The 2010 World Series of Poker $10,000 buy-in No Limit Hold’em Final begins with you and 9,999 other entrants. Odds for the top players are posted. Your inexperience makes you a 30,000 to 1 underdog prior to the start of play. You are knocked out during the first day’s play. At one point during your last hand, you were the biggest underdog to win the tournament in WSOP World Championship Finals history. What were the odds against you? Describe the hand and other relevant circumstances.
Solution
You are at a table with the eight players who are the top pre-tournament favorites. Your table has had no new players since the tournament started and will be one of the last tables broken.
• Your chip position — you are down to your last $25 chip at the start of the hand.
• The hands — you are dealt the 2 of clubs and 2 of spades and are all-in on the big blind.**
• Four of your opponents have 5/10 and fold.
• Another opponent folds a 4/3.
• Another opponent folds with the other two deuces.
• The button goes all-in with the A/K of hearts.
• The small blind calls with the A of clubs and the A of spades.
• Odds on winning the hand — You cannot win the pot, but can tie and get your $25 chip back if and only if the board ends up quads* plus the remaining ace. Before the flop, the odds against you are 1/34 x 24/33 x 3/32 x 2/31 x 1/30 plus 24/34 x 4/33 x 3/32 x 2/31 x 1/30 =1/46,376.
• Odds on winning the tournament — if you tie the hand you still have only $25 out of $200,000,000 in play in the tournament, or 1 /8,000,000 of the chips. Thus, your chances are 1/8,000,000 x 1/46,376 = 1/ 373,888,000,000, diminished by your inexperience, difficult table situation, and the fact you are the small blind the next hand. This makes you at least a 500 BILLION to one underdog.
Of course, this is the worst case.
* Quad 6s, 7s, 8s, 9s, Js, and Qs are possible.
** You could have any pair 2-4, 6-9, or J-Q. The small blind’s 2 aces must be in the same two suits as your two cards. The player who had 2/2 would instead have the same pair as you.
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Mike Eikenberry got his undergraduate and law degrees from the University of Virginia, where he played varsity basketball and tennis. Founder of a leading national tennis camp, Mike is an avid amateur poker player and casino gambler. He has played both tournaments and cash games for more than 30 years. Mike currently writes a column for Poker Player and his first book, The Great, the Bad and the Lucky, is currently in its second printing. He may be reached at theeiks@comcast.net.
