Cascading Collusion: HCF

I've noticed that some casinos with High Card Flush will let you play multiple hands at once. First you look at your first hand, and make a decision. Then you look at your second hand, and make a decision. Then you look at your third hand, decide, etc.

So while you could have access to dozens of cards, you can use the knowledge regarding all of them on the last hand, but each previous hand will be played with less information which is why I call this "cascading collusion".

Do you think it's possible to get an advantage while playing High Card Flush with this method?

Maybe casinos will let you place more chips on the last hand. I don't know - as some members have realized, I'm a low-roller who only does the minimum bet.

When you have multiple hands at a time, you are required to act on your highest bet first. I’m learning about collusions too.

I am the author of an article on WOO defining near-optimal strategy on how to make the raise/fold decision on a 10-high 3-card flush on High Card flush. The link to my article is here: High Card Flush Advanced Strategy article

I also have done private analyses on the advantages of collusion for high-card flush; those analyses have not been published.

When seeing an additional 7 to 14 cards in High Card Flush I found that the only decisions that might be influenced are Raise/Fold for 3-card flushes that are 10-high. Basically, when seeing 14 cards outside of your hand you will (almost) always fold a 9-high (or lower) 3-card flush and always Play/Raise a Jack-high (or higher) 3 card flush.

So, 3-high 10 card flushes are not common and the number of times that the cards in other hands will be skewed enough to make you change decisions will be fairly small. And the amount of EV you gain for each changed decision is usually quite low.

Basically, for the cases I looked at*, I concluded that collusion can only make a tiny dent in the house advantage for High Card Flush. By tiny dent, I mean that ΔEV was like 0.1% or less, as I remember it.

*Again I only analyzed casual collusion -when you see the cards of 1 or 2 players (such as the hands of the players sitting next to you.} I did not look at cases involving knowing all the cards in everyone's hands at the table and computer perfect play (such as a collusion team) but even then I doubt it makes much of a difference in player EV. IMO, the High Card Flush game is structured in such a way that it is not vulnerable to collusion.

According to this article it appears that someone named Steven How found a collusion method for HCF - but it only works if you know all six player hands. It does seem reasonable to believe that knowing all cards except ten would make decision-making really different than knowing all cards except a few dozen.

However this does not involve the "cascading" situation that I see online

I read this online article from Eliot too. As I understand it, it says knowing only the suit combinations of 42 exposed cards except ten cards would make the game advantageous by a +7% edge to a player. It’s not knowing both the suits and ranks of 42 cards.

Gordon researched this game. He must know this.

Quote: aceside

I read this online article from Eliot too. As I understand it, it says knowing only the suit combinations of 42 exposed cards except ten cards would make the game advantageous by a +7% edge to a player. It’s not knowing both the suits and ranks of 42 cards.

Gordon researched this game. He must know this.
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Steven How is a brilliant analyst (I know that the Wizard, Mike Shackleford, has that opinion as well.) I have probably read almost everything that How has posted on his website - it's a bit of an education to do so.

I consider Eliot Jacobsen to be a good capable analyst who was on a mission to alarm the gaming industry (so that he would be employed in game protection) and who sometimes presented unrealistic scenarios as clear and present dangers.

I have always assumed that Howe's and Eliot's published work on HCF is the reason why HCF tables have had only 5 chairs in the B&M casinos that I have played in.

The "10 cards remaining" scenario is trivial to analyze. You can look at the probability distribution for the suits of 10 cards: everything from 3-3-2-2 to 10-0-0-0 and then calculate the probability of the dealer having a 2,3,4,5,6,7 card flush for each of those suit distributions. Then you can analyze how a player would change his Fold/Play decisions based on dealer's probabilities for each suit distribution. When I have time I might do this calculation and post it here; alternatively maybe someone else will do it and post it (Charlie? ssho88? mental? a zillion other guys?)

I analyzed the situation in which player knows the suits and ranks of 21 cards, with 31 cards remaining from which to make a dealer hand in HCF. In that case, I found that knowledge about the ranks of cards created more player equity than the suits of cards. Extreme example: If you have a Jack-high 3-card flush and your two neighbors have 14 cards that are all in the range 2-10 then your jack-high 3-card flush is probably beat by a higher-ranking 3-card flush or better. and you fold your hand.