Implied odds of the bad beat jackpot

At my local poker room there's a bad beat jackpot. A certain amount is taken from the hand [I don't know how much it is] and this funds the jackpot.

In the short time I've been playing the bad beat jackpot (BBJ) is usually around $10,000 - $20,000. One time it got up over $60,000. When it's high the poker room is busier.

The jackpot is awarded when quads or better beats Aces full of tens or better. The rule is also that both players have to use both of their cards to form the winning and losing hand. The payout is losing player gets half the BBJ, winning hand gets 25%. The remaining 25% is shared among other players at the table.

A hand came up one time where a player 3 bet on an early position raise and two callers. The big reraise ended up chasing everyone out and the player made over $20 on the hand. At the time the BBJ was around $60,000.

After the hand a regular in the poker room suggested to the player who 3bet that there may have been some consideration to slow playing, i.e. just overcalling with the premium hand. That would have ensured a multiway pot and possibly got others in. With a premium hand it had a better chance of cracking the BBJ.

So the regular's point was that the BBJ was so large that the implied odds of cracking the BBJ were enough to be possibly more worthwhile than the big 3bet which would most likely just win the hand preflop.

It's an interesting concept because in a way it violates the principle of table stakes; which all of modern poker is built on. Although it violates table stakes in a good way. You still can't lose or be forced to call more than the amount in front of you on any hand. So table stakes still holds on the downside. On the upside though it becomes possible to win money which is not on the table at the beginning of the hand.

Afterward I thought about it some more over the next few weeks. Then I realized that it should be possible to quantify the implied odds of the BBJ.

I wanted to determine the chance of being on the losing side of the BBJ. I quickly realized you would need to be dealt AA to have a measurable chance of being in a BBJ hand. Since you only need Aces full of tens then it's relatively not too unusual to form the losing side of the BBJ.

In this example Hero is holding Aces UTG in a 10 player game. I want to calculate the chance that this will be a BBJ hand.

I believe the most likely scenario is that Hero and another player holding a pocket pair flop a set. Then Hero goes on to make full house 10 or better. The other player hits the 1 outer to make quads. This doesn't account for other scenarios such as quads over quads or losing to a straight flush. However it should be at least an approximation.


Part one, chance to form the losing BBJ hand starting with Aces

In this case Hero flops a set and then makes a full house.

The chance then of being on the losing side of the BBJ is

(1 / 8.5) * (1 - ((40 / 47) * (36 / 46))) * (1 / 3) = 0.0130960802

So dealt Aces there's about a 1.3% chance of ending up with a hand that can be a losing BBJ hand.


Part Two, another player is dealt a pocket pair. Villain flops a set and makes quads

In this example Hero is dealt Aces UTG at a 10 player table. I used my preflop overpair equation that I derived in the past to determine the probability that someone else at the table has a lower pocket pair. The chance of an underpair to AA is the same as the chance of an overpair to 22. So using the overpair equation I determined there is a 39% chance someone has a pocket pair.

The chance then of someone at the table having a pair, flopping a set and making quads is then

0.396140781 * (1 / 8.5) * (1 - ((44 / 45) * (43 / 44))) = 0.00207132435

About 1 in 500.



So multiply part one and part two to determine the chance then that the BBJ will go on this hand. That comes out to.

0.0130960802 * 0.00207132435 = 2.71262298 × 10^-5

Which is 1 in 36,864.



So that's not very good. Even if you account for other ways for the BBJ to form such as straight flush or more than one opponent being dealt a pocket pair then the best you can hope for is probably around a 1 in 20,000 chance of being on the losing end of the BBJ when starting with Aces.


From there then we can determine the implied odds of the BBJ when dealt Aces preflop. Being a bit generous and setting it at 1 in 20,000.

If the BBJ is $60,000 then the implied odds of the BBJ is about $1.50.

If the BBJ is $100,000 then the implied odds of the BBJ is around $2.50.


So we have determined that the BBJ must be extremely large in order to create enough implied odds to alter your preflop strategy to slow play instead of 3 bet. It would have to be around $400,000 - $500,000 + to even come into your thoughts.

Of course people at the table who have already folded or were going to fold anyway would prefer you slow play Aces against a preflop raise. They want to freeroll for a slice of the 25% of the BBJ that goes to the others at the table.

Offered chop in the SB

This is an interesting situation that sometimes comes up playing live. It's folded to you in the small blind. Neither you nor the big blind has looked at your cards yet. The big blind offers to chop the hand.

Now in $1/$2 live it doesn't often fold into the blinds. But it can happen sometimes, especially if some people are sitting out and away from the table. What a chop means is that the SB and BB both just pull their blinds back and the hand is over.

I've been offered a chop three times in the SB. All three times I accepted it. I think it's a good deal for the SB. Both the SB and BB have a random hand (since neither has looked at his cards yet). Given that BB has position on SB throughout the hand then with position the situation is profitable for BB and unprofitable for SB. So I think it's a good result for SB to accept a chop and thus break even on the hand.

Plus there's other considerations live around accepting a chop. The first time I was offered a chop in the SB the others at the table were keen for me to accept it. That makes sense because then the hand is immediately over and the folders can get a new hand right away without having to wait for a blinds battle to play out. So it keeps the game friendly and fast. Keeping the game fast and friendly is valuable so there's a meta game consideration to accepting the chop and quickly moving on to the next hand.

No limit hold'em theory and practice

As part of my transition to playing live I wanted to read a no limit book. I ordered No limit hold'em theory and practice online. I'd heard good things about this title. Coming from Sklansky and Miller I was looking forward to some good material.

And it was good. Like Sklansky's Theory of Poker, it was not an easy read. Some parts were hard to get through. But it was worth the effort. I feel I got a lot out of it. I didn't really fully grasp and appreciate everything but that's OK. Like Theory of Poker I likely will read it again in the future. But like the authors said, after reading the book go play some hands, and then come back and read the book again. So now I'm off to play some hands.

The structure of the book was interesting. They spent a fair amount of time discussing the differences between limit hold'em and no limit. To some that might seem unimportant but it was great for me as I have predominantly played limit up until now. So that was great.

Also I didn't really realize this until I played at the casino, but this book is geared toward live play. That's fine too since I'm now a live player. So all in all this was a very good book and well worth the time and effort to work through it.

I will probably read it again some time in the future. But not too soon. I need to do some light reading next to give my mind a rest. Plus I want to read at least one different poker book first. There's still about four poker books that I want to read at some point.

Stars reload

I recently took advantage of the PokerStars WCOOP 50% reload bonus offer. I chucked in another $100. This is the first time I put money in at Stars since I first started playing for real money around 3 years ago on about a $90 deposit.

A great thing about Canada is that it is so easy to get bankroll onto the sites. I just entered my regular credit card number in and swoosh it went right through no problem. Same as last year when I put in $50 on UltimateBet. Yay Canada.

I've been playing more cash on Stars anyway so I figure I might as well get paid to play by working off a bonus. In fact I was thinking of putting some new money in on Stars anyway to bankroll some new games I want to try. This just does it a bit sooner but this bonus offer is timely. I hope Stars continues to do these from time to time.

At $10 NL it doesn't seem to be clearing very fast but that's OK. I may have a plan in mind to do something about that.

Played live at the casino

I played live poker for the first time last weekend. It was a great experience! It was at the Halifax Casino.

I had wanted to play for a long time and I finally saved up enough bankroll to play $1/$2 no limit hold'em. That's the smallest game available. I didn't know what to expect or really know what to do.

Anyway I sat down and got chips. I decided that I was going to play full. So I bought in for $200. There were a mixture of players, people bought in for $40 (the minumum), $60, $100 and $200 mostly. It was a pretty friendly game. There were a number of regulars there I could tell who knew each other well.

Due to my inexperience I made some mistakes mostly about not posting my blinds quickly or knowing when it was my turn. I was directly to the dealer's left so it was at times hard to tell when the big blind or the action was on me. Also I found the table felt kind of sticky and it was hard to lift my cards to see them at times.

Mostly I didn't have much to work with. So I just folded if I had a bad hand. One guy was sitting to my left and he was bugging me about folding preflop. He seemed to like being in almost every hand. He went to a new table after a short while.

There were some interesting hands along the way. One hand in the first hour I raised in early position to $8. A guy who seemed to be good 3bet me to $28. Everyone folded. I thought for a bit and decided to fold. He showed KK so I made a good fold.

Around a half hour later on I again raised to $8 first to act. Again the same KK guy 3bets me, this time to $25. This time I moved all in for $200. He thought for a little while and then folded. I didn't show. He brought that hand up with me a couple of times in the next two hours. I didn't tell him what I had but I agreed with his reasoning that when a guy shoves $200 preflop it is almost always very strong, like QQ-AA, maybe AKs. He said later on he had 99. We agreed it was a good fold to the shove.

I think that was the second hand I won. For my memory this is the first hand I won live. I called in the SB with 9s 7s and 4 limpers. Six of us saw a T88 flop. It was surprisingly checked through. The turn was a J, giving me a straight but putting two clubs on board. I bet $8 into the $12 pot. One guy called and the others folded.

The river was an offsuit Jack making the board T88JJ. I checked and the other guy checked too. He showed K9 I believe and my straight was good.

There was an interesting hand late in the evening. I raised Ad Jd in early postition to $8. An aggressive player on the button 3bet me to $18. I called $10 and we saw the flop heads up. The flop was AK2 giving me top pair. He bet $25 into the $39 pot and I called. The turn was a 7. The turn went check check and now I'm feeling a bit better about my pair of Aces. The river was another deuce making the board AK272. I didn't think the river helped him much. I led $50 into the $89 pot. He pondered for what seemed like a good while and finally called. He showed K7 and my Aces up were good to win it on the river over his turned two pair.

Thanks to that late AJ hand I was able to book a small profit for the evening. I was enjoying it and stayed until 3 AM. It was an enjoyable experience (probably more enjoyable because I won a bit) and I'll be looking to play some more there when I get the chance.

MTT cash

I cashed in an UltimateBet tournament for the first time recently. I finished 15th out of around 250 in a $2.20 event for around a $6 payout. Since my UltimateBet bonus expired I've reorganized my online play a bit. I play cash on Stars and tournaments on UltimateBet. My cash game lately is mostly $10 NL.

I'm defining MTT a bit more strictly. I have had some multi table tournament success this year. I've won a couple $2.20/90 man tourneys on Stars. But those are strictly speaking SNGs. They have a cap on the number of entrants and they begin as soon as they fill.

There's nothing special or unusual about an MTT cash. When I checked my records though I saw that this was my first MTT cash in 2009. I had gone 13 in a row with no cashes back to last December. That's the nature of MTT though. On a site like official poker rankings you'll notice that for even the biggest winners they have long soul crushing strings of zeros punctuated by the occasional cash and the more occasional big cash. But it's good to be in the money again in 2009.

I find UltimateBet has a pretty good tournament structure. Especially in the early levels there's more opportunity to play tight and wait for good hands. Although in the later stages when the blinds are increasing in larger chunks the 12 minute levels are a bit tougher. The fields are smaller than some of the huge tourneys on Stars but that means there's more regulars who you can recognize over time and get notes on.