So, I was sitting at a 2-5 game at Caesars with Alex on Friday. The Bad Beat Jackpot was around $118k and creeping up.
Yet, another statistical puzzle...
I limped in MP (Seat #9) with two black Q-Q, and the girl to my immediate left (Seat #10) limped in as well with unknown cards. To her left (seat #1), the aggressive Asian guy pops it to $30 (my plan worked… I'm gonna 3-bet smash this guy when it gets to me!!!). But, the next action, to his left, is a rock, in LP position, whose VPIP and PR %s are probably <>
The girl next to me is a regular at Caesars, and cried out… "This is why the bad-beat never happens at a 2-5 game!"***. I nudged her, and she showed me 7h-8h, suited mid-connectors. I smiled, thinking, what a crock, she's crying about 7h-8h? She's disgusted and mucked. The rest of the action is largely irrelevant --- I think it folded around preflop, and the rock took the smallish pot.
But, the questions lingered --- her statement contained an ounce of truth. In a 2-5 table, AA, KK, QQ will nearly always push out the other bad-beat elligble hands: baby pairs, suited 1 or 2 gappers, etc, thereby making it that much more difficult to hit the BBJ. What's the likelihood of hitting the BBJ in Holdem? What's the likelihood of having a table with at least 2 or more BBJ qualifying hands to start with? (eg. Pair vs Pair vs suited connector, Pair vs suited connector, etc.).
What if you play $2 / $4 Limit Holdem with a crew of 10 players, and everyone limps who have BB elligible hands, pocket pairs, and suited connectors to crack the BBJ. A-A will not raise the pot, and the crew will behave in ideal conditions. Check the flop, turn, and river, and only bet the river to fulfill the mandatory $20 pot requirement.
What are the odds? On average, under "checkdown" conditions, how many hands will it take for your crew to crack the $120k BBJ? And, how many hours / days?
So, I created a poker holdem simulator - one that randomly deals 10 hole cards, and runs a board (flop, turn, river), and determines if there's a "bad beat" b/n any two players.
On average, after a run of over 1/2 billion simulations:
>>> assuming the minimum requirements are any Quads
>>> 49% of the time - nearly half the time, the table has a BBJ elligble starting hand, preflop; at least 2 pocket pairs, or suited (1-2-3 gapper) connectors.
>>> if it goes all the way to the river, the BBJ will happen in 1 in about 200,000 hands.
>>> note, however, the cost of playing 200,000 hands even on the cheap side, requires you to pay the BB-drop, and occassionally a dealer tip on $7-$9 pots (SB + BB + limp + limp + maybe another limp)
>>> if your 10-person crew played 24 hours a day, at 50 hands an hour, it would take you about 166 days.
>>> the most common form is Quads vs Quads
But, what if your 10-person crew tried to crack the BBJ online, with the help of an auto-folder software? Running 16 tables each? At a rate of 80 hands per hour, it would take you only 7 days!!! Who wants in? Hahahaha. PartyPoker's BBJ is currently $167,916!!! That's $16k per person for 7 days of work…. Who wants in?
*** Note that the BBJ at the Borgata was hit at a 2-5 table, recently.
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