4 Card Poker - Beating the Game

I've read through the odds tables and strategies for 4 card poker and understand the edges against me based on the table and strategy I employ. My question is whether playing multiple hands at the same time reduces your variance?

On a recent trip to the casino, a friend of mine and I got the idea to pool our bankroll and play 4 hands at a time, since the house allows each player to play up to 2 hands simultaneously. Our results were astounding. While we did have a few losing sessions, our winning sessions far exceeded our losing ones. Granted we employed some good strategies, similar to the optimal betting lines recommended by the Wizard of Odds; however, did we just ride a heater or did we actual stumble upon a potential edge? It certainly felt like our variance was greatly reduced and I'm curious to know whether we can expect to continue to beat the game?

I'm not sure if anyone has done a collision analysis of the game yet. That's where to start.

Thanks for the reply. I'm not particularly strong in mathematics. Can you point me to the formula for how I would solve this equation or another example of collision analysis?

How did you play the hands? Did you use info from the other hands to determine how to bet the later ones? In order to conclude that this was the result of anything but luck, you'd need to show that you did something to alter the edge of the game.

Note: reducing variance only smoothes your slide down the drain. A game with a 3% house edge and 0 variance results in a 3% loss per hand, for example...

Good questions! Yes in most cases, we would be looking at one hand at a time and deciding on what to do. So with each hand we had more information to bet optimally. At times there would be a third player at the table, but most of the time we were not picking up information about their hand(s).

Quote: jsteins

Thanks for the reply. I'm not particularly strong in mathematics. Can you point me to the formula for how I would solve this equation or another example of collision analysis?

This is a job for Eliot Jacobson at https://apheat.net/

An important situation in 4CP (Four Card Poker) is when the player has a one-pair hand versus a Dealer Card that is higher in rank. Such as

KKxxx vs A
JJxxx vs Q, K, A
22xxx vs 3-A

What the player needs to look for is whether there is a card in his hand that matches the rank of the dealer card (I call this a "match card.") Such a card in a player's hand reduces the chance of the dealer pairing the upcard and increases the odds that the player will win (by about 6%) - which sometimes leads to a change in the optimal betting strategy.

If you could see a second 5-card hand in 4CP, you would know whether or not another match card is in those 5 cards - and thus no longer available to pair the dealer's card. So, seeing a second hand would be a substantial advantage.

By the way, I have modeled 4CP extensively and am writing a book with a section on Four Card Poker mathematics and strategy. I have found several ways to reduce the house advantage that have never been published on the internet or in books.

Stephen How created a simple collusion strategy with the dealer up card, but it only cut the house edge in half.

https://discountgambling.net/category/four-card-poker/

Quote: tringlomane

Stephen How created a simple collusion strategy with the dealer up card, but it only cut the house edge in half.

https://discountgambling.net/category/four-card-poker/

This sounds about right to me. Off the top of my head you can collude in any game, though there's only a few that I know of that you can actually get a decent little advantage on. The rest of the time it shaves fractions of a percent off the house edge, but doesn't actually get you an edge.

Not only that, when you do collude, you need to make some very interesting strategy plays pending the cards. If you guys "for the most part" played by the book but every now and then changed things based on your cards, then you more than likely just ran a heater. Playing more hands will have an increase in co-variance. i.e. If the dealer has a crap hand, both hands have a good chance of winning... If the dealer has a great hand, both hands stand to lose together as well. This is similar to playing multiple hands in blackjack.

Actually there ýs one exact way of beating casýnos at long term. Lunar poker (Russýan Poker) ýs a poker game whých u can play at European casýnos. U can play thýs game 1-4 boxes. If u play more than one box u need to play blýnd. They do not allow you to see the cards of the other players before you make your actýon (draw, fold or game) . But at North Cyprus most of the casýnos allow you to play 2-4 open boxes . In thýs case ýf you play the correct game you play wýth plus house edge 2 to 4 boxes %2-7 plus edge . And also you can take some dýscounts on your loses %5-20 cash back . There alot of pro players from all over the world who play there and they wýn at long term. But the thýng ýs ýf casýno belýeves that you are a poker pro they wýll take u to theýr blacklýst after few games . u can fýnd all detaýls about the edge of the game at , and for Cyprus casýnos search on web merit, carts, elexus etc

Quote: cypruspokerking

Actually there ýs one exact way of beating casýnos at long term. Lunar poker (Russýan Poker) ýs a poker game whých u can play at European casýnos. U can play thýs game 1-4 boxes. If u play more than one box u need to play blýnd. They do not allow you to see the cards of the other players before you make your actýon (draw, fold or game) . But at North Cyprus most of the casýnos allow you to play 2-4 open boxes . In thýs case ýf you play the correct game you play wýth plus house edge 2 to 4 boxes %2-7 plus edge . And also you can take some dýscounts on your loses %5-20 cash back . There alot of pro players from all over the world who play there and they wýn at long term. But the thýng ýs ýf casýno belýeves that you are a poker pro they wýll take u to theýr blacklýst after few games . u can fýnd all detaýls about the edge of the game at , and for Cyprus casýnos search on web merit, carts, elexus etc

Could you repeat that please in several threads? I need to hear it over and over again.

I don't think there's one poker game where playing two hands gives a collusion edge. In the few where you can collude and get an edge, you generally need a full or nearly full table. The strategies aren't easy either.

Maybe Lunar Poker is an exception, but you would be an autistic savant if you could pull this off. The game is so complex, no one has even found an exact optimal strategy to this game yet.

So yes, I would say you're just running good.

Quote: Romes

...The rest of the time it shaves fractions of a percent off the house edge, but doesn't actually get you an edge...

To analyze collusion It's probably quite hard to analyze every combination, so one way is to use a simulation.

Sometime ago I was looking at a call or fold like game. I gave the player their hand (the first cards in the deck) and the dealer their hand (the last cards in the deck) but the player could look at the first N cards in the pack (i.e. peeking at other players' hands). The method I used brute force by looking at all the cards remaining in the deck (ignoring the ones the player knew about) and working out what the dealer could get.

Using no peeking showed the game got the normal House Edge; however you needed to see over half the pack before there was an edge. As has been hinted by other games this changes the marginal decisions depending on how many cards that you want (or don't want) the dealer to have are out in the players hands. In this case the normal HE was about 3% and reduced to just over 1% with a full table and it was fairly complicated which cards helped.

jsteins, were you playing the optional aces up bet also.