You will find correct statistics on few gambling strategy sites. People who are competent in math don't gamble (unless it's gamble or death - let's say the mob will kill you if you don't pay back $100,000; if you gamble the $10,000 you do have, there's a 10% chance you won't be murdered). They also don't waste the time making strategy guides.

To answer a question whether it is better to bet one large or many small amounts, that depends on your goal. If you gamble for entertainment, the goal would be to extend your entertainment, not bet your bankroll on one roulette number - a 36 in 37 chance your fun is over in 30 seconds. Play bingo, it wastes all your time for little money. If your goal is to win money, then you should invest in this site's bankroll or open your own casino.

Just like interest compounded daily earns you more than interest compounded monthly, more bets of the same player bankroll earns the casino a compounding return.

Strictly speaking, one large bet has a better probability of a given return vs bust, if the goal is the single bet win payout.

What do I mean by "the goal" - this takes some explanation. Let's take the roulette table, with 2/37 house edge (5.26%). If my goal is to make 35x my bankroll, betting 100% of my bankroll on a number gives me a 2.6% chance of meeting my goal. Betting 1% of my bankroll on a series of number bets until I meet my goal or go bust is a near 100% chance of bust.

If your goal is simply to come out ahead after a set number of bets (where you have enough money to not go bust until you've placed all the bets):

A. the chance you will meet this goal betting a single number with one bet is only 2.6% - although it has a bigger payoff potential, there is a 97% you leave down (actually busted). However, if you bet 100 times on the single number, the chance you will leave the table ahead is 49.1%.

B. the chance you will meet this goal betting once on a color is 47.4%, but after betting 100 times in a row on a color you only have a 26.5% chance of being up at the end.

(If you place the 100 bets in sequence and bet more than 1/100th your bankroll on each bet, there is a chance you go bust before the bet sequence completes, and this further lowers your chance of ending ahead.)

Similarly, if I state my goal is either to double my money or go bust on just-dice, the chance that I double my money with one bet is 49.5%. If I bet 1/10th of that on the same bet until I either double my money or go bust, the chance is higher I go bust (not going to waste my time in R to tell you the odds...)


I'll add a conclusion to my post: gamblers like variance. People buy lottery tickets not because the house edge is 50%, but because there is miniscule chance of millionaire status. The more you bet, the more you reduce variance. If I have 10,000BTC and bet it once on double my money, 49.5% chance I double my money. If I bet 1000000 0.01 BTC bets, the variance is gone and payout approaches the house edge, I might as well be sending 10000 BTC to a site that pays 9900 back.