was re-raised, and just called. This demonstrates that he has a hand, but it’s not that great, probably not a pair, and he’s hoping the flop will help him out. He’s being transparent.

    After the flop, Booth acted like he hit something big but if he did, why wouldn’t he just slow play it? He’d get more out of Ivey by slow playing than just going all in- since Ivey wouldn’t call such a huge bet. Once again- obvious he is overplaying a bad hand.

    I don’t know what was going on in Ivey’s mind. Pretty obvious that Booth was bluffing. Maybe he wanted to look weak so other players would throw their money at him later.

    I think Booth going first probably affected the game- Ivey had to respond to his bets instead of vice versa.

  • http://roguepolymath.wordpress.com Jay Johnson

    In my opinion, the most best thing about the bet was how it was made. He moved the cash in the middle instead of the chips, knowing the effect it would have on Ivy. A well calculated move.

  • http://ww.franchise-info.ca michael webster

    @Jay:

    That is interesting. Could you expand a bit more on that thought?

  • Daniel

    Lets take away the other possible motivation like the Ivey factor (bluffing Ivey on national T.V)for self promotion, and analyze this:

    In Booth’s position it is reasonable to put Ivey on any over pair J’s and higher.

    Booth bets 300,000 into 54,100 getting 1 to 5.5
    Booth needs Ivey to fold here more than 85% of the time to make this profitable.

    But 2s4s has about 20% equity against the over pairs.

    Lets use 10 to keeps numbers small

    Booth expects to win 2 out of 10 2×354,100=708,200
    Booth expects to lose 8 out of 10 8×300,000=2,400,000
    net loss per 10 =1,691,800
    folds needed to offset net loss =31 out of 10 or 76%

    Booth needs Ivey to fold here more than 76% to break even. or Ivey needs to call 24% of the time to stop Booth from crossing 0EV threshold.

    If Ivey puts him on that exact hand 2s4s it is a -EV fold but if Ivey puts him on 8d9d or a set is is a +EV fold

  • Daniel

    edit:

    Booth needs Ivey to fold more than 76% to make a profit (76% is break even point)

  • Daniel

    Now you could argue that he would not shove with a set or a made straight because he is missing value. So Ivey puts him either on open ended and flush draw or pair and straight draw.

    or maybe he would shove with above hands because he knows that Ivey knows… so he is polarizing his hand.

    at this level of poker there are many levels :-)

    I could go through the reasoning for all possible events but it would take some time and I will wait to see if this is appreciated first.

  • bigjeff

    It’s a classic problem:

    I know what he has, so I can take advantage of it.

    He knows that I know what he has, so he can take advantage of it.

    I know that he knows that I know what he has, so I can take advantage of it.

    And so on, and so on. Whoever is more aware of what the other person is thinking has the advantage.

    Since I can’t imagine Booth as being bad at poker (which he would almost have to be to make that kind of bet), he must have figured out that it was very likely Ivey had something like jacks, queens, kings, or aces. Booth’s pre-flop action could conceivably have been an odd attempt to hide a low set like 3′s, 6′s or 7′s, or an ace-high flush draw. Booth is known as being unpredictable, and it would be just like him to do something like that. The absolute last hand Ivey can put Booth on is low suited unconnected cards.

    I think Booth pegged Ivey with a high pair pre-flop, and after the abysmal flop and Ivey’s big bet was absolutely certain it was a very high pair, aces or kings. This gave Booth an opportunity to confuse the living daylights out of Ivey and steal the hand. Ivey has to fold, because you don’t last very long in poker if you call all-in when you are confused about the hand.

    Given the risk (300k) vs the reward (50k) Booth needs to win that hand seven times out of eight tries to make money on it, but I’d be willing to wager he looses a lot less often than one in eight when that situation arises. Of all the possibilities, the bluff is the least likely, and not many people are going to risk all their money (especially when it really is their own money!) on a hunch. Safer to give up the $25k you put in, even if you are absolutely sure he is lying, than to call him on it and be wrong.

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