How many cards should be marked?
 

One of the ruses for cheating one sees on T.V. is to mark the cards with something you can see with your glasses. This made me think of an interesting question. Suppose you are able to mark cards, and all you know is the card is marked or not marked (that is, the marks are all identical, so all you know is the card has been marked; there aren't different marks for different cards).

In a hold 'em game (or any other, but this was the first one I thought of), what would be the optimal number of cards to mark?

Re: How many cards should be marked?
 

read:
Poker Protection - Cheating and the World of Poker by Steve Forte
every person who plays live should read it.

Re: How many cards should be marked?
 

Did he have anything to say about my theoretical question?

Re: How many cards should be marked?
 

so are you basically trying to cheat?
anyways, mark key cards... A,K,Q,J, all with different marks per card(aces = mark in spot xyz)

Re: How many cards should be marked?
 

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so are you basically trying to cheat?

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No, I'm just a math buff.

Re: How many cards should be marked?
 

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anyways, mark key cards... A,K,Q,J, all with different marks per card(aces = mark in spot xyz)

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My question is assuming all marks are identical, so you can't mark differently. Obviously, if you marked cards differently, then you'd want to mark as many as possible. However, if all marks are the same, then you reach a point where marking more cards becomes counter-productive. When do you reach that point?

Re: How many cards should be marked?
 

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anyways, mark key cards... A,K,Q,J, all with different marks per card(aces = mark in spot xyz)

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My question is assuming all marks are identical, so you can't mark differently. Obviously, if you marked cards differently, then you'd want to mark as many as possible. However, if all marks are the same, then you reach a point where marking more cards becomes counter-productive. When do you reach that point?

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they were talking about blackjack. that should clear it up.

Re: How many cards should be marked?
 

You can't see any of the cards to come because of the burn card, so my intial reaction would be to just mark the four aces. Aces serve as top pair or the top kicker often enough to make this a pretty useful piece of information that you'll see with some regularity.

The other thing I was thinking was maybe marking the 10s and 5s, since you can't make a straight without them, but I don't think that situation would come up quite enough. For similar reasons you could mark all 13 of a suit.

Even marking ALL of the red cards (or black cards, or any two suit combinations) could potentially give you some advantageous information - you can rule out flush draws in some instances. So, I think marking up to 26 cards would still be useful.

If you're marking more than that, then it's counter productive - if you want to mark three suits, for example, you should mark them by leaving them unmarked (and marking the leftover suit).

[This is trying the question how many would be optimal as the OP put it, assuming identical card markings]

Re: How many cards should be marked?
 

This is an extremely complex question, as it goes to the a tradeoff between your prior information from the markings and the information opponent will give you by her particular betting patterns as they interact with the markings. Say you mark aces, sevens, and deuces. Solid opponent raises UTG = AA (6/66 hands possible with the markings). Solid opponent limps after two limpers = 77, 22, A7s, A2s (20/66). Combine that with known cards and reaction to the flop, and you get pretty good info.

On the other hand, marking cards which tend to be played in similar ways would benefit you when you are to act before opponent. Marking aces, kings, and queens would let you know with 100% certainty that a player behind you has a strong to monster hand. Very good. But if two marked cards are to open in front of you, you will get minimal additional information from the expected open-raise.

There is clearly no straighforward mathematical answer.

Re: How many cards should be marked?
 

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This is an extremely complex question, as it goes to the a tradeoff between your prior information from the markings and the information opponent will give you by her particular betting patterns as they interact with the markings.

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I also think there is lot more to the question than posted. If you have information regarding opponent's tendencies, frequencies, ranges, etc., then you're in far better shape to determine an optimal number of cards to mark.