Math Hulk VII: Librarian verses Stealers

Now, the librarian should never lose a combat while he has psi points left since he can of course not use them once he is dead. He can choose to spend them after seeing the dice so there is not even risk involved. Stealers will be attacking him just to sap away points limiting what else you can do with him(like smite the broodlord). Basic combat percentages are win 34%, tie 16.6%, and lose 49.4%. This is better than a standard marine since he has the +1 but still not very good compared to the close combat specialists.

So the first question is do you spend your points up to get the win or the tie. Average number of points spent to get a tie is 1.08 while the win is 1.74. A healthy jump but I would think you would want to go with the win since just getting the second tie costs you 2.16 on average then so the win straight away is cheaper in the long run. You might go for the tie if the stealer is out of action points and will block additional stealers from getting to you this turn, but that is a general rule of thumb for most of the marines.

What about the Librarian on Guard? The question here is when should he reroll his die (tie or loss) and when should he just go for the win straight away with points. The optimal decision for conserving psi points on average is to buy your way to victory if you have a combat score of 5 or 6 (die 4 and 5 +1) since the stealer also has a 5 or 6 in these cases. You should also buy your way out of a 4-4 tie but other than that reroll. So you would reroll any die of 2 or 1 and a 3 if you are currently losing the fight. This decision tree will get to a 1.12 psi points for the victory on average. If you are playing for the tie the psi point average can be as low as .6.

When rerolling here, I would remind you that this is averages and if you are low enough on psi points such that you could roll a result you could not buy your way to victory and are sitting on a point where you can buy yourself out off currently, I would probably take the sure thing. These reroll decisions are for use when you have the psi points to gamble and want to try to get the most use out of everyone. Never gamble the life of your librarian to try to save those last few points.

Math Hulk VI: Thunderhammer Terminator verses Genestealer

The thunderhammer terminator is pretty good in close combat as you would expect with the Block ability stripping a die from the stealer and a +2 to his attack roll he starts in a pretty good place. A thunderhammer terminator will win combat 58.3%, tie 14.8%, and lose 26.9%. So in this combat the terminator only dies 1 in 4 times.

Adding in guard makes him really survivable. Again a decision is required about rerolling ties but since their can only be a tie on 3-6 outcomes it is less likely event. Ofcourse on a 3 (roll of 1+2 bonus) you would reroll since you cannot get lower. Using that as the starting point the guarding thunderhammer terminator wins 71.6%, draws 17.4%, and will lose only 11.0%. Looking at these numbers tells us that a thunderhammer terminator on guard should not reroll a tie unless he rolled a 1. Any die roll which results in a chance to lose (1/6 = 16.7%) is worse than just letting the stealer attack you again. You might try a reroll if you are tied on a 4 and you need that stealer out of the way so you can go forward.

How should genestealers deal with the thunderhammer terminator if he is so good? If the terminators need to get someplace while you have unlimited stealers I would just use 1-2 stealers to block his path and use you blips to try to come at them a different way. You have a much better chance if he is forced to attack you.

Math Hulk V: Close Combat Genestealer vs Lightening Claw Terminator

For this installment of Math Hulk, we look at the close combat battle between a genestealer and the terminator with lightening claws. Stealer gets his roll 3 and pick highest while lightening claw gets to roll 2 and take highest +1. Remember that this bonus die and +1 only comes into by for the terminators front space. So attacking from the flank or rear causes this terminator to fight just like a regular powerfister. The plus 1 makes a big difference since now no matter how well the stealer rolls, a 6 from the terminator wins the fight. The probabilities for the terminator is 30.6% 7, 25% 6, 19.4% 5 , 13.9% 4, 8.3% 3, and 2.8% 2. These compare to for the stealer of 6 (42.1%), 5 (28.2%), 4 (17.1%), 3 (8.8%), 2 (3.2%), and 1 (0.5%).

Combining these two sets results in 52.8% terminator wins, 19.2% tie, and 27.9% stealer wins. So the lightening claw terminator is twice as good as the powerfist ones in close combat.

Now if you place the lightening claw terminator on guard, how does he perform? Unlike the powerfist terminator this is no need to worry about whether to take your reroll or not. If you won you have no need of the reroll, if you lost you always take it, and if you tied you just save the tied die and reroll the other die which is lower or equal to it. This makes the lightening claw terminator on guard with 64.8% win, 18.5% tie, and 16.7% lose. This is pretty good. Essential as good as a stealer attacking a normal terminator.

Tactics for the lightening claws are all about using guard or attacking in close combat since you have no ranged weapon to go on overwatch with. Most of the time going to guard is probably the best bet unless the stealer is isolated and can get around you without killing you. If there is an isolated stealer with an exposed flank it might work out to attack him since this event is most likely to happen in a room where the stealer can avoid your close combat death dealer anyway or attack you from the flank.

Math Hulk IV: Close Combat Stealer vs Powerfist Terminator

Now it is time to bring Math Hulk to the realm of close combat. Starting out simple with genestealer versus a marine with a powerfist. The first thing we need to know about is the probabilities for the stealers roll. It seems like it would be tricky to calculate what the highest roll for 3 dice would be but it is pretty straight forward. For example, the chance to get a high of 5 is the answer to the question what is the chance of rolling 3 dice all less than 6 (5/6*5/6*5/6) minus the chance of rolling 3 dice all less than 5 (4/6*4/6*4/6). For a 3P6 roll (roll 3, 6 siders and Pick highest) the breakdown is 6 (42.1%), 5 (28.2%), 4 (17.1%), 3 (8.8%), 2 (3.2%), and 1 (0.5%). So a stealer is pretty likely to be sitting on a 5 or 6 in this arrangement. The powerfist has a single d6 to try to beat the stealer with so he is in a tough spot.

The final outcome is 17.3% the terminator wins, 16.7% draw, and 66.0% genestealer kills terminator. The 17.3% is just above the probability for the terminator to roll a six which is where most of his wins will come from.

Terminators also have the option to be on guard to defend themselves better in combat. Since the Terminator gets to pick whether or not to reroll his assault die after seeing the stealer roll, a decisions are required. You will of course reroll anytime you have lost the combat, but what about on a draw. If the guarding terminator is willing to accept a draw on the first die(not use his guard) then the probabilities come out to 25.2% the terminator wins, 27.6% draw, and 47.2% genestealer kills terminator. So the guarding terminator has increased both his chance to win or draw the combat by 50% compared to the original value and reduced his chance to be killed by like 30%.

Now what about those draws on the first die, when should you reroll them? If the stealer has no more action points then hold the draw. You can shoot him in your next turn with much better odds than close combat. Other than that the decision depends on what the stealer has rolled. Obviously if you both have a 6 you should probably not reroll since you cannot win. If the stealer has a 1 you should always reroll since you cannot lose(even if the stealer is out of action points). Here is a plot of the results of the combat based on where you draw the cutoff for rerolling. 0 cutoff means never rerolling in a tie while 6 means always rerolling which are both past the limits for reasonable actions.



If the stealer has a 5 you need a 6 to win which is slightly worse than just a totally refresh attack without guard and since you still have guard active it is better to hold the draw in that case. With a stealer with a 2 or a 3, you have a much better chance of killing the stealer this action with a lower chance of being killed then waiting for it to attack again so reroll in these cases.

The tough call is when the stealer has a 4. This is pretty much a push since you have about the same chance of killing and dying as you do next attack but it forces the stealer to use one more action point to try to get you so I would probably hold the draw on a 4 especial for stealers low on remaining action points. So the general rule of thumb is hold draws on 4-6 and reroll on 1-3. This has a marine winning 26.3%, tying 25.9% and losing 47.7%. Only a slight improvement in killing over the willing to accept all draws but a little bonus can be helpful.

The last part of this discussion is whether you should even use guard on powerfist terminators. Given that you essentially have a better chance of killing the stealer from your first shot on overwatch with no chance of just dying and it only gets better if they have to take 2 actions to close on you. Guard does have the advantage that the only way to lose it is to get killed while if a stealer hits you in close combat you lose overwatch. I see using guard being reasonable at corners where the stealer might only make 1 step in LOS or in a room where stealers are likely to attack you from the side. I can see situations where stealers can attack from the front or the side depending on using guard or overwatch. If he can get to you either way with more than 1 action point I would probably go with guard. If you are on overwatch he will attack you from the flank such that even if his first stealer goes down your overwatch is lost so the frontal attack can then proceed.

Tzeentch Challenge!

This past weekend was the Tzeentch Challenge Blood Bowl Tournament here in Ann Arbor. I was glad to see some out of town coaches come out for the event so I could show them how we play it up here. Boy did I show them with my 0-4-1 record for the event being outscored like 10-1 and out casualtied probably 20-3. I did so poorly that the host decided they needed a wooden spoon for me when one was not planned. I would also note that I did not play the 1st or 2nd place coaches from the event so they earned their placements without easy points from me.

What does it take to go 0-4-1? Blame should first go to the coach. In most of the games I made 1 stupid mistake of pushing too hard forward on offense or missing an easy move. These types of mistakes usually result in a 2 point swing since you miss the score and your opponent takes your mistake the other way for a score. Next comes down to roster. I took a Necromantic team that I had never played before. I had done some games with undead but necromantic is just different enough that I did not use them well. I had a roster which lacked focus, instead of deciding how I was going to play I was too worried about how my opponents would play. I took a few skills that rarely came into play and when they did they did not help. I was out blocked and mightly blowed by all of my opponents and did not take advantage of my speed since I was spending too much time pick people up off the ground. Of course, luck also comes into play. It seemed like anytime I really needed the dice to come up one way they would not. The tone was set when my first block of the first game was double skulls rerolled to double skulls. Not even both down where I could blame the organizer for restricting Block access. I think my sure hands ghoul failed to pick up the ball more times than he was successful out in the open.

While I went to event with no plan on winning it hence an untried team, I was not expecting to go winless. Well at least, I got a few minis for being the wooden spoon and will send in some spares minis to replace my draw from the prize pool.

Math Hulk III: Shooting The Broodlord

The broodlord has the hard to kill ability which means it essential take 2 wounds from a single shooting weapon attack to kill him. First this means that the flamer or the Liberian psychic storm power cannot kill him. It also makes life pretty hard on the stormbolter armed terminators who need double sixes to get him normally (2.8%) but a little better with sustained fire (11.1%). Now when it comes to overwatch the survivability of the broodlord really starts to shine. He has like a 70% chance of moving 6 spaces toward the overwatch marine. That is pretty good given that a normal stealer was usually toast after 2 moves without a jammed storm bolter. Here is the chart. Life is a little tougher if the space marine unjams the bolter but that action essentially gives you two squares of easy movement before the sustained fire returns to give its low but reasonable kill chance.



Definitely looks like a Broodlord can storm the castle.

Now the assault cannon is a different story. With 3 dice it is a lot easier to score two kills so you can bring the big beast down 33.3% of the time with normal fire which goes up to 50% with sustained fire. The assault cannon is the broodlord killer so stealer players should try to reveal him as from the assault cannon as possible while the space marine player needs to be bringing this big gun to bear on him. Here is the overwatch chart.



The broodlord should probably not move infront of an overwatch assault cannon unless the first squares of movement lets him assault it(ie there is 1 empty square between them) or will get him out of sight.

Math Hulk II: Stealer vs Assault Cannon

To say that a stealer vs the assault cannon is heavily in favor of the assault cannon is an understatement. With 3 dice and killing on a 5+ (4+ with sustained fire), an assault cannon will drop the stealer 70.3% of the time(87.5% with sustained fire). Since the kill rate is already pretty good, the assault cannon can be used on the move unless you just have to kill that target this turn. Ofcourse it has limited ammo and can explode after being reloaded but its explosion rate is 2.8% for those last 10 shots so you can expect 1 explosion every 4 games or so.

Overwatch is a nightmare for stealers versus the assault cannon. Even with the reloaded gun that can explode, it looks unlikely for any stealer to get beyond the initial square if the cannon has not exploded.



The numbers on the plot are the probabilities of the outcome for a stealer trying to go 3 paces at which point the results have pretty much leveled out. The stealer is dead but maybe the gun has exploded. This is a log plot compared to the earlier plot where I have cut off the stealer being alive without the gun exploding to keep the scale reasonable. Chances of a live termi and live stealer after moving 6 squares in overwatch range is 0.0007% or about 1 in 100K. Not very good.

Why would you then charge an assault cannon on overwatch. First is that he has to shoot. He has no choice so he uses up 1 precious ammo counter. Also if he is low on ammo reloading should take him off overwatch which means to reload and return to overwatch will cost him 6 command points during your turn which is more than what he probably has.

An interesting thought for stealers is that closing a door infront of the assault cannon on overwatch causes him to shoot the door. He will probably open back up for you so while you did not go a square forward you did cost him an ammo and moved him one step closer to having to reload.

Next Up is the series is shooting the Broodlord.

Math Hulk I: Storm Bolter vs Stealer

Starting a little series discussing probabilities in Space Hulk. Now in space hulk since each piece gets to do several things, tactics and probabilities collide into dependent chains of events. It is not as simple as 40K where calculating the number of dead marines after being doomed then attacked by fortuned harlies. Each piece can have several actions and what they do later depends on what happens first since you do not have to declare more than 1 action at a time.

We will look at the odds of the individual events in space hulk and some common chains of events. We will start with the simple space marine storm bolter shooting at a genestealer.

For basic shooting of a storm bolter at a stealer you have a 30.6% (11/36) of killing it. With sustained fire that goes up to 55.6% (20/36) for that second shot. Now there are several ways for Terminators to shoot at the genestealers, you can walk toward them and shot with each step or you can move the first step and then stand still the second. The first one gets you toward the destination faster but does not benefit from the sustained fire rule. Assuming the genestealer lives through the first shot, the second shot with sustained fire has a 81.5% better chance of killing the stealer but you did not get to move. This is where the tactics come in, move and shot or just shot. Do I need that extra square or do I need this stealer dead.

Now stealers going after a model on overwatch is another place where probabilities and tactics run into each other. First shot to kill 30.5%, successive shots 55.6% with the 16.7% chance of jamming every time. Here is a chart for a stealer running into the storm bolter on overwatch were the space marine player does not spend any command points to clear a jam. The plot is whether the stealer is alive or dead and whether the space marine has an active overwatch or a jammed storm bolter.



As you can see, you get that first square pretty easy but after that you are pretty much only going to make it far if he jams early. You are essentially not making it past 2 squares unless he jams so what to do if you have a group of stealers and he has not jammed after moving your 2 squares. Do you push you luck and move the one more(55.6% chance of being dead and no longer blocking LOS) or do you leave the front stealer where he is then move up one behinds using the first to block line of sight?

Or maybe he has jammed? Does he have a command point to clear it? Well since he cannot spend the command point to clear it until you do something in his LOS again you can move up the square to see if he clears it. If he does you are back at a non sustained fire level on your next move so you have a good chance of getting the next square(69.5%) before moving the rest of the pack up behind.

Choices and More Choices

So the local blood bowl tournament is this weekend and I need to pick a team. The event has some special rules which are certainly going to affect what people take. Basic 1M teams with 150K after roster for skills or stat improvements. Players can get multiple skills but the cost gets more for more skills up to 3.

The most important rule is that the skills Block, Wrestle, Dodge, Leader, Guard, and Claw cannot be choosen to spend the advancement money on. Positional players who have them get to keep them but Norse lineman for example lose Block but are 10K cheaper. Since a lot of teams standard builds come from getting block and guard on players things are going to be different.

In choosing a team to take I would like the team to have some starting players with either block or dodge so my Skaven seem like a good first choice, but since I have 28 teams I think I should play another team. Both my Skaven teams have seen the table in recent months so I would like to use a team that has not seen the table in the modern era. This still leaves plenty of choices. I have considered a total bashy team of Orcs since they can have 4 Block players but only get gobbos with dodge. I am also considering a Necromancer team. I got a necromancer team about 4 years ago as a booster to my undead to get the 2 extra ghouls and the extra zombies. Later picked up the extra werewolve and flesh golem but the necromancers have never seen the table. I also have Norse team which could be interesting even if the lineman do not have Block anymore.

Ofcourse once I pick a team I have to pick the skills so another set of choices. I have no concern about winning the event since I am a marginal player but would like to make sure I have a good time and not get slaughtered.

Quick Update

Not much going on with the hobby things right now. Had a gaming filled long weekend? Well for me with 2 league blood bowl games in.

First on was against the Norse team that beat me the first week. They were a little weak after getting taken down a peg by the Nurgle team the game before and I was constantly breaking armor in the game. Got a 3-1 win even though I made many mistake mainly because anytime he needed to roll a die to score it and its reroll would fail. I did finally get a lasting injury with my Dirty Player linerat getting a niggling injury.

The second game was against the nasty Nurgle team which has a team value like 300K above mine. Got the protective 2 babes and 2 apothecaries since I did not have the 340K for Headsplitter again. Game was a 1-1 tie but it might have well be a loss for me since I made only 20K to his 60K and picked up a -1 MA on my guard blitzer. He pretty much knocked me around all game but in the first half just could not bring down my ball carrier so I scored on like an 8 turn drive with skaven. Second half he scored on a 4 turn drive. I almost scored in the 8th turn with a desperation play but it did not go my way.

Also picked up space hulk but I have not even got a chance to assemble the figures yet. When I was not playing Blood Bowl I pretty much was playing with my daughter all weekend since I have the Blood Bowl Tourney next weekend. Still not sure what team to bring.