Fire bet: Calculating the odds.

The wiz of odds used simulation to calculate the odds on the fire bet. Isn't there a way to calculate them using just math? I tryed and came up with the following(it doesn't add up to 1 due to rounding):


0 points = 0.5939393939
1 point = 0.2607504920
2 points = 0.1012753555
3 points = 0.0334342122
4 points = 0.0087981784
5 points = 0.0016399331
6 points = 0.0001624347

If the Wiz couldn't figure it out using math, there's a reason why.

Part of that reason is because it's too hard to figure into it all the extra points made along the way.

Remember, a FireBet is 4, 5, or 6 DIFFERENT points.

I believe the reason this bet is nearly impossible to calculate is because the bet is dependent on itself. Such as hitting 456 has different odds than 654. In order to calculate this youd have to calculate each situation independently.

I get the following, which is exactly consistent with miplet to the precision given. This isn't rocket surgery. And no, the order of the points does not matter.

0 points = 98/165
1 point = 78834/302335
2 points = 1970803095086/19459848690711
3 points = 1308430294936495236340268/39134473632501557375602251
4 points = 397827275553303559561275300153332123/45217004661600798293395811871070645620
5 points = 205475014116867547145317940818694649261505/125294750887234054523299013860064832861616986
6 points = 3700403899126040038831518494284887738125/22780863797678919004236184338193605974839452

BTW, the reference to rocket surgery was not a dig at the Wizard, whose sites are excellent, but rather a dig at the notion that because he hasn't computed the exact probabilities of a horrible sucker bet, it must be infeasible.

I'll go ahead and explain why the calulation is feasible. There are only 2^6=64 possible states once the fire bet has started, as you either have or have not made each of the 6 points. For each of these 64 states, it is easy to calculate the probability of getting to each possibile new state, and the probability of remaining at the same state. There are no loops (because you can only make new points or seven out), so it really is then just a direct calculation of the probability of reaching each state and ending the bet on each state. (In contrast, if there were loops then treatment as a Markov chain would be required.)

Quote: ZPP

There are no loops (because you can only make new points or seven out)....

You can also make REPEAT point, (or seven out while trying to repeat.)

As I already pointed out, the FireBet is paid after making 4, 5, or 6 DIFFERENT points.

Quote: DJTeddyBear

Quote: ZPP

There are no loops (because you can only make new points or seven out)....

You can also make REPEAT point, (or seven out while trying to repeat.)

Yes, technically I meant that there are no loops other than self-loops, as was already implied by stating that the probability of remaining at the same state can easily be calculated. It is trivial to deal with. If the probability of remaining at the same state is p, just adjust the other events at that state by a factor of 1/(1-p).

Quote: DJTeddyBear

As I already pointed out, the FireBet is paid after making 4, 5, or 6 DIFFERENT points.

Yes, that is why there are 64 states rather than 7 states (0 through 6).

i actually work for a prominent CT casino that just took the bet out because they believed they were losing money on it.

edit4313-1

Quote: SammyJankis

i actually work for a prominent CT casino that just took the bet out because they believed they were losing money on it.

Hmmm.... There are only two casinos in CT, and to the best of my knowledge, only one had the FireBet. I wonder which casino you're not naming.... ;)


When I was in Vegas in September, I stayed at Sahara. They have the FireBet mentioned on the in-room TV channel that features the casino, but it's not on the table, so I asked. They said it had been taken out a year prior. The reason? Not that they were losing money on the bet, but that they were losing money during the time that the table was shut down for surveilance review each time it hit.

It wasn't just the time that the table was closed, although that probably didn't help. Too many people, who otherwise would be giving some winnings back while thinking the hot streak wasn't over, had to wait and had time to think, and would cash in after getting paid.