Hello my wonderful people!
Today’s post may feel a little odd to what you’re used to, and rightly so! As for the first time ever in BHO history there is a guest writing for the blog!
Now can you guess who it may be?
Maybe I am my very own menopausal mother, Claire. Or I could be the edgy son of Christopher, the BHO's main writer, Miles. Maybe I could be Molly… but then again my grammar is far too good for it to be her (sorry Molly). Or maybe, just maybe I’m Jacob and I’ve finally gotten off my arse and stopped slaying goblins for five minutes!!!
If you guessed any of the above… you’d be absolutely incorrect, as I am in fact everyone’s favourite source of joy, Mr Lee himself!
Now I hope I have you fine people wondering what has prompted me to write a guest post for the BHO blog, and it’s quite simple really!
I’ve been getting re-acquainted with the superb game of Yahtzee, and while reigniting my passion for the game, I’ve also been enjoying strategies based on the probabilities of each score box (specifically the bottom scores in particular).
So let me start by showing you a table of these bottom score probabilities below:
I’ll begin by talking about our “Three of a Kind” and “Four of Kind”. The interesting thing about these scores is that despite being substantially different probabilities, they both are only capable of a maximum of 30 points each. So with this knowledge, you should always aim for your “Four of a Kind” as your “Three of a Kind” is substantially easier to score. BUT with that being said, on the off chance that you have to put a 0 in either of the two, always pick your “Four of Kind” as like I previously mentioned both are capable of the same score and you can score a “Four of a Kind” in a “Three of a Kind” but not vice versa.
Moving on to our “Full House” which is worth a whopping 25 points! My general strategy surrounding this score is just to simply ignore it… CRAZY RIGHT! But I have found in doing so you’ll most likely stumble, tumble and roll yourself two doubles at some point during a game with your first roll (which is roughly a 10.37% chance, and across thirteen turns you’re almost bound to achieve it). And that is the moment when you should strike for your “Full House”, as with two rolls left and one dice to roll you have roughly a 55.6% chance of securing your full house. This method is also a great way of securing your “Three of a kind”, but only prioritise your “Three of a Kind” over your “Full House” if you’ve either already scored (or Zeroed) your “Full House”, or the total sum is greater than the 25 points you’d get from a “Full House”.
Now onto our straights. Both the “Large Straight” and “Small Straight” are absolutely crucial for a good score in Yahtzee, as when combined they account for a whopping 70 points! And that could just be the push you need to come out on top. Much like your “X of a Kind” they also both have critically different probabilities, so the same strategy applies, always aim for your “Large Straight” as this is a lot harder to attain than your “Small Straight” and is worth 10 extra points! A simple strategy for this is to score your “Small Straight” in a single roll (which is roughly a 12.3% chance), and then use your final two rolls to achieve your “Large Straight”. The probability of this varies depending on what you’ve rolled. So for example if you’ve rolled a “Small Straight” consisting of 1, 2, 3, and 4, you’d have to roll a 5, which is a 33.33% chance with two rolls left. However if you were to roll 2, 3, 4 and 5, you will have two viable numbers to achieve your “Large straight” being a 1 or a 6, which will then increase your probability to 55.6% (matching the full house strategy probability). And again much like the “X of a Kind” if you run into the problem of having to zero either your “Small Straight” or “Large Straight” always opt for your large, as sacrificing your small has a greater and substantial chance of resulting in losing the entire 70 points dedicated to your straights, whereas vice versa will still grant a far greater chance of achieving at least your “Small Straight” and still gaining 30 out of the 70 points available in these slots.
Here’s where we talk about the easiest box to score in the entirety of Yahtzee… Your “Chance”. The “Chance” box is what I like to think of as your fall guy, the box to turn a terrible roll into a decent score, as you can put literally any combination of dice added together into your “Chance”. So with that being said, the probability of scoring in this box is absolutely 100%! BUT because of this you should only use it if you absolutely need to, SO NEVER PRIORITISE IT (unless it’s your final score to fill). On the off chance (no pun intended) that you have to prioritise your “Chance”, a score 20 points or above is generally considered a good score for this slot. The probability of scoring 20 points or above in your “Chance” slot is roughly a 44.06% and could just be what drags you just above all your opponents. I previously mentioned you should only prioritise your “Chance” if it’s your final box to score, well, I lied! There’s actually one other reason which you may prioritise this box, and that would be if the probability of scoring above 20 on your “Chance” far outweighs anything you may be able to score which can be determined on your first and second rolls.
Now we are finally onto your “Yahtzee”, the hardest Slot to score in the entirety of the game…
Now the “Yahtzee” has an overall probability 4.64% in a single turn, which means across 13 turns you’d only have a probability of roughly 60.32% of scoring a “Yahtzee” if you spent the entire game trying. So in my own experience I find the best way to approach this score is to not approach it all! Now you may think that sounds silly, but I find worrying about the rest of the score sheet leads to a higher chance of victory than focusing all of that energy on a “Yahtzee” and as a great man has said many times before a “Yahtzee” isn’t a guaranteed win. The only time I think anyone should approach that monstrous beast is if the first roll boosts that probability. For example if you were to roll a triple number, the probability of scoring a “Yahtzee” the next two turns would be an 11.57% chance, so with that knowledge I’d only approach the “Yahtzee” if I had either my “Chance”, “Three of a Kind” or the appropriate top score slot available to fall back on if I fail. Otherwise the risk far outweighs the reward as you may end up zeroing a score, or potentially putting yourself at a disadvantage to get your Bonus.
Now on the rare occasion of rolling a Quadruple number on your first roll (which is a 1.93% chance), your odds are greatly increased to roughly 33.33% of achieving your “Yahtzee” and I personally think that the risk of rolling for a Yahtzee IS worth it, especially if you’ve got a backup plan such as a readily available slot if it fails like previously mentioned, but on the occasion you might not have a backup and you fail to score your “Yahtzee”, I’d cut your losses and Zero the Yahtzee as it’s more hassle than it’s worth, and remember your opponents have the exact same probability as you do and will likely end up doing the same leaving the playing field pretty even in the grand scheme of things!
Now whether you decide to follow my strategies based on these probabilities is entirely up to you, it’s your game after all! And of course these strategies aren’t going to give you a guaranteed win, but they will give you a consistently good score and upper hand, as when testing these strategies myself recently, I have found that across thirty games, twenty nine of them resulted in a score above 200 points, and 7 of which were above 300 points also.
Thank you very much if you’ve gotten this far, and I hope you’ve enjoyed my mathematically riddled guest post!
Happy Rolling! 🎲
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