How To Calculate A Bet Payout
Tommy, who is one of my blog readers asked how to calculate payout percentage of any given slot machine after reading this slot strategies article. I started writing a reply to his question in the comment, but the answer turned out much longer than I had initially planned so I decided to dedicate the answer a full post I believe it deserves.
- How To Calculate A Bet Payout Amount
- How To Calculate Lay Bet Winnings
- How To Calculate A Bet Payout Results
- How To Calculate A Bet Payout Chart
- How To Calculate A Bet Payout
- How To Calculate Sports Betting Payouts
Calculate your winnings quickly and easily with our online bet calculator. To work out the return on any bet, simply enter the Odds and the Stake. For example, if you were betting £100 on a 9-4 chance, enter: Odds = 9 (to) 4, Stake = 100, then click 'Calculate' The.
Please note that the payout percentage can only be calculated this way if each spin is completely random. The only way you can be sure it’s completely random is if you play in a casino, which is licensed by a jurisdiction dictating the outcome of each slot spin must NOT be predetermined, it has to be completely random. Casinos bound by this restriction are all legally operating casinos in Las Vegas and Atlantic City as well as most licensed online casinos.
In order to calculate payout percentage on a slot machine with completely random RNG (Random Number Generator), you need to know 2 things beforehand: occurrence of all symbols on each reel and paytable. In a very simplistic example suppose we have a slot machine with 3 reels and with only 2 symbols
and
Total number of symbols on each reel is 3: 2xBAR and 1xSeven
Payout table shows 2 winning combinations for each $1 bet as follows:
wins $1
wins $15
First we need calculate the probability of each combination:
For 3xBAR the probability is 2/3 * 2/3 * 2/3 = 0.3
For 3xSeven the probability is 1/3 * 1/3 * 1/3 = 0.037
Note that the probability to get BAR on 1 reel is 2 out of 3 times, hence 2/3 in the formula and for Seven it’s 1 out of 3 (1/3)
We multiplied probabilities 3 times because the combination is made up from 3 times the symbol.
Now we can calculate the payout of each combination:
For 3xBAR the payout is $1 * 0.3 = $0.3
For 3xSeven the payout is $15 * 0.037 = $0.56
Finally we add the payouts of each combination together to get the total payout:
$0.3 + $0.56 = $0.86
Since we payout we just calculated is for $1 nomination (according to the paytable) then the payout for this nomination is $0.86 (each time we bet $1, on average we win back $0.86) or in other words the payout for $1 nomination is 86% (without bonus game or progressive jackpot)
Note that payout percentage can vary depending on the nomination. Higher nominations often offer better payback.
If the slot game has a bonus round, we also need to take that into account and start by calculating the probability of getting into the bonus round. Then multiply it with the average amount you can win at the bonus round and add the result to the total payout.
Suppose in our example 3xSeven puts us into a bonus round where we are given a choice of 3 pots of gold. If we choose the right one, we win additional $3
On average we would win 1 out of 3 times in the bonus round. Since the win amount is $3, then the total amount we would win on average is 1/3 * $3 = $1 each time we get to the bonus round.
Since we have already calculated the probability to get to the bonus round (3xSeven = 0.037), then we can add another $1 * 0.037 = $0.037 to the total payout which now stands at $0.86 + $0.037 = $0.90. Now that we have taken the bonus round into account, the total payout is 90%.
If it’s a progressive slot, we need to multiply the probability to hit the jackpot with the jackpot amount and add the result to the total payout as well.
Suppose the probability to hit the progressive is one in a million and the jackpot is $10 000
1/1 000 000 * $10 000 = $0.01
After adding it to the total payout, we get $0.9 + $0.01 = $0.91 or 91% payout.
Suppose the progressive jackpot is $100 000 instead
1/1 000 000 * $100 000 = $0.1
After adding it to the total payout, we get $0.9 + $0.1 = $1 or in other words 100% payout.
How To Calculate A Bet Payout Amount
If you were an advantage gambler who has done the homework like we just did here, you would know that whenever the progressive on this slot machine reaches $100 000, the total payout percentage reaches 100%, at which point playing on that slot machines becomes profitable in the long run. ‘A long run’ in this case would probably mean a few million spins, but you would be guaranteed to make profit if you had a sufficient bankroll and a lot of patience (or an army of apes pulling levers).
As you can see the math behind calculating the slot machine payout is quite simple. The most difficult part of the whole process is probably finding the information regarding the occurrence of each symbol on the reel as casinos don’t tend to publish this simply because an average gambler has no need for this type of information.
If you have any questions, feel free to post them as comments and I’ll try answer them as best as I can.
UPDATE: Tommy asked how to calculate the keno video slot payout percentage, so I figured I’d throw it in here as well.
I have to admit I’m not a big fan of keno video slotmachines myself, but I believe I have a fairly good understanding how they work.
Suppose we mark 3 spots. First we need to calculate the total number of ways possible to draw 3 balls out of 80.
80/1* 79/2 * 78/3 = 82 160
Notice we substract 1 after each draw. That’s because the ball we just drew cannot be drawn again, it’s now out of the “bubble”.
Since the game draws 20 winning balls, we have to calculate the total number of ways 3 spots can be amongst the winning 20.
20/1 * 19/2 * 18/3 = 1140
The probability to hit all 3 spots is therefore 1140/82160 = 0.0139 or 1.39%
Suppose the paytable shows $40 prize for hitting all 3 on a $1 bet. The payout for hitting 3 spots out of 3 is then $40 * 0.0139 = $0.56
Suppose paytable is generous enough to award us $2 should we hit 2 spots out of 3 with every $1 bet.
The total number of ways to hit 2 spots out of the winning 20 is 20/1 * 19/2 = 190 and the total number of ways possible, that 1 ball remains amongst the 60 that don’t get drawn, is 60/1 = 60. This means there are a total of 190*60 = 11 400 different possible ways to draw 2 winning balls and 1 losing ball.
We already calculated there are 82 160 possible ways to draw 3 balls, therefore probability to draw 2 winning + 1 losing ball is 11400/82160 = 0.14
This adds another $2 * 0.14 = $0.28 to the total payout which is now at $0.56 + $0.28 = $0.84. That means the total payout is 84% for $1 card played with 3 spots.
If the paytable is the same for both 1- and 20-card version, the payout percentage remains unaffected so whether you play 1-card keno 20 times or 20-card keno once, it doesn’t really matter.
How To Calculate Lay Bet Winnings
It is difficult to believe but, there are plenty of people around who have little idea exactly what a bet is or what is meant whenever I mention being interested in betting or the fact that I run a Web site about online football betting.
How To Calculate A Bet Payout Results
Obviously in England most people have come across betting at some stage in their lives and high street bookmakers’ shops have been around in their multitudes for decades. However, most of my family lives in Germany and belongs to the innocent or ignorant section of society which has little notion.
I recently spent hours trying to explain to my Father what a bet is. Also, the fact that one can bet on various outcomes in the same football match was a new and slightly confusing concept to many of my family members.
Therefore, today’s article sets out exactly what is meant by the terms “bet”, “betting”, “odds”, “stake”, “bookmaker” and “mathematical advantage”.
Betting on the example of a coin toss
Imagine tossing a coin: there are two possible outcomes, either it will land showing the ‘head’ or the ‘tail’ facing up. The separate ‘likelihood’ (or ‘probability’) of both results is exactly 50/50. In other words, after 100 throws, in theory the result should show 50 ‘heads’ and 50 ‘tails’.
Now we will apply the concept of betting to these results: one person believes the next coin toss will be ‘heads’, whilst the other believes the outcome will be ‘tails’ and both parties agree to wager (bet) money on their guesses. In betting terminology, the money risked by both parties in this transaction is called the ‘stake’ and for this example the stake shall be one Euro. This means each party bets one Euro on their chosen result to win.
The coin is tossed: if ‘heads’ lands face-up then the party who guessed/wagered on ‘heads’ wins and vice versa if it lands ‘tails’. The player who guessed correctly keeps his stake AND wins the stake of the other person; the opponent loses his stake (in this example one Euro).
If this game is played, say 100 times, and both parties stick religiously to their selections (i.e. each betting 100 times always on the same result), then after 100 coin tosses, according to theoretical probability, both should be neither the richer nor the poorer than at the beginning. As seen, for one player there should theoretically be 50 times ‘heads’ meaning 50 wins of one Euro, cancelled out exactly by the coin landing 50 times ‘tails’. Of course, this situation is also parity for the other player.
How To Calculate A Bet Payout Chart
However, perhaps the game doesn’t pan out according to the theoretical rules? Maybe the perception is that ‘heads’ lands face-up more often than ‘tails’? The game now evolves and receives an ‘edge’ if one party is no longer willing to pay out one Euro should ‘heads’ win but reaches an agreement with the other to pay say, 90 Cents instead. This means that in future if ‘heads’ wins he will now only earn 90 Cents each time but, if ‘tails’ wins, then his opponent wins the bet and with it the whole of ‘heads’ one Euro stake.
This change now guarantees a loss on one side and a profit to the other, over the longer term: If one bets 100 times ‘heads’ and as expected, the coin lands 50 times ‘heads’ then 45 Euros will be won (50 x 90 Cents = 45 €); however when ‘tails’ lands 50 times then 50 Euros will be lost (50 x 1 € = 50 €). In this way, whoever puts their selves in the position of mathematical disadvantage in a gambling transaction will for sure lose money in the long run. In our example, after 100 bets, the player of ‘heads’ will have lost five Euros. The winner of this transaction received one Euro every time the coin landed ‘tails’ and only paid out 90 Cents when the coin landed in favour of their opponent, ‘heads’.
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