Gambling probability problem

A slot machine works on inserting a $1 coin. If the player wins,
the coin is returned with an additional $1 coin, otherwise the original coin is
lost. The probability of winning is 1/2 unless the previous play has resulted
in a win, in which case the probability is p < 1/2. If the cost of maintaining
the machine averages $c per play (with c < 1/3), give conditions on the value
of p that the owner of the machine must arrange in order to make a prot in
the long run.


New Member
Do you think that it is possible to calculate probabilities of gambling games? Of course, there are some theories and even tasks regarding calculating the dice or other gambling probabilities. But, in my opinion, it is pointless to try to figure out the chances of winning in gambling games. In real life, most of the theories do not work, and you lose despite all predictions. That’s why I prefer betting on soccer games rather than playing cards or gamble in casinos. When you bet on soccer games, you are more likely to win something if you know something about the teams you are betting on.
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Less is more. Stay pure. Stay poor.
If the inputs are known, yup. Six sides to a fair die, number of cards in a deck or slots on a Roulette wheel, etc.


Ambassador to the humans
If the inputs are known, yup. Six sides to a fair die, number of cards in a deck or slots on a Roulette wheel, etc.
Come on now - you know better. This is a 3 year old thread about a homework problem. Let's not encourage resurrecting these threads with input that doesn't really add anything.


Less is more. Stay pure. Stay poor.
I couldn't remember if you couldn't post a thread until you commented say 6 time or vice versa. I am thinking it is vice versa. But I thought may be they we tryin to hit the eligibility criteria. But yeah, necromancing is all the rage!

See, I just added another non-contributing post to this gem of a relic!
All 36 numbers are painted black and red equally (18 black and 18 red; only zero is green). You can choose whether to bet on "red" or "black. If you bet a chip on "red" and guess, the casino gives you back twice what you bet. Why double rather than triple or quadruple? Because the probability of guessing when betting on red or black is 18/36 or 1/2. And therefore, your reward will be twice the bet (i.e., equal to the fraction's denominator). According to roulette rules, you can put a chip on a specific number or the black-red and close several numbers at once with one chip. That is why the probability of winning in MGM99WIN is not tiny.
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At school, in math lessons, we passed problems for calculating the probability of gambling, but as you know, these are fictional tasks. Yes, in life you can find the probability of what the outcome of events will be, but in any case it is luck and chance that affects the result. You cannot calculate and expect the result that you have calculated. I used to play here a lot together with his brother, he always tried to find some strategy to win, but his plan always collapsed and he did not get the desired result. No mathematician or brilliant tactician will be able to outwit the casino, because the casino in any case remains in the black.
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Active Member
long term prob of success about pstate1inf * .5 + ( 1- pstate1inf)*p, where
pstate1inf = .5*2*q/ (2*q + 1)
according to wolfram. solve recursion pstate1(t + 1) == .5 * pstate1(t) + q * ( 1- pstate1(t) ).

q = 1 - p;
State = .5; #1 = fair, #0 = p
probs = c(.5,p);

f = function(i){
      y = rbinom(1,1,  State )
      if (y ==1){State <<- probs[2] }
      else if (y == 0){ State <<- probs[1] }

games = lapply(1:1000, f )
games = as.vector( unlist( games ) )

A = matrix( c(.5,p,.5,1-p), nrow=2, byrow = T)

# a recurrsion
#pstate1(t + 1) == .5 * pstate1(t) + q * ( 1- pstate1(t) )
#thanks wolfram, for solution.
state1p = function(n,q){

  (   ( .5 - q)^n + 2*q ) /  (2*q + 1)


pstate1inf = 2*q/ (2*q + 1)
psuc = pstate1inf * .5 + ( 1- pstate1inf)*p
better late than ever.
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Less is more. Stay pure. Stay poor.
I think the G-word caused the bots to attack this thread. All of these avatars are just too cool and polished.


We should test this by starting a new thread with the G-word in the title and do a little snake hunting. However, given I posted in this thread my days are already numbered until everything around me contain G-word adds.


Ambassador to the humans
I love that you humans still think captcha photos are about trying to keep bots out. They help train the bots but they're not much of a detriment...


Active Member
im still wondering why i felt compelled to respond to this thread. must be my skynet control chip got activated like the other bots. Like most people I had one installed with my covid vaccine.