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In our last session, we encountered an interesting situation when we got down to the final two.
One player had all 6 of his remaining dice while his opponent was down to one.
Of course this led to much discussion and side betting.
Mainly, we set out read: argued to answer the following questions: If best casino slot machines, what are the odds for the player with only one dice?
And just like that, a bet was born.
A bet not even involving the two players actually playing the game.
The Strategy Before we get to the bet, we needed to agree on what the strategy of the player with all 6 dice would do.
So, given dice 1, 1, 3, 4, 4, 5, he should call four 4s 1s are wild.
The Bettors After taking https://internetbingogames.info/best/best-casino-game-odds-reddit.html game theory courses in college, I tend to assume there is always some kind of strange optimal strategy.
I was unable to find said strategy but I of course immediately started trying.
My goal was to find some consistent strategy one that did not allow best dice gambling games easy variable bluffing, despite it being a key component of the game and then calculate the odds of how often it would win.
A statistical and thus, sure fire, right?
On the other side of this bet was my friend Kurt.
Instead, he rapidly starts running through thousands of iterations in his head of how the game might play out.
His intuition about odds and seeing the game so many times allows him to determine how often each player will win.
The Bet My quick math showed me that the person with all 6 dice would only lose if the opponent had the same number they called, or had a 1 wild card.
Given 1, 1, 3, 4, 4, 5 and a call of four 4s, the underdog only wins when he has a 4 or a 1, thus allowing him to call five 4s and win.
Rolling a 1 and another specific roll will happen 1 in 3 times and it needs to best tampa to play rock the hard slots 6 times in a row in order to lose.
In other words, only 1 in 729 times will the underdog win.
The Result The first few turns went exactly according to plan.
For the most part, the first 10 games went great.
Kurt rolled a couple 1s in there but would pretty much lose on the next turn every time.
But then, somewhere around the 10th game, something happened.
I rolled 1 1 3 4 4 5 and, per the strategy, called four 4s, the most I could safely call.
Kurt then comes back with four 5s, having rolled his own 5.
I ended up winning that game anyways, but he did get me down to three source />I went through the next few games no problem and won the best dice gambling games easy />But my interest had been piqued.
I must find out what they actually are.
Simulation Now realizing the problem is possibly more complicated than simple statistics can solve, I set out to write a simple simulation script that could run many many trials to get an estimate of the odds.
It also seemed to be a good opportunity to test out Jupyter Notebooks, something I had been meaning to do for a while.
All of the code and iPython notebooks for this project is.
The real variable in this situation is the strategy that Kurt should use.
Run 1 — The One-Upper As a sanity check, I wanted to check my original odds and give Kurt a basic strategy.
Whatever I bid, Kurt bids one more of that and hopes that he has a 1or whatever number I called.
Not smart, but a good starting point.
It also, perhaps more importantly, shows that the code is working.
Time to start optimizing.
Run 2 — The Good Guesser Maybe we can do better by trying to trap Matt on the initial bid.
Rather than letting Matt drive the action, Kurt can try and guess the number that Matt would have called anyway.
An initial guess of three of whatever die Kurt rolls seems like a good guess.
This actually makes sense, mostly because of gameplay.
Once Kurt wins the first turn, Matt gets to go first in subsequent turns.
So really this strategy only affects the very first turn of the game.
When it gets down to Matt best dice gambling games easy two or less dice Kurt wants to guess two of whatever his dice is.
The hope is Matt check this out 1, 3 and Kurt rolls 4.
Matt guesses two 3s, Kurt comes back with two 4s and wins.
Kurt is only getting to the final two dice about 1 in 80 times anyway.
As a refresher, Matt rolled 1 1 3 4 4 5 and called four 4s.
Then Kurt then came back with four 5s, having rolled his here 5.
The hope is that Matt has only one natural roll of that number and the rest 1s.
Results: Best dice gambling games easy Complete ------------------- Num Simulations: 10,000,000 Took: 294.
Kurt wins 1 in 112 times now.
This situation of having all 1s link one natural actually happens a lot, especially towards the end of the game when there are fewer dice.
In the last case, if Matt calls three 4s and I have a 3, for example, Kurt would call four 3s.
From what I can tell, this only happens when Matt rolls all 1s, so probably not a whole lot.
Matt guesses one 4, Kurt should guess one 5 but would previously guess two 5s.
Kurt wins this way 1 in 28 times!
It kind of makes sense maybe.
Kurt just needs to get through a couple turns by rolling a 1 or the same as me and then has to count on me rolling 1s.
It definitely happens, and it turns out it happens about 3.
Outcome So, 15 runs at 2:1 odds are actually looking pretty good right now.
This is truly fascinating to me, just by drawing on best dice gambling games easy experiences and seeing so many dice rolls, Kurt was able to almost exactly predict the odds of this complex scenario.
At least I still won the bet.
Constantly struggling to figure out whether I like software development or the Dodgers more.
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