Effect of change of number of hands being played at table..

Just returned from another few days of play in Las Vegas. As usual I noticed how the change in the number of players (hands) at a table often changes, sometimes dramatically, whether you win or lose for a short period of time. Never thought too much about it before as I normally just accept it and go on. I am pretty much a "camper" at a table and most times when a dealer is beating up on a table the other players leave and then I make my comeback.

For some reason to-night I got to wondering if any of you have any thoughts on the subject. Many players will switch to two or more hands in an attempt to break a cold spell and obviously sometimes it does and sometimes it don't. I can't think of any rational explanation as to how changing the number of players makes the hands better or worse, just know that sometimes it does. The cards are most times crazy so maybe I am simply attempting to gain some insight into "crazy", always a exercise in futility.

Random changes in the number of hands played simply affect play speed. But if correlated with the count in any way then obviously more hands being played during negative counts helps you while more in positive counts hurts you. Nothing is better than having the table clear out as the count gets high. Nothing is worse than having some Wongers come into your table just as it turns positive ev. The more people you have to eat bad cards the better, the more good cards you can get all to yourself the better.

on this, but all of the probabilities in our counting systems are based upon heads-up play. When there are numerous other players at the table, I think the statistical predictability of the next hand you're going to get becomes diluted because it is not until two or three more hands are gone from the deck that you get yours. What I do in that situation is wait until the deck gets more extreme before I increase my bets. However, I play the hands according to the count without regard to the number of players.

When there are numerous other players at the table, I think the statistical predictability of the next hand you're going to get becomes diluted because it is not until two or three more hands are gone from the deck that you get yours.

I think Don has explained to some people until he was blue in the face about this point, as many of us have.

The count does not become diluted if others get cards before you. If the TC is +3 your edge is exactly the same if you get the first cards out, cards from the bottom of the deck, the middle of the deck, 1st, 2nd, 3rd base, etc. The effect of other players at the table as it regards the true count will be on the number of rounds you get dealt at that TC, or in that shoe. It has absolutely no effect on the probabilities on a given round. The expected true count after N cards dealt is always the same as it is now.

Remember, the true count is the excess divided by the # of decks remaining in the shoe... that means the next card all the way to the last card dealt in the shoe. The true count does NOT divide the excess by the number of players at the table on a given round. We recalculate the TC after the round is completed. The group of cards that came out on the current round could have been arranged in any order, or could have been pulled from anywhere in the shoe. It makes no difference. We use the pre-round TC for betting and the post-round TC to bet the next round. You can use the intra-round TC for play strategy, in which case more players at the table helps you because you get to see more cards and thus have more information.

more players means there are a greater number of cards between your betting decision and your playing decision? I appreciate your comments on this because it's been a question in my mind for some time, and I've always groaned (silently of course) whenever more players sat down. Not because the number of hands became fewer, but because it seemed to me they would dilute the probabilities. I took one statistics course in college and certainly grasped the essentials, but this is something that I just wasn't sure about.

there are a greater number of cards between your betting decision and your playing decision?

It seems some people are confused about what the count really means to us. What it gives us is a better way to predict the composition of the cards to come. It has to do with probabilities. The more information you have the better. You make your bet based on the true count, as you know it to be, based on the cards you have seen. YOu can't do better than this. Now, would you rather make play decisions based on this same amount of information or have more information?

The cards that the other players get don't really affect the probabilities of what you will get. They only affect your ability to assess the probabilities. If you could look at 30 cards behind the cut card before you made your play decision it would have a greater impact on the true count than the other players at the table. These cards also would have absolutely no effect on what you actually draw. Seeing them will only give you more information upon which to make your decision.

The affect of the players drawing cards at the table is that the order of cards to be dealt are different, and different in a totally random way that has no net affect on you. They may take your bust card, they may take the card that would have made your 21.

Let's say you are playing single deck and the TC is +1. You are about to make your play and then see a ten on the bottom of the deck. Now the TC=0. Did this change the card you were about to draw? No. It just gave you more information to more accurately assess the composition. The bet that you made before the round would also have been different had you seen the card on the bottom of the deck first.

If you want to really make sure that all the probabilities stay the same, just close your eyes and don't look at any of the other players cards. Ignore all new information until it is time for you to play. This isn't going to help you. But it will make sure that your betting decision and play decision are based upon the same information in deriving the TC.

I've written many posts on this subject over the years, as has Don and many others. Here is an example I've used in the past:

There are five cups. Under one cup is a $100 bill. The other four cups have nothing. After you make your choice, before your cup is exposed, they take away one of the empty cups and allow someone else to pick from among the remaining four. Does this mean that you now have a 25% chance instead of only the 20% chance you had to start with? Nope. The new guy picking from four has a 25% chance. Your bet was based on the information you had when you made the bet. If you do this a billion times you will win roughly 20%. The second guy to pick will win 25%. Getting the additional information after you made the bet did not change your probabilities. Now, if you got to make a second bet at this point, and were able to pick from among the four remaining, the new pick would have a 25% probability. You have more information on the second pick. You know which of the original five cups definitely does not have the $100 bill. So you have a 25% chance on your second pick and still have a 20% chance on your first pick. Do this a billioin times and your first pick will have 20% winners while you'll have 25% winners on your second pick.

The decision at the bj table is the same thing. The new information does not have any effect on the edge you had on the bet you made before gaining this information. The only thing it does is increase your edge on the play decision, the 2nd decision for which you had more information, same as the 2nd decision when picking from 4 cups in the example above where you had more information.

I also grown when the other players join the table. Not because they will dilute the true count, but because they will eat more of the true count. +3 is +3 regardless of the number of players. But with more players you will get fewer of the good cards. They will be depleated faster... meaning in fewer rounds. The rich segment may last 60 cards. Five players eats this up faster than three. If the richness is equally distributed throughout the remainder of the shoe, as we assume it to be, then we still suffer because there will now be fewer rounds dealt in the shoe. As I said in my first response, more players joining during a negative TC helps, more player joining in a +TC hurts.

1. What are the true probabilities for the second guy to make a pick from among the cups, assuming that he sees you make your first pick and then sees them remove one of the empty cups, leaving him to pick from any of the remaining 4?

2. What are your true chances on the second pick?

This is the same as the famous Monte Hall problem. The percentages I gave above are correct based on the second player having less information than he has here. Above we assume that he just walks in and is told to pick from among the four. He does not know that you picked one of five and that one of the empty cups was then removed. And the probability for your second choice above would be correct if we assumed that the cups were reshuffled and you did not know which of the cups you had picked first.

Remember "Let's Make a Deal"? It was an old game show of the 70's.

In the big deal of the day, the highest contestant got to trade his "winnings" for one of three doors. Behind one of the doors was usually a ZONK... nothing. Behind another was a medium prize like a range. Behind the last door was the big deal... say a car.

After the contestant picked one of the three doors, Monty would often expose one of the doors you did NOT choose to reveal that it was NOT the car. Then he would offer to let you SWAP the door you picked for the remaining door. The question is: Do you swap?

Assume that Monty ALWAYS exposes a "bad" door, and also ALWAYS gives you a chance to swap (which he did not always do).

Swap and your odds of first off picking the wrong door become your odds of claiming the main price, in other words increases from 1/3 to 2/3, or in still more other words: you double your odds by swapping!

John Patrick would probably advice you not to swap and say "Hold on to your first choice, you should always trust your first instinct".

Even after I tell them the odds (2 out 3 wins), they INSIST that with 2 doors left, you have a 50-50 chance of having the correct door. Funny...

I'll give the answers to my question above.

You pick from among five cups. After you pick, one losing cup is removed and a second guy gets to make a pick. You are also given the opportunity to make a second pick.

1. If the second player does not have knowledge of your pick, his chances are 25% since that is the mean probability among the four. The probabilities must sum to 100%. But if he knows that you picked from among five, and that one of those you did not pick has been discarded, then he can make a better choice if he knows what your pick was. He should know that your pick has a 20% win probability. This means that an 80% probability is distributed among the other three cups. So picking one of those three his chances are 1/3 of 80%, or 26.667%.

2. If you get to make a second pick, and the cups are not reshuffled, then you would also have a 26.667% win probability on your second pick if you chose from the other three. The original pick retains a 20% win probability.

The Monte Hall problem is usually given as a puzzle or riddle. But it is really an excellent example of how your probabilities do not change if you gain additional information after you make a bet. Your probability of winning only changes if you are given the chance to make a new choice based on the new information. In the Monte Hall, 3 door problem, the player has a 33.33% chance in advance, and retains the 33.33% chance after gaining the new information about one of the losing doors. His edge doesn't change unless he is allowed to apply this new information to making a new decision.

The player on third base makes a bet at a true count of +3 in a double deck pitch game. His cards have been dealt and are face down in front of him. Will his expected win be any different if we turn over the cards of the other players before we look at his? Nope. He made a bet based on the running count divided by the unseen decks remaining before the deal. While he can be helped by gaining information about the unseen cards before he makes the bet, getting this information after he makes the bet cannot help or hurt him (except in regards to his play decision). If all three players had their hands face down on the table at this point, and you were given the opportunity to bet on any one of them, the choices would all be equal (again, except for the edge in play strategy for the one who plays last). Logically, you would bet on third base if you had to bet on one of them. You would NOT bet on first base using the argument that he got his cards when the deck was closer to the pre-deal true count thus making you able to predict your edge more accurately (before the tc was diluted?). That argument, though it continues to come up, does not make sense.

Thanks!