[gwbrooks]

A million years ago, when you could still find video poker games with 100%+ theoretical return or poorly thought-out promotions offering enough cash-back to get you over 100%, we'd calculate the Kelly number for a given opportunity -- the bankroll necessary to ride out hills and valleys in favorable situations.

Spoiler: It's almost always 3-4x the value of a royal flush. So you needed $12-16k if you were playing a $1-per-coin game with a 1% edge at a pretty good clip.

And what do you earn with perfect play in that situation? The princely sum of around $30 an hour.

[bdjsiqoocwk]

I would like to understand in detail what you just wrote.

"$1 per coin game" is this a game where you put in $1 to play and get paid either $2 or $0 with 50-50 probability (0 expected).

And the what does it mean %1 edge? Does it mean the probabilities are such that the expected payout is 1c per coin flip?

[bayesianbot]

He means video draw poker machines, where you get paid a multiple of your bet depending on your final hand. Most online casinos used to have bonuses where the required wagering amount to clear the bonus multiplied by the return value of certain games led to a positive expected value for the player. So as example you'd deposit say $100, get $100 bonus, wager on video poker for $2000, getting back 99% of the wager for average of $20 loss from the wagering and $180 cashout. Much more rarely there also were some games that when played optimally, would give slightly over 100% return for your bet. The casinos were banking on most players playing them suboptimally and/or getting hooked.

Even though it's +EV for the player, you'd need some bankroll to ride out the variance as you could lose on X casinos in a row. Ages ago these were really +EV and you could usually just autoplay them with small bets, so the bankroll requirements weren't that harsh. Later on the wagering requirement on the bonuses grew, often making the small bet grind unprofitable, but you could still find profitable situations when played with correct bet sizing. But those needed much bigger bankroll as usually it was more +EV the bigger the bets you made, so you'd often play many casinos for just a few minutes with big bets losing your deposit and bonus, but sometimes winning big and covering the losses with profit left over.

[gwbrooks]

Single-line (that is, five dealt cards) video poker can be played with 1-5 coins. However, there is a disproportionate payout for a royal flush (A-K-Q-J-10, all suited) with five coins played. There are no video poker games you can play with less than five coins that are anything near breakeven payout.

Every video poker game in Nevada is required to be truly random. And every game has the payout for every possible poker hand shown on the game. A bit of math allows you to calculate both the correct strategy for any five cards dealt (which you memorize, just like proper blackjack strategy), but it also tells you the theoretical return of the game with perfect play.

As an example, 9/6 Jacks or Better (a game that pays nine coins for each coin played for a full house and six coins for each coin played for a flush) has a theoretical payout of 99.54% with perfect play. This puts it in the range of blackjack. And, like blackjack, you will eventually go broke because it's still not over 100%.

Unlike blackjack, you can't count cards. But what you can do is seek out returns in other ways. In the 1990s and 2000s, some casinos would compete on cashback comps. Add 0.33% or 0.5% cashback to the game I just described, and you're close to (or barely over) 100% payback. Find a game with a baseline payout of over 100% (full-pay Deuces Wild is 100.76, as a [rare] example), and you're deeper into the profitability zone.

Small returns unless you're playing higher denomination returns with a giant bankroll. Most people who do this make it a bit of a lifestyle -- pushing tens or hundreds of thousands of dollars through the machine gets you noticed by the casino, leading to free rooms, free meals, invitations to parties, etc.

Others look (or looked -- it's rarer now) for poorly planned promotions where a scarce hand pays off grandly and changes the math. Most of the life-changing wins in this space came from those sorts of situations.

[jiggawatts]

Isn't that a pretty good return? Multiply by 100: this is the equivalent of $3,000/hour on $1.2M of capital!

[nighthawk454]

Not if you’re throughout limited with $1 games

[jiggawatts]

Play 100 accounts in parallel.