Using Kaibaman, you can special summon Blue-Eyes very easily without using monsters for tribute summon. Part of what makes this card good is because it can be obtain from the card trader instead of packs, making it easy to obtain and having more than 1 copy, as well as special summoning a high attack monster compared to Black Dragon's Chick.
Last Gamble Can be used in your Main Phase, starting from the fifth turn. Upon activation, reduces your LP to 100 and discards 2 cards from your hand. You roll a die and draw that number of cards. This skill can only be used once per Duel.
What makes this deck strong is using BEWD together with Champion's Vigilance. With just 3 cards, you can summon a high attack monster that can prevent your opponent from summoning monsters, or negate a spell/trap card to prevent their plays.
Starting the duel
Early in the duel, you can either summon BEWD right away with Champion's Vigilance if you have them, or set a Blue Dragon Summoner to get a BEWD. Once you manage to get BEWD and champion's vigilance, you can regain board control by preventing your opponent from summoning so you can direct attack, or use it to negate traps your opponent might use that can stop your attack.
Playing it safe
Setting a champion vigilance early before you summon BEWD can be good to get it ready for when you summon the dragon, but there's always a risk of it being locked by Sergeant Electro, or Nobleman of Extermination. If you want to play it safe, set it once you summon BEWD and don't attack if you are unsure if your opponent has a Mirror Wall or any other defensive cards.
Any bewd deck looks like nerfed at some point, but you can do it better including the 3 kidmodo because in that way after enemy BP you have 1 normal summon available in your turn and a bewd in the field (if they kill the pretty thing). Kaibaman should be replaced with 2 ancient rules man.