I play a poker-like game on a casino site, which offers dynamically changing coefficients for each hand on the table.
Each round (blind, preflop, flop, turn) gamblers can bet that one of each hands or combinations win. For example, I think that this game will be won by the hand number 2, and I put my stakes on that. The casino provides a coefficient for that stake (
3.5 for example), and in case the second hand actually wins, I get my stake times the coefficient of profit.
The same goes to combinations: you put bet that this type of combination will be the winning one. For example, when I bet on Two Pairs winning the game, I bet on ANY Two Pairs winning, but ONLY Two Pairs. If it just so happens that a Straight is on the table, I loose the bet.
So, the interesting part is: you can even bet blind. Which means that no information available: just gambling. BUT. The coefficients are off. Of course, casino takes a margin off of each bet, but some bets are more valuable that others. They offer such coefficients for the combinations:
High card wins: 100 Pair wins : 5.80 Two pairs win : 3.10 Set wins : 6.80 Straight wins : 5.70 Flush wins : 8.70 Fullhouse wins: 8.70 Quads win : 80 Straight flush: 100 Royal flush : 100
It's interesting to see, that seeing a high card on the river is comparable to seeing a royal flush. Of course, a child would know that you are better off betting on straight flush
100:1 than a royal flush with the same coefficients, but it would be interesting to see real calculations. I've been thinking about it, but nothing comes to mind, except bruteforcing every possible table of every possible 6-hand sets, but
C(52, 12) * C(40, 5) sounds too brutal.