I apologize in advance for the somewhat complicated nature of this problem and the long run up before my question.
A little background:
I'm in a bowling league, and it's just a fun league between family and friends, so we have a smattering of good and bad bowlers. People mainly only show up to hang out and drink.
I run a mini poker game, played with two standard playing card decks, jokers removed. I use two decks because one just doesn't have enough cards. The rules are as follows:
1. One dollar buy in, per person, per game. Three games total to coincide with the games we bowl.
2. For every strike thrown, or for every split converted, you may draw a card.
3. Maximum of 5 cards, per person, per game.
4. Best hand, following standard poker hand rankings, at the end of the game wins the pot for that game.
Natrually, this favors the better bowlers because their chances of drawing 5 cards a game is higher. So, in the spirit of giving everyone a better shot at winning, we added another rule:
5. Any one with an average score of under 150 can draw a card after two consecutive spares. (Bowling 3 spares in a row would not give 2 cards.)
A few weeks ago, someone suggested that, to give the lower average bowlers a better chance of winning, we use Pinochle decks instead of standard playing cards. A pinochle deck is different from a standard deck. Instead of having 2 through Ace of every suit and 52 cards total, a pinochle deck has 9 through Ace of every suit twice
, and 48 cards total. The idea was that, by using these cards, people who pulled fewer cards would have a better shot at having a decent poker hand because the card values are more concentrated.
What I want to know, if there is a black and white solution, is does switching to a Pinochle deck favor the lower average bowler?
We tried it out last week, and the top bowler in the league won the pot two of the three games. Now, I know I can't really make assumptions on such a small sample, but the more I think about it, the more it seems to me that it actually favors those who are drawing more
cards, not less as was the intention. I guess it's entirely possible that the chances for everyone are the same as with a standard deck, too. I just want to make sure I'm not changing something and having it do the opposite of what was intended.