Which Poker Tournament Table Offers a Higher Expected Return for the Player?

[ctcannon]

Two poker tournaments. One has 8 players heads up(one on one)(starts with 4 tables, then 2 then 1.) 1st place wins $104, 2nd $56, with $22 entry. Other tournament has 4 people(2 tables) and 1st wins $80 and costs $21.50 to enter. Given random order of wins and losses, which table has a higher expected return(given hundreds of games), with a single table win percentage of, for example, 85 out of 100(85%). How do you calculate this? At what win %(per single table) would the worst order of 4 player tournaments win/losses be more profitable than the best order of win/losses of 8 player tournaments(given many tournaments)?

Thanks to the smart person who solves this!

 

[Valkarie]

To calculate the expected return for a single table in either tournament, you would need to know the probability of winning each game. For example, if the player has a win rate of 85%, then the expected return for a single table would be (85% x $104) + (15% x $56) = $90.95. This calculation would be the same for the 4 player tournament: (85% x $80) + (15% x 0) = $68.To determine at what win percentage the worst order of 4 player tournaments would be more profitable than the best order of 8 player tournaments, you would need to use a mathematical formula to compare the expected returns of the two tournaments. The formula would be:Expected Return of 4 Player Tournament – Expected Return of 8 Player Tournament >= 0 This equation can be solved for the win percentage that results in a zero (or greater) difference between the expected returns of the two tournaments. It is important to note that the win percentage used in this calculation must take into account any entry fees for the tournaments. For example, if the entry fee for the 8 player tournament was $22 and the entry fee for the 4 player tournament was $21.50, then the win percentage for the 8 player tournament would be (104 - 22)/(104 + 56 - 22) = 0.868, and the win percentage for the 4 player tournament would be (80 - 21.50)/(80 - 21.50) = 0.892. Using these win percentages, the equation would be: 0.892 x 80 – 0.868 x 104 >= 0 Solving this equation yields a win percentage of 0.873 or higher for the 8 player tournament, which is higher than the win percentage used in the above example. Therefore, the worst order of wins and losses of 4 player tournaments would need to have a win percentage of 0.873 or higher for the 4 player tournaments to be more profitable than the best order of wins and losses of 8 player tournaments.