Problem to Solve, with Proof
If Player A receives 4 cards and Player B receives 3 cards plus a Bonus 4th Cards, and standard poker card values obtain,
a) how often does Player B win his hand against Player A using just his 3 cards?
b) how often does Player B win using 4 cards?
Assume Player B wagers 1 credit on each hand he plays.
Assume further Player B will be paid differently for 3 card and 4 card wins.
For example, Player B is paid 1:2 for a 4 card win and 3:2 for a 3 card win Or 2:1 (latter being more difficult).
Ties push / hand is re played. Player A and B win equal number of hands overall.
c) In the above, what is Player A’s outcome / result in terms of credits paid?
For example, does Player A have a 5.0% credit advantage if he pays 3:2 for any 3 card Win? Does Player A have a 4% advantage if he pays 2:1 for any 3 card Win?
d) If Player A pays 1:2 for any 4 card Win, how much can he pay for any 3 card Win and still retain a 5% or more advantage?
Further work will ensue following solution per the above.
This work above is $150.00, follow on work will pay $100.00 for related questions, assuming there are same.
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