Before I attempt to answer some of Henry's questions let me talk a about the e-mails I receive. I appreciate all your support and all your e-mails. I truly enjoy answering the ones that ask questions or pose a simulation. Not all of them are answered in print for obvious reasons. I do have a request.
When you pose a question or describe a situation involving your hand, please supply all or at least enough information for me to set up a simulation.
At minimum I need the following:
1. The rank and suite of all your cards. Not just the two winning or losing cards or cards of interest.
2. If relevant, the exact holdings of your opponent and not just the two cards that beat you.
3. If relevant, the rank and suit of the board cards.
Other information that would be useful in duplicating the situation would be:
1. The number of players that started the hand or how many you would like the simulation to be run with.
2. The stakes in which your situation occurred or what stakes you would like to have it simulated at.
3. The type or texture of the game. Was it a tight, average or loose table? It is impossible for me to duplicate every factor such as betting action. I am able to control those listed above.
Henry, [As]-[2s]-[Ks]-[Kc] is a great starting hand. It is ranked 74th out of 270,725! A great hand to raise with before and after a flop of [3s]-[4c]-[5s]. After that flop I would be hard pressed to stop raising. If it were no limit, I would be all in unless I felt I could get more money in the pot by not pushing all in. Let's take a little inventory:
1. You have a made nut low.
2. Your low cannot be counterfeited.
3. You have a straight which may win the high.
4. You have a draw to the nut flush.
5. You have an inside draw to a straight flush.
6. There are no pairs on the board.
There are 5 spades out, leaving 8 in the deck. You are not concerned if the board pairs with the 4 of spades so that you will have the nuts on the turn if any spade comes. There are 8 spades and 45 unseen cards. Your chance of hitting a spade on the turn is 1 in 5.63 or 17.8%. If you don't catch a spade on the turn you have an 8 out of 44 chance on the river or 1 in 5.5 or 18.2%. The board may pair with a 3, 4 or 5 on the turn. As mentioned before, the 4s would be a blessing in disguise. So that leaves exactly 8 possible cards to pair the board, (9-1 = 8). The math is exactly the same as for you to catch a spade.
The key thing to remember here is that your wheel may not be the best straight. You would still be a dog to a 6 or 7 high straight.
The chart below shows the results of dealing 1,000,000 rounds to the hands indicated with the given flop at a full tight table.
The A-2-K-K with the given flop is indeed a good hand. It wins 68% of the time and returns an average net win of $91.04 in $10/20 game. Interestingly, the A-2 suited with two randomly dealt cards given the same flop actually performs better.
It wins 72% or 4% more often and return $102.77 or $10.96 more. The reason for this is that you randomly hit often enough some of those 73 other better hands. Remember you are still guaranteed a portion of the pot.
Looking at the K-K with two randomly dealt cards and the same flop the results are much different. The win rate drops to 5% and the net falls to a loss of $6.57.
Let's take a quick look at what hands you win with and lose with and how and when you win holding the A-2-K-K with this flop.
The chart below shows the high hands that win and lose with this combination of starting hands and flop. You win with your straight slightly over 31.5% more then you lose with it. You do lose with your flush over 6.5% of the time. This is obviously not to a higher flush but a different or to a full house or better. Your opponents will complete a better straight flush than you less then 10% of the time. More then half of your straight flushes are completed on the turn.
Well, Henry, I hope I answered your questions, and I thank you for your input.
Getting back to the development of our point-count system, last time we were looking at the net win for various non-suited A-2 starting hand combinations. I mentioned then that the A-2 combined with a pair affords us an excellent way to evaluate the value of pairs.
This is attributable to the A2 being common to all hands. In the chart below I compare all the A-2 non-suited hands that contain a pair and listed the hands in their natural order from low to high. In this case I decided to set the performance factor (PF) equal to the net win rounded. One problem does exist. The chart does not contain a value for the A-A or A-2. To resolve this issue, I plotted the values on a chart and extended the graph in both directions to derive a value for the 2-2 and the A-A.
The result of that extension assigned a value of 34 to the A-A and 12 to the 2-2. See the chart to the right for the rest of the values.
But now you say, OK, Guru, but how do you know your results hold water? The answer is, I don't, at least not at this point. I do, however, have a method of testing these values. In Wilson's software you may enter your own count system and then assign it to a profile and save that profile under a different name. By choosing the new profile name the player will play the new system. In order to hold as much constant as possible I used the same profile to play 3 different point-count systems in a tight game. I ran 500,000 simulations using each. The results are listed below. Note that the only part of the pointcount system I changed was the values assigned to pairs.
The count system labeled "original" in the chart on the left, is the original (K) count system "out of the box" assigned to profile (20). I then took a different existing count system, (I) and assigned it to the same profile, (20). Those results are listed under the unaltered caption. The purpose of this was to be able to check the results of profile 20, playing count system K, I and the count system I modified. The modified results are reported on the "altered" line.
Next time I will expand upon these results, disclose the original point-count systems for pairs and why I decided to modify them in the first place.
So what have we learned? [As]-[2s]-[Ks]-[Kc] is certainly a great hand. You may replace the K-K with two random cards and improve the net win. If you try replacing the A-2 with two random cards you will take a great hand and turn it into a loser.
