Ask The Wizard #221

I don’t play much poker, so had to ask David Matthews Let me explain what a 'dealer's add-on' is. Here’s a summary of the concept.

The dealer's add-on is an optional fee presented at the time of registration. The money collected from this add-on is exclusively for the dealers, serving as a reward for their efforts in managing the tournament. Generally, you receive extra starting chips, often increasing from 2000 to 2500.

Deciding whether to tip should always be a matter of personal choice, regardless of purchasing the add-on. If I had opted for the add-on, I might be less inclined to give a tip. Just to clarify, I usually do go for the add-on. While I can’t be certain if it’s the best decision from an expected value (EV) perspective, it simply feels logical to me if I plan to participate in the tournament.

I concur with what Dave said. I would like to expand on that by expressing my disapproval of pressuring players in tournaments that have optional fees such as re-buys or wildcard entries, unless there’s some return for the players, which usually isn’t the case. If a tournament isn’t financially viable for the casino otherwise, I think it would be more straightforward to just raise the initial entry fee.

In instances where there's no dealer add-on involved, I believe it is appropriate for winners to tip the dealers. If I had to be specific, I'd say a tip between 1% to 2% of the winnings seems reasonable, with a higher percentage for smaller wins. In such cases, I would calculate the tip based on the total dealer add-on amount multiplied by my win-to-total win ratio. If this calculation results in a tip of zero or less, then you’re faced with a real conundrum. I would likely do what I do when restaurants enforce an automatic gratuity of 18% to 20%, providing just a small token amount for the sake of appearances.

Without any wind, the trip will take 2 hours each way, leading to a total travel time of 4 hours. If there is a tailwind, the plane will fly at 600 mph, resulting in a travel time of 1000/600 = approximately 1.67 hours. Conversely, against a headwind, the speed drops to 400 mph, making that leg of the trip take 1000/400 = 2.5 hours. Therefore, with wind conditions factored in, the overall travel time is 4.17 hours, which is about 10 minutes longer.

This illustrates why averaging out averages can lead to misleading conclusions. One cannot claim the average trip speed is 500 mph if the one-way speed is 400 mph and the other is 600 mph, as the slower leg takes significantly more time.

If this concept isn't clear, think of it this way: With a 500 mph wind, while the plane could cover the distance in one hour with the wind at its back, it would effectively go nowhere against the wind, meaning it would take an infinite amount of time.

There are four suits available for the three cards that could form a royal. The number of ways to select three ranks from the five available is represented as (5,3)=10. Additionally, there are combin(47,2)=1,081 combinations for selecting the remaining two cards. Overall, the total combinations for choosing five cards from a deck of 52 is combin(52,5)=2,598,960. Hence, the probability of drawing 3 cards towards a royal flush is calculated as 4×10×1,081/2,598,960, which amounts to roughly 1.66%. combin Are you acquainted with 'The Fundamental Formula of Gambling'? I'd really appreciate it if you could share your insights on it, as it hasn’t been referenced on your website. The formula states:

However, that formula isn’t the only approach to tackling such problems. It could be alternatively expressed as:^bCan you suggest a method to convert any five cards drawn from a standard 52-card deck into an integer ranging from 0 to 2,598,959? 9/6 Jacks or Better Certainly! Start by assigning each card a value from 0 to 51. Denote the cards as c1 through c5, with c1 being the lowest and c5 the highest. You can then use the following function:

int GetIndex(int c1, int c2, int c3, int c4, int c5)

.05 = (1-0.00002476)ⁿ
n
log(.05) = n × log(1-.00002476)
-1.301 = n × -0.000010753
n = 120,989

In this function, combin will yield the conventional value, but if the first parameter is less than the second, it should return 0, as follows:

If your intention is to use this to access an element from an array, you would initialize the array as shown.
{
index_array[count]=YourDesiredValue;
}

This includes strategies and accurate mathematical data for various casino games such as blackjack, craps, roulette, and many more.

int combin(int x, int y)
{
if (y>x)
return 0;
else
{
int i,n;
n=1;
for (i=x-y+1; i<=x; i++)
n*=i;
for (i=2; i<=y; i++)
n/=i;
return n;
}
}

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count=0;
for (c5 = 4; c5 < 52; c5++)
{
for (c4 = 3; c4 < c5; c4++)
{
for (c3 = 2; c3 < c4; c3++)
{
for (c2 = 1; c2 < c3; c2++)
{
for (c1 = 0; c1 < c2; c1++)
{
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count++;
}
}
}
}
}