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If you enjoy crunching numbers and working out odds, these games are the perfect choice for you. Each game mentioned here is a timeless classic and each is now available on mobile, so you can play on the move with people from around the world.
First up is the classic game Yahtzee. Based on poker, players must make ‘hand’ combinations using dice rolls. There are five dice, and after the initial roll players can decide which dice and how many of them to roll again. After a total of three rolls, scores are recorded in one of thirteen categories. The object is to get the highest possible score.
At first glance, Yahtzee looks like a game of pure chance. But aside from the basic arithmetic involved with adding up dice values, the game also involves an intense amount of probability.
Having a solid understanding of the odds of dice rolls will help you to improve your strategy.
The odds of rolling a Yahtzee (five of a kind) with any number are 4.61 percent, meaning it should happen once every 22 turns. The odds of rolling a Yahtzee with a single number, 6s for example, is just 1.33 percent.
The maximum score a player can achieve in a standard game of Yahtzee is 375 (plus 1,200 bonus Yahtzee points). According to computer calculations, shooting for Yahtzee every time results in an average score of 171. Playing optimally, however, should result in an average score of 254.
Maths can be used to work out which dice to roll again in any given situation. For example, if your first roll is three 1s and two 2s, then you could hold for a full house (25 points) or roll the 2s again to aim for Yahtzee (50 points). As it happens, sticking with the full house yields a higher average score, although there may be situations in which you should go all out – such as if you are behind in a game and need to take a risk to catch up.
An optimal strategy for the game has been formulated and is known as MaxProb. But like any good strategy game, even knowing the optimal line is not enough to succeed with certainty.
Yahtzee also involves human motivation, risk taking, and adapting to other players. What seems like a simple game involving little more than flukey rolls of the dice turns out to be a complex mathematical equation that is difficult for even a computer to solve.
The Yahtzee with Buddies app is available on iOS and Android. There are also dozens of similar, unofficial dice game apps.
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Next up is the classic casino game, blackjack. The aim is to make a hand with a value of 21, or as close to it as possible, while beating the dealer. Going over 21 will result in a ‘bust’ and the hand will automatically lose.
In European blackjack, also known as no hole card blackjack, each player is dealt two cards and the dealer is initially dealt one. The player makes their decision of whether to stand, hit, split or double according to their own cards and the card the dealer is holding.
A deck has 52 cards. There are four Aces in the deck. There are 16 cards with a value of 10 (face cards and the 10s), and 32 cards with a value of 2-9. Aces are the strongest card in blackjack and have a value of 11 or 1.
That means a little less than a third of cards have a value of 10. You need one of these as well as an Ace in your hand to make blackjack (21 using two cards). The odds of making blackjack, therefore, are 4.8 percent.
Using maths, it’s possible to solve aspects of the game and come up with more effective strategies. For example, when your hand value is 12, you have a 31 percent chance of exceeding 21 and going bust with your next card. If your hand values 14, this jumps up to 56 percent. You can also work out the odds of the dealer going bust depending on what card they are showing.
Because blackjack is grounded in mathematics, experts have devised basic strategy charts that outline optimal play. Card counting can also be used in live casinos to gain a further edge, although it is frowned upon.
Blackjack is available at popular online casinos, which can be downloaded for both iOS and Android.
Here’s another classic game that you might not realize is so rooted in maths. Monopoly. At first glance, it looks like you just roll the dice and buy everything you can afford, right? Well, kind of…
Once again, the maths behind this game involves the understanding of dice. In Monopoly you roll two dice, meaning you can move 1-12 squares. But you have a greater chance of rolling one of the middle numbers, because there are more possible combinations of, say, 7s, than there are 12s.
You can only roll a 12 by hitting two sixes for a total of two combinations: 6+6 or 6+6. You can hit a seven, however, with any of the following six combinations: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1. You’re actually three times more likely to roll a 7 than a 12.
You can use this knowledge of dice odds to predict the squares that you’re most and least likely to land on next and plot a statistically likely route around the board. And just like you would have to do if you started a new business at home or abroad, you’ll also need to calculate your risks and income opportunities in a game of Monopoly.
Did you know, for example, that the Orange properties provide the most profitable prospect when it comes to the balance between cost and return? On average, you’ll get your money back quicker. Furthermore, more people will land on oranges over the course of the game, because of Jail. After leaving Jail, players who move 6, 8 or 9 places will pay the price – and as mentioned before these middle numbers are common when rolling two dice.
Like all games mentioned here, Monopoly is available to play on iOS and Android.