Probability Tables

[Vulturedoodle]

I used a binomial probability calculator to generate a spreadsheet detailing the odds of getting X results (up to 16) on Y d6s (up to 20). I used the results to create a group of tables with percentile results along one side and attack dice along the top, showing the expected number of hits. If there were no modifiers used (i.e., only results of 4-6 being successes, rather than 3-6s, or 5-6s, etc.) it would work as a nice alternative to rolling handfuls of dice. Sadly, I can't see a way to use a single table with modifiers. To closely model the results of the attack mechanism, separate tables for each modified result would have to be used.

In other words, one table where 4-6 is a success, another where 3-6 is a success, another where 5-6 is a success, and so on. This is no good.

However, and this is the point of this message, in doing this research I did come up with a nice set of matrixes for the various probabilities of getting the numbers needed when rolling any amount of dice. If someone wants them, PM me and I'll be happy to send them along. Be sure to include your regular email address. If a lot of people should want them, maybe someone will put them on a server and provide a url.

Regards,
Steve F.

[Vulturedoodle]

Still trying to get something useful out of the probability tables, I decided to steal a page from DDM/SWM and convert them to D20. The results, smoothed a little at the extreme ends, are decent. They offer an alternative to people who dislike rolling handsfulls of six-siders.

The tables have the D20 results along the left side (each pip being 5%), and the number of D6 attack dice to be rolled along the top. Cross-referencing the row and column yields the number of hits obtained. There is a table for each type of result possible: 2-6, 3-6, 4-6, 5-6 and 6. I've played around with using modifiers (+5/-5, +10/-10) on the standard 4-6 table, but the results aren't reasonable. In other words, adding +5 means very different things if you roll a 10 versus a 19. Using column shifts is much closer (a unit with 15 attack dice, but a -1 for being disrupted, might shift left and use the 10 attack dice column, for example).

These tables would also permit something like "Critical Hits" or "Failures." One possibility would be that a natural 20 means a vehicle firing on another vehicle gets a second roll on, say, the "2 attack dice" column and adds the results to the hit total. Lots of possibilities there. I plan to try them out as a house rule game.

In any case, the numbers are reasonably close to the actual probabilities. In the raw tables, I considered any result of 99.99% or higher equal to 100%, and any result less than 0.5% equal to zero. Thus, while there is a miniscule chance of rolling 15 successes or failures on 15 dice, the maximum in the table is 12 and the minimum is 4.

Regards,
Steve F.

[Frogslayer]

The best use for the tables would IMHO be to calculate the chances before deciding which unit to attack. The use of a D20 would change the game too much, I believe.

For example, an AT guns chance of rolling 8 hits while disrupted and thus blowing an undamaged crusader a med range away is VERY low, but the chance is there. Likewise, a tiger may score o hits vs a jeep at close range. A D20 only operate in 5% steps.

But I agree that the dice-rolling is sometimes too much. You roll 10 dice at once and then you´re "confused" for a few seconds counting them.(ok, counfused is a bad word, but you now what I mean) You miss that instant success/failure feeling. You could roll them a couple at a time, but that takes too much time.

My personal solution is to use special "hit/miss" dices. Threy´re basicly D6s, but 3 sides has big explosion markers on them, and 3 sides are blank. I also have dices with 4 hits/2 misses and 4 misses/2 hits. Using these dices kind of gives that instant success/failure feeling, you immediately see the number of hits and does not become "coufused".

[Vulturedoodle]

The best use for the tables would IMHO be to calculate the chances before deciding which unit to attack. The use of a D20 would change the game too much, I believe.

For example, an AT guns chance of rolling 8 hits while disrupted and thus blowing an undamaged crusader a med range away is VERY low, but the chance is there. Likewise, a tiger may score o hits vs a jeep at close range. A D20 only operate in 5% steps.
Change the game, yes. Change it too much? In a tournament setting, certainly, but these are House Rules. If you're talking solely about the odds, I disagree. The chance of getting 8 successes in 9 dice while disrupted is tiny (0.0006653057267068663%), close enough to zero that it can be considered zero. Yes, you might succeed (using 9 d6s) on the very first try, but you're just as likely to succeed only after 1500 tries.

This is exactly what AH did with the tougher tanks. It's certainly possible to kill a Tiger at long range with one shot from a 6 pounder, IRL. But the odds are so vanishingly small that they didn't include the possibility of a one-shot-kill in this case.

My personal solution is to use special "hit/miss" dices. Threy´re basicly D6s, but 3 sides has big explosion markers on them, and 3 sides are blank. I also have dices with 4 hits/2 misses and 4 misses/2 hits. Using these dices kind of gives that instant success/failure feeling, you immediately see the number of hits and does not become "coufused".
This is a good idea. I may steal it. This has started me thinking about another means of spreading the possibilities (i.e., the Memoir '44 dice, or something along those lines).

Regards,
Steve F.