Craps analysis can get complicated. Does the table offer double odds? Are you betting Come on every roll, or just betting the Pass line? Maybe you want to annoy everyone and bet the Do Not! I’ve published the results of such simulations here before, but let’s keep things much simpler.
Suppose that the House offers even-money on a 49% proposition, for a 2% vig. To change $1 into $8.39 million you need simply win 23 times in a row, doubling up after every win. You will achieve this with a 1 in 13.4 million chance for a net vigorish of 32.2%. That vig is smaller than that of a lottery but still large enough to dispel the misconception that it is the single-bet vig that should be compared.
However that is not the betting policy that glowacks asks about, and indeed you’ll have trouble making those wagers! After twelve passes you’ll have $4096; spectators will be cheering … and looking on in horror afraid that you’re about to lose it all. By now you may be forced to switch tables: the casino may have $1 minimum tables and $10,000 limit tables, but they’re probably not the same tables! After 18 passes, when you’re asking the pit boss if you can bet $262,144 there’s a fair chance he’ll say “OK, but it’s your last bet here whatever happens. Fair enough?” By now I hope your friends are carrying you away from the table!
Instead glowacks assumes that your bet size remains more-or-less constant. Now the chance that you will increase it “significantly” is almost indistinguishable from zero. Lets assume the same 2% vig even-money game, and suppose that you bet $10 a turn and play 10,000 turns. I’ll simulate this scenario a million times. You might win $100,000 but the chance of that is much less than 1 in a googol.
Here are the results of those 1 million simulations:
You lost $2000.04 on average, very close to the $2000.00 prediction.
10% of the time you left with a $3280 loss or more
20% of the time you left with a $2840 loss or more
30% of the time you left with a $2520 loss or more
40% of the time you left with a $2260 loss or more
50% of the time you left with a $2000 loss or more
60% of the time you left with a $1740 loss or more
70% of the time you left with a $1480 loss or more
80% of the time you left with a $1160 loss or more
90% of the time you left with a $720 loss or more
97.7% of the time you left with a loss
1.1% of the time you left with a gain of $300 or more
0.13% of the time you left with a gain of $1000 or more
Out of the 1 million simulations there were just 29 trials where you finished with a $2000 profit or more.
Of these, there were 9 winning $2200 or more with $2900 the highest.
In addition to the 29 trials finishing with $2000 or more, there were another 150 where you were ahead $2000 at some point.
There were two trials where you could have quit with $3000+:
Once you achieved $3070 at one point but went home with $2080 after completing the 10,000 turns.
During the best-in-a-million $2900 success you were up $3340 at one point.
TL;DR: Ignoring entertainment value, casino games as they are usually played are not sound alternatives to a lottery.
Yeah, this is definitely why citing Wikipedia isn’t always a good idea.
If 0 and 00 couldn’t be bet on then calling them the “vigorish” is merely abuse of terminology. But since you can bet on them then it’s completely and totally wrong. In terms of betting just single numbers, they are identical to all other numbers. Is betting 14 also called “vigorish”? Exact same odds and expected returns.
Singling out any one aspect of betting on roulette makes no sense whatsoever. The whole totality is what gives the house its edge.
The presence of two extra numbers added to 1 to 36 is what gives roulette “vigorish.” The two extra numbers are … 0 and 00. Similarly, in a horse race you can bet on any of the horses. There isn’t an extra horse named “Vigorish,” but the track or bookie is still making a profit.
I’ve not read the Wiki article, but I’m tentatively crediting it with the win here.
ETA: This sidetrack appears to be about semantics. To be useful, please rephrase any claims as a testable claim about gambling.
Sure. And for almost all the other bets, they aren’t. For red/black, low/high, dozens, etc. bets, it’s the 0 and 00 *specifically *that are losers and give the house edge. There is no equivalent of these bets for the zeroes and there can’t be.
So fine, if roulette was a game solely about betting on single numbers, I might accept your argument, but still point out how odd it is that they decided to paint them different colors and set the payout table to be 36/38 and not some other fraction.
But that is not roulette, which is a game that has red/black bets and others, and always pays out an integer multiple of your bet. It would not have been possible–without breaking the game–to have the numbers be truly symmetrical, such that there’s just 1-38 and you get paid 36 cents on a winning bet of 38 cents on red.
Again, you can bet the greens! Just to be clear. You can bet one or both of 0 and 00. (To bet both you just put your chips on the line between them.)
So you can bet any one color (red, black or green) and if that color doesn’t come up you lose. The expected return on your bet is identical in all 3 cases.
Want to bet 3 numbers including a green? Just split your bet up on those numbers. Options like betting a row are merely there to speed things up. And the faster betting goes the more games are played per hour and the more the house wins per day. But there is no requirement that you have to bet only 3 numbers in the same row. You can bet 3 numbers anywhere including the green ones.
Chronos also makes the key point about the number of slots vs. the payoff basis. That is all that matters. The fact that the payoff basis is 36 just makes the Math easier. They could have chosen 35.7 or 36.111… but then the speed and ease of making payouts would suck.
I’m not sure what this subthread has degenerated into. If the etymology of “vigorish” is the topic, please start a new thread in Cafe Society. Calling 0 and 00 the vigorish in roulette is a simple and effective way to demonstrate and measure that vigorish. Sure bets are allowed on 0 and 00, just like you can bet Do Not at craps (where they bar 6-6 to get vigorish), but this does not negate the several advantages of using those green numbers to demonstrate and measure the vigorish.
OP’s question is about the arithmetic of gambling games. To be on-topic, a post should contain a potentially falsifiable claim about the arithmetic of gambling games.
One thing about Powerball is that, as calculated above, you could play all the time and still almost surely not win; not much psychological reinforcement there. At the other extreme, if you walk into a casino and start making (relatively) safe bets like Red or Black on roulette, you will quickly find it extremely boring.
That is not the end of the story, though. The Powerball jackpot prizes can be ludicrously massive. And (I haven’t tried this), it might be more exciting to gamble a million dollars, or your life savings, on a spin of the wheel. Therefore, it seems that there are some optimal odds (or mix of odds)- not too long or too short- that make a game of chance fun, and those are in turn tempered by the value of the stakes. Does anybody know more about it?
