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Poker Game Probabilities Problem

The Prettiest ZombieCoeur d'CoeursRegistered User regular
edited December 2008
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.

Metacortex on

Posts

• Registered User regular
edited December 2008
Hm. That's a tough one. Are you allowing people with only three cards to have a hand? Best poker hand technically has to have five cards, but it sounds like you're sliding around that.

You're improving greatly the chances of getting pairs, two pairs, trips, full houses, and quads, lowering the chances of getting a straight, and leaving untouched the chances for a flush. You're reducing moderately the chances of one hand that requires five cards, but you're greatly increasing the chances of getting two others that require five cards. On the other hand, small hands have greatly increased chances of getting one of the few hands for which they actually qualify.

I think you're significantly increasing the chances of a small hand bearing some sort of fruit, but you're also moderately improving the chances of a large hand. In the end, however, no amount of card stacking is going to outweigh the enormous statistical advantage of drawing five cards instead of four.

MrMonroe on
• Registered User
edited December 2008
Texas Holdem

rfalias on
• Registered User regular
edited December 2008
Why would you really want to do that? We ran a similar poker game in our bowling league, and didn't even have the handicap additional rule. It's certainly a fun addition, and the still-learning bowlers would often buy in just because it's a diversion to think about the cards while you wait to bowl again. However, adding handicap after handicap might take some of the fun out of it for the better bowlers. Or is the goal to have something that might be a bit more rewarding for the still-learning bowlers to compensate?

Darkewolfe on
What is this I don't even.
• Registered User regular
edited December 2008
rfalias wrote: »
Texas Holdem

Hahaha! I was thinking about suggesting this. Just separate the bowling from the poker entirely and play a real gamblin' man's game.

MrMonroe on
• Registered User
edited December 2008
MrMonroe wrote: »
rfalias wrote: »
Texas Holdem

Hahaha! I was thinking about suggesting this. Just separate the bowling from the poker entirely and play a real gamblin' man's game.

I was also suggesting because it only needs 2 cards per person, but that works too.

rfalias on
• Registered User regular
edited December 2008
Now there's a thought. You could play multiple games. With every second card you earn, you get into another pot. Someone who earns two cards in a night plays in the first hand, and someone who earns six plays in three.

MrMonroe on
• Registered User regular
edited December 2008
MrMonroe wrote: »
Now there's a thought. You could play multiple games. With every second card you earn, you get into another pot. Someone who earns two cards in a night plays in the first hand, and someone who earns six plays in three.

Problem with that is that the pot would be split a great deal, which would then remove a lot of the sense of reward for having participated. (Even when we don't win, higher stakes are simply more exciting to have competed for. It's why people get more excited about a contest which gives away \$1 million than a contest in which 1 in 5 winners will get a dollar.)

Darkewolfe on
What is this I don't even.
• Registered User, ClubPA regular
edited December 2008
Switching up to Hold'em or another community card game really might not be a bad idea. It'd favor no one in that you wouldn't need a full hand to play, and still offer all players a chance to make the pot.

though at that point you may as well remove the bowling aspect and just run a side game, since I'm assuming near everyone would be able to draw two cards

Monoxide on
• Registered User regular
edited December 2008
If everyone's drawing from a the same deck, stacking the deck with high cards is not going to give any one class of players an advantage.

Edit: though it may make it more interesting, until you realize that your odds of winning haven't changed.

Djeet on
• Registered User
edited December 2008
Monoxide wrote: »
Switching up to Hold'em or another community card game really might not be a bad idea. It'd favor no one in that you wouldn't need a full hand to play, and still offer all players a chance to make the pot.

though at that point you may as well remove the bowling aspect and just run a side game, since I'm assuming near everyone would be able to draw two cards

Cigars and visors not included.

You could allow people to re-draw cards if they wanted. Advantage to good bowlers while less than good ones still have a shot. Cap re-draws or set criteria to re-draw, like a turkey or something. (Just an example)

rfalias on
• Registered User regular
edited December 2008
Djeet wrote: »
If everyone's drawing from a the same deck, stacking the deck with high cards is not going to give any one class of players an advantage.

Edit: though it may make it more interesting, until you realize that your odds of winning haven't changed.

This. I think you're increasing the chances that everyone will have a viable hand (since it's easier to get pairs) but it won't change the underlying idea that more cards in your hand = better chance for a winning hand.

tsmvengy on
• The Prettiest Zombie Coeur d'CoeursRegistered User regular
edited December 2008
Thanks for all the replies.

Hold'em actually sounds intriguing, but like you said the bowling wouldn't matter at all, really. Splitting pots would be another concern. I'll run it by a few people and see what they think.

When I said "I run a mini poker game," what I meant was that I just collect the money, shuffle the cards and pay the winners. The game was being played before I got into the league, so I'll generally leave the decisions up to the public.

It's a bit of a tough call with all this. I mean, the league is mainly made up of an extended family and friends of their family(I'm in this category), so everything is real friendly and it's not like \$3 for some card action is a heck of a lot. Most of the bowlers that join probably do it for the fun of drawing cards and the excitement of maybe getting a nice hand, more than for the money. Most of them could probably give two shits what kind of card game we play. When I tried telling some of them we were using Pinochle decks last week, they just shrugged. I think they're all just a bunch of degenerate gamblers.

I'd just like for everyone to have equal chances(though it's not really possible), but like you all said, you can't remove the inherent advantages of having more cards without trivializing the bowling aspect, and without that, there's no reason to run it all, really.

I mainly just wanted to make sure that Pinochle decks wouldn't favor the better bowlers, because they already have the upper hand.

Metacortex on
• Registered User
edited December 2008
Metacortex wrote: »
Thanks for all the replies.

Hold'em actually sounds intriguing, but like you said the bowling wouldn't matter at all, really. Splitting pots would be another concern. I'll run it by a few people and see what they think.

When I said "I run a mini poker game," what I meant was that I just collect the money, shuffle the cards and pay the winners. The game was being played before I got into the league, so I'll generally leave the decisions up to the public.

It's a bit of a tough call with all this. I mean, the league is mainly made up of an extended family and friends of their family(I'm in this category), so everything is real friendly and it's not like \$3 for some card action is a heck of a lot. Most of the bowlers that join probably do it for the fun of drawing cards and the excitement of maybe getting a nice hand, more than for the money. Most of them could probably give two shits what kind of card game we play. When I tried telling some of them we were using Pinochle decks last week, they just shrugged. I think they're all just a bunch of degenerate gamblers.

I'd just like for everyone to have equal chances(though it's not really possible), but like you all said, you can't remove the inherent advantages of having more cards without trivializing the bowling aspect, and without that, there's no reason to run it all, really.

I mainly just wanted to make sure that Pinochle decks wouldn't favor the better bowlers, because they already have the upper hand.

I think texas hold'em with a slight variation will be best. Poor bowlers can get 2 cards with semi-flexible rules, and good bowlers can have the opportunity to achieve better hands by drawing another card (discard a previous) on some condition. This rewards good bowlers but does not really penalize the poor bowlers nearly as much as 5 card does since Hold'em is a community card game.

You could also set betting increments like at the start of the bowling game, 5 frames in, and 10th frame. It would allow for competitive betting that makes hold'em great, with the rewards of bowling good.

Rules could be simple:
Set the river from the start, instead of burning per bet.

X = 1 Card
Spare Pickup(2 pin) = 1 Card

For a new draw, make it harder
XX = draw
7-10 split = draw
stuff like that.

Set a max draw limit of like 2 cards total or something. It presents a risk for the bowler drawing a new card as the old card has to be discarded completely so it isn't like they have an immediate advantage over the bad bowlers. If you draw a card, discard your choice before you get a new card and the new card that was picked up has to be used or discarded on the next XX or 7-10.

That's just how I imagined it working and as long as everyone can manage 2 cards then everyone has roughly the same chance, with a small edge going to good bowlers. But good bowlers should have an advantage since it is a bowling game.

rfalias on
• The Prettiest Zombie Coeur d'CoeursRegistered User regular
edited December 2008
That seems like an excellent layout to me, but I would probably need to simplify the redraw rules a little bit for the rest of them. But I'll definitely run something like this by them the next time we bowl, thanks a bunch.

Metacortex on
• Registered User regular
edited December 2008
Do you start with zero cards? If so then I would think a Pinochle deck would favor the better bowlers as it's far more likely that someone with 5 cards will get 2 pair and up. I'm not 100% sure of the math, but I know the bowlers at my league play a game like this as well, but everyone starts with 5 cards and then when you draw a card you also discard a card and build the best 5 card hand. This removes the inequality potential in the number of cards and adds a little more luck into the game.

khain on
• Registered User
edited December 2008
Metacortex wrote: »
That seems like an excellent layout to me, but I would probably need to simplify the redraw rules a little bit for the rest of them. But I'll definitely run something like this by them the next time we bowl, thanks a bunch.

Yeah, it shouldn't be hard to explain.

"If you have 2 cards and want to swap one out, then you have to bowl **** to get another. You can only do this X times per game"

Start of the game is buy in, 5th frame is first bet, after 10th frame is bowled last bet is placed and hands laid down.

Sounds fun actually, I should do this

rfalias on
• Registered User regular
edited December 2008
I'll admit I'm in a hurry, so I only kind of skimmed, but I got lost there for a second. Here's what we do for our bowling league team. It's very simple and it seems to give everyone a decent chance (I'm terrible, and I've won a few times.)

We use two decks. There is no limit to the amount of cards you can have. For every strike, you take two cards. For every spare, you take one card. Jokers are wild. Since I'm a vastly inferior bowler to the rest of my team, I also get a card everytime I manage to get nine pins in a frame. Then at the end, you build the best five-card hand you can put together with your cards.

We've never had a problem with that method.

xbl - HowYouGetAnts
steam - WeAreAllGeth
• The Prettiest Zombie Coeur d'CoeursRegistered User regular
edited December 2008
khain wrote: »
Do you start with zero cards? If so then I would think a Pinochle deck would favor the better bowlers as it's far more likely that someone with 5 cards will get 2 pair and up. I'm not 100% sure of the math, but I know the bowlers at my league play a game like this as well, but everyone starts with 5 cards and then when you draw a card you also discard a card and build the best 5 card hand. This removes the inequality potential in the number of cards and adds a little more luck into the game.

That was my line of thought as well. With the Pinochle decks, someone with 2 or 3 cards is going to have a decent shot at pair at least, but the value of a pair is complete shit. Anyone able to pull 5 cards has such a high chance of getting 2 pair or 3 of a kind that it seems it would favor them more. I just wish I had some numbers confirming it, and it's been a long while since I studied probability.

I kind of like the idea of starting with cards, but that would require at least an additional deck.

Metacortex on
• Registered User regular
edited December 2008
The material advantage is conferred by the better bowlers getting to have more cards and thus more opportunity to improve their hands. Letting everyone start with a full hand will help handicap the less skilled bowlers somewhat, but if better bowlers have more opportunities to draw they will still have an advantage. If you defaulted to let anyone draw after each frame, but penalized good bowling by not letting those guys draw it would give an edge to the less skilled bowlers. But that's kind of messed up no?

Assuming everyone's drawing from the same deck, the composition of the deck is irrelevant. It could be all aces, that would make it real obvious that those who can fill their hands will do better than those who cannot.

But how many hands get played in a night, 4 or 5? If you just want to keep it interesting you could just keep changing the game slightly. Using a Pinochle deck might do that. If you want the winnings to be biased towards the lesser skilled bowlers, maybe lowest hand wins?

Djeet on
• Registered User regular
edited December 2008
I don't think he wants the game biased toward the lesser skilled bowlers, he just wants them to have more of a chance to win. I really think the big problem is starting with zero cards as it means anyone that can get a 5 card hand has a pretty significant advantage over those who can't regardless of what type of deck you play with.

Also I don't think Hold'em would work that well. I'm assuming you have people on multiple lanes playing the game and at least in my league there's a pretty big time gap between when the first match finishes and the last match finishes so you can't have everyone bet on the 5th frame or show the flop on a certain frame.

khain on